Dnomd343
5 years ago
28 changed files with 27688 additions and 810 deletions
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## 命令行参数 |
## 华容道的统计与建库 |
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+ show命令：根据编码输出实际布局样式 |
这是一个关于华容道性质的研究项目，它会找到所有华容道布局并分析它们之间的关联，同时取得其各方面的参数，并将收集到的资料建成数据库加以整理； |
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```bash |
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--show <code> [square_width] |
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Purpose: Visualize the <code> |
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exp: ./engine --show 1A9BF0C00 |
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./engine --show 1A9BF0C00 4 |
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``` |
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+ cal命令：计算输入布局的最少步解法 |
对于华容道布局规则、移动规则及各种术语，这里给出了严格的[公理化定义](./docs/klotski.md)； |
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```bash |
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--cal <code> [file_name] |
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Purpose: Find the minimum step solution of <code> |
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exp: ./engine --cal 1A9BF0C00 |
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./engine --cal 1A9BF0C00 demo.txt |
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``` |
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+ cal-target命令：计算两布局之间的最短路径 |
为了方便研究，每个华容道布局都有一个唯一的编码，它是一个九位长度的十六进制数，这里是[编码的规则](./docs/klotski_code.md)； |
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```bash |
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--cal-target <code> <target> [file_name] |
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Purpose: Find the shortest path from <code> to <target> |
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exp: ./engine --cal-target 4FEA13400 43EA73400 |
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./engine --cal-target 4FEA13400 43EA73400 demo.txt |
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``` |
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+ group命令：计算起始布局的所有衍生情况，即计算其所在群的全部元素 |
经过统计，符合定义的华容道布局共有29334498种，其数量级较为庞大，这个过程将在[云服务器](./docs/ecs.md)上完成； |
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```bash |
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--group <code> [file_name] |
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Purpose: Find all elements of the group where <code> located |
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exp: ./engine --group 4FEA13400 |
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./engine --group 4FEA13400 demo.txt |
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``` |
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+ analy命令：分析布局的具体参数，包括层级结构，层间链接，解与最少步解，最远布局等 |
为了快速遍历所有布局，这里使用C++编写了一套计算统计引擎，统计将由它来完成；同时，它也可以用于最短路径/最远布局/解的个数等其他方面的运算，这里是它的[使用方法](./docs/usage.md)； |
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```bash |
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--analy <code> [file_name] |
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Purpose: Detailed analysis of the <code> |
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exp: ./engine --analy 1A9BF0C00 |
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./engine --analy 1A9BF0C00 demo.txt |
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``` |
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+ analy-quiet命令：同analy命令，但不输出计算过程 |
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```bash |
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--analy-quiet <code> <file_name> |
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Purpose: The same function as --analy, but doesn't show the specific process |
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exp: ./engine --analy-quiet 1A9BF0C00 demo.txt |
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``` |
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+ analy-group命令：分析`code`衍生出的群中所有元素的具体参数，并输出到`最远布局信息`和`解的信息`两张csv表格中 |
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```bash |
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--analy-group <code> <file_name_farthest> <file_name_solution> |
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<file_name_farthest>: As the output file of "farthest" |
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<file_name_solution>: As the output file of "solution" |
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Purpose: Analyze the whole group where <code> located |
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exp: ./engine --analy-group 1A9BF0C00 farthest.csv solution.csv |
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``` |
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+ analy-group-integral命令：同analy-group命令，但`解的信息`中将会输出全部解的编码及步数 |
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```bash |
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--analy-group-integral <code> <file_name_farthest> <file_name_farthest> |
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Purpose: The same function as --analy-group, but all solution case will be output |
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exp: ./engine --analy-group-integral 1A9BF0C00 farthest.csv solution.csv |
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``` |
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+ analy-multi-group命令：多群组同时分析，相当于多次执行analy-group命令，结果合并输出到`最远布局信息`和`解的信息`两张csv表格中 |
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```bash |
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--analy-multi-group <input_file_name> <file_name_farthest> <file_name_farthest> |
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<input_file_name>: As the input file of seeds |
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<file_name_farthest>: As the output file of "farthest" |
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<file_name_farthest>: As the output file of "solution" |
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Purpose: Analyze the whole group where each seed located |
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exp: ./engine --analy-multi-group 5-4-0.txt farthest.csv solution.csv |
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``` |
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+ analy-multi-group-integral命令：同analy-multi-group命令，但`解的信息`中将会输出全部解的编码及步数 |
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```bash |
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--analy-multi-group-integral <input_file_name> <file_name_farthest> <file_name_farthest> |
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Purpose: The same function as --analy-multi-group, but all solution case will be output |
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exp: ./engine --analy-multi-group-integral 5-4-0.txt farthest.csv solution.csv |
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``` |
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+ all命令：找到所有可能的布局，同时得到其分类情况及群组关系，计算结果会输出到All_Case.txt（所有布局的编码），main.csv（所有布局的编码及其分类），\*-\*-\*.txt（各群组的第一个子布局集合） |
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```bash |
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--all |
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Purpose: Find all the cases of klotski with detail |
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exp: ./engine --all |
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``` |
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+ all-code命令：简化版的all命令，仅输出全部布局的编码 |
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```bash |
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--all-code <file_name> |
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Purpose: Find all the code of klotski |
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exp: ./engine --all-code All_Case.txt |
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``` |
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+ help命令：显示所有命令的使用方法 |
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```bash |
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--help |
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Purpose: Display instructions for use |
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exp: ./engine --help |
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``` |
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## 编译 |
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+ Windows下，要求计算机有mingw环境或其他C/C++编译器 |
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+ Linux下，要求计算机有gcc编译器 |
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+ Android下，可以在termux中安装clang编译器 |
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编译指令 |
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```bash |
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g++.exe -O3 -c ./src/engine/HRD_analy.cpp -o ./src/engine/HRD_analy.o |
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g++.exe -O3 -c ./src/engine/HRD_cal.cpp -o ./src/engine/HRD_cal.o |
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g++.exe -O3 -c ./src/engine/HRD_group.cpp -o ./src/engine/HRD_group.o |
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g++.exe -O3 -c ./src/engine/HRD_statistic.cpp -o ./src/engine/HRD_statistic.o |
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g++.exe -O3 -c ./src/engine/main.cpp -o ./src/engine/main.o |
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g++.exe -o ./engine.exe ./src/engine/HRD_analy.o ./src/engine/HRD_cal.o ./src/engine/HRD_group.o ./src/engine/HRD_statistic.o ./src/engine/main.o |
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``` |
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或直接使用 |
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```bash |
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g++ -O3 ./src/engine/*.cpp -o ./engine |
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``` |
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## 库的调用 |
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### HRD_cal |
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描述：华容道快速计算库 |
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+ 判断编码正确性 |
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+ 对起始布局求解（仅返回搜索到的第一个最少步解的一个解法） |
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+ 找到两布局间最短路径（仅返回搜索到的第一条最短路径） |
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+ 找到起始布局衍生出的所有情况 |
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使用：包含头文件"HRD_cal.h"，类名为HRD_cal； |
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示例： |
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```c++ |
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#include <iostream> |
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#include <vector> |
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#include "HRD_cal.h" |
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using namespace std; |
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int main() { |
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cout << "Klotski fast calculator by Dnomd343" << endl; |
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vector <unsigned long long> dat; |
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HRD_cal demo; |
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// 将编码转为文本(参数为unsigned long long 返回string类) |
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cout << "4FEA13400 is " << demo.Change_str(0x4FEA13400) << endl; |
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cout << "----------------" << endl; |
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// 将文本转为编码(参数为*char 返回unsigned long long) |
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cout << "1a9bf0c00 is " << hex << demo.Change_int("1A9BF0C00") << dec << endl; |
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cout << "----------------" << endl; |
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// 检测编码的正确性 |
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if (demo.Check_Code(0x123456789) == false) { |
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cout << "Code error!" << endl; |
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} |
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// 计算最少步数(参数为unsigned long long 返回vector类) |
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dat = demo.Calculate(0x1A9BF0C00); |
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cout << demo.Change_str(0x1A9BF0C00) << "'s solution"; |
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cout << " need at least " << dat.size() - 1 << " steps" << endl; |
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for (unsigned int i = 0; i < dat.size(); i++) { |
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cout << i << ": " << demo.Change_str(dat[i]) << endl; |
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} |
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cout << "----------------" << endl; |
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// 计算到某一布局的最短路径(参数均为unsigned long long 分别为起始编码和目标编码 返回vector类) |
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dat = demo.Calculate(0x1A9BF0C00, 0x1ABE70C00); |
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cout << demo.Change_str(0x1A9BF0C00) << " to " << demo.Change_str(0x1ABE70C00); |
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cout << " need at least " << dat.size() - 1 << " steps" << endl; |
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for (unsigned int i = 0; i < dat.size(); i++) { |
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cout << i << ": " << demo.Change_str(dat[i]) << endl; |
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} |
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cout << "----------------" << endl; |
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// 计算某一布局衍生出的所有布局 |
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dat = demo.Calculate_All(0x1A9BF0C00); |
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cout << demo.Change_str(0x1A9BF0C00) << " can derive " << dat.size() << " cases" << endl; |
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cout << "----------------" << endl; |
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return 0; |
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} |
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``` |
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### HRD_analy |
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描述：华容道分析库 |
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+ 编码解析为具体排列 |
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+ 检查编码是否合法 |
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+ 根据起始布局分析出层级结构，包括各层间的链接关系 |
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+ 得到布局的具体参数，包括全部最远布局、全部最少步解、全部合法解及其步数 |
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+ 将分析结果导出到文件 |
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使用：包含头文件"HRD_analy.h"，类名为HRD_analy； |
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示例： |
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```c++ |
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#include <iostream> |
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#include "HRD_analy.h" |
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using namespace std; |
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int main() { |
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cout << "Klotski Analyser by Dnomd343" << endl; |
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HRD_analy demo; |
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// 显示编码的实际布局样式 |
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demo.Output_Graph(0x1A9BF0C00, 4, 1, "&%"); |
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// 解译编码 |
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demo.Parse_Code(0x1A9BF0C00); |
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cout << "code: " << demo.Change_str(demo.Parse_dat.code) << endl; |
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cout << "status" << endl; |
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for (int y = 0; y < 5; y++) { |
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for (int x = 0; x < 4; x++) { |
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if (demo.Parse_dat.status[x][y] <= 9) { // 0 ~ 9 |
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cout << int(demo.Parse_dat.status[x][y]) << " "; |
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} else if (demo.Parse_dat.status[x][y] <= 0xE) { // A ~ E |
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cout << char(demo.Parse_dat.status[x][y] + 55) << " "; |
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} else if (demo.Parse_dat.status[x][y] == 0xFE) { // space |
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cout << ". "; |
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} else if (demo.Parse_dat.status[x][y] == 0xFF) { // undefined |
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cout << "* "; |
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} else { // error |
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cout << "! "; |
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} |
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} |
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cout << endl; |
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} |
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cout << "type" << endl; |
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for (int i = 0; i < 15; i++) { |
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if (i < 10) { |
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cout << i; |
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} else { |
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cout << char(i + 55); |
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} |
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cout << " -> "; |
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switch (demo.Parse_dat.type[i]) { |
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case 0: |
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cout << "2 * 2" << endl; |
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break; |
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case 1: |
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cout << "2 * 1" << endl; |
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break; |
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case 2: |
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cout << "1 * 2" << endl; |
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break; |
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case 3: |
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cout << "1 * 1" << endl; |
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break; |
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default: |
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cout << "undefined" << endl; |
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break; |
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} |
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} |
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cout << "---------------------------" << endl; |
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// 分析布局 |
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demo.quiet = false; // 输出分析状态 |
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demo.Analyse_Case(0x1A9BF0C00); |
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demo.Output_Detail("demo-1A9BF0C00.txt"); // 输出分析结果到文件 |
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cout << "---------------------------" << endl; |
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// 查看某布局的前后情况 |
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int layer_num = 29, layer_index = 190; |
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// 得到全部父节点 |
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for (int k = 0; k < (*(*demo.Layer[layer_num][layer_index]).adjacent).source_case.size(); k++) { |
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cout << " (" << (*(*(*demo.Layer[layer_num][layer_index]).adjacent).source_case[k]).layer_num; |
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cout << "," << (*(*(*demo.Layer[layer_num][layer_index]).adjacent).source_case[k]).layer_index << "):"; |
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cout << demo.Change_str((*(*(*demo.Layer[layer_num][layer_index]).adjacent).source_case[k]).code); |
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} |
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cout << " ->"; |
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cout << " (" << layer_num << "," << layer_index << "):" << demo.Change_str((*demo.Layer[layer_num][layer_index]).code); |
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cout << " ->"; |
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// 得到全部子节点 |
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for (int k = 0; k < (*(*demo.Layer[layer_num][layer_index]).adjacent).next_case.size(); k++) { |
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cout << " (" << (*(*(*demo.Layer[layer_num][layer_index]).adjacent).next_case[k]).layer_num; |
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cout << "," << (*(*(*demo.Layer[layer_num][layer_index]).adjacent).next_case[k]).layer_index << "):"; |
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cout << demo.Change_str((*(*(*demo.Layer[layer_num][layer_index]).adjacent).next_case[k]).code); |
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} |
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cout << endl; |
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cout << "---------------------------" << endl; |
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return 0; |
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} |
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``` |
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### HRD_group |
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描述：华容道群组批量分析器 |
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+ 搜索某一群组全部元素的具体参数（输入群组中任一布局编码） |
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+ 排列分析多个群组（输入储存种子编码的文件名） |
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使用：包含头文件"HRD_group.h"，类名为HRD_group（依赖HRD_cal）； |
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示例： |
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```c++ |
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#include <iostream> |
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#include "HRD_group.h" |
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using namespace std; |
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int main() { |
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cout << "Klotski batch analyser by Dnomd343" << endl; |
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HRD_group demo; |
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// 计算群组中所有元素的具体参数并输出到文件（此处即计算1A9BF0C00所在群的数据） |
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demo.Batch_Analyse(0x1A9BF0C00, "farthest.csv", "solution.csv", true); |
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// 计算多个群组的分析信息，同时合并输出到文件（编码储存于5-4-0.txt中，最后一行切不可为空） |
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demo.Multi_Analyse("5-4-0.txt", "farthest_5-4-0.csv", "solution_5-4-0.csv", true); |
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return 0; |
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} |
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``` |
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### HRD_statistic |
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描述：华容道统计器 |
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+ 搜索全部合法的华容道布局编码 |
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+ 计算搜索到编码分类，即各布局的jiang_num-bing_num-style_num-group_num-group_index信息 |
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+ 取各群组的种子编码输出到文件 |
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使用：包含头文件"HRD_statistic.h"，类名为HRD_statistic（依赖HRD_cal与HRD_analy）； |
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示例： |
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```c++ |
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#include <iostream> |
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#include "HRD_statistic.h" |
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using namespace std; |
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int main() { |
|
||||
cout << "Klotski statistician by Dnomd343" << endl; |
|
||||
HRD_statistic demo; |
|
||||
|
|
||||
// 找到全部合法的编码 |
|
||||
demo.Find_All_Case("Output-All_Case.txt"); |
|
||||
|
|
||||
// 找到全部合法的编码并进行分类输出 |
|
||||
demo.All_Statistic(); |
|
||||
|
|
||||
return 0; |
|
||||
} |
|
||||
``` |
|
||||
|
|
||||
|
|
||||
## 基本定义 |
|
||||
|
|
||||
### 华容道布局 |
|
||||
|
|
||||
+ 棋盘大小为4 x 5 |
|
||||
|
|
||||
+ 棋子为2 x 2，2 x 1（1 x 2），1 x 1三种 |
|
||||
|
|
||||
+ 棋子间不能重叠，且至少存在两个空格 |
|
||||
|
|
||||
+ 有且仅有一个2 x 2块，其他类型不限定 |
|
||||
|
|
||||
*（一个合法的华容道布局必须满足以上四点）* |
|
||||
|
|
||||
合法华容道布局共有29334498种 |
|
||||
|
|
||||
### 合法布局举例： |
|
||||
|
|
||||
<img src="/images/legal_1+2.png" alt="legal_1+2" style="zoom: 40%;" /> |
|
||||
|
|
||||
<img src="/images/legal_3+4.png" alt="legal_3+4" style="zoom: 40%;" /> |
|
||||
|
|
||||
|
|
||||
### 非法布局举例： |
|
||||
|
|
||||
<img src="/images/illegal_1+2.png" alt="illegal_1+2" style="zoom: 40%;" /> |
|
||||
|
|
||||
<img src="/images/illegal_3+4.png" alt="illegal_3+4" style="zoom: 40%;" /> |
|
||||
|
|
||||
**错误原因：** |
|
||||
|
|
||||
+ 缺少2 x 2块 |
|
||||
|
|
||||
+ 仅有一个空格 |
|
||||
|
|
||||
+ 存在两个2 x 2块 |
|
||||
|
|
||||
+ 存在3 x 1块 |
|
||||
|
|
||||
|
|
||||
|
|
||||
|
|
||||
### 布局间的关系 |
|
||||
|
|
||||
+ 移动原则：棋子只能平行移动，不能进行旋转； |
|
||||
|
|
||||
+ **一步**：某一棋子做任意步移动后的结果； |
|
||||
|
|
||||
+ **子布局**：某一布局通过一步移动可以得到的布局称为子布局； |
|
||||
|
|
||||
+ 性质：布局A是布局B的子布局，同时必有布局B是布局A的子布局； |
|
||||
|
|
||||
+ **相邻布局**：两布局互为对方子布局时，两者为相邻布局； |
|
||||
|
|
||||
|
|
||||
### 步的举例 |
|
||||
<img src="/images/step_exp_1.png" alt="step_exp_1" style="zoom: 40%;" /> |
|
||||
|
|
||||
<img src="/images/step_exp_2.png" alt="step_exp_2" style="zoom:40%;" /> |
|
||||
|
|
||||
<img src="/images/step_exp_3.png" alt="step_exp_3" style="zoom:40%;" /> |
|
||||
|
|
||||
|
|
||||
### 标准情况 |
|
||||
|
|
||||
标准布局：存在5个2 x 1（或1 x 2），4个1 x 1棋子的合法华容道布局（363480种） |
|
||||
|
|
||||
非标准布局：除标准布局外的全部合法华容道布局（28971018种） |
|
||||
|
|
||||
|
|
||||
|
|
||||
### 编码 |
|
||||
|
|
||||
合法华容道均有编码，长度9位，每一位是单个16进制数（0\~9与A\~F）；同一布局只能有唯一编码，同一编码亦对应唯一布局，即编码与布局一一对应； |
|
||||
|
|
||||
**位置编号** |
|
||||
|
|
||||
<img src="/images/address.png" alt="address" style="zoom: 40%;" /> |
|
||||
|
|
||||
2 x 2棋子的左上角在棋盘中的位置编号有12种情况，对应编码分别为：0、1、2、4、5、6、8、9、A(10)、C(12)、D(13)、E(14)，将其置于编码第一位；剩余8位十六进制位储存其他棋子信息。 |
|
||||
|
|
||||
其余棋子（空格此时暂时视为棋子）按从左到右，从上到下的顺序排列（取左上角排序） |
|
||||
|
|
||||
它们对应的代号（二进制）如下： |
|
||||
|
|
||||
| 棋子类型 | 代号 | |
|
||||
| :-: | :-: | |
|
||||
| 空格 | 00 | |
|
||||
| 2 x 1 | 01 | |
|
||||
| 1 x 2 | 10 | |
|
||||
| 1 x 1 | 11 | |
|
||||
|
|
||||
十六进制可按位转为二进制，对应关系如下： |
|
||||
|
|
||||
| 十六进制 | 二进制 | 十进制 | |
|
||||
| :-: | :-: | :-: | |
|
||||
| 0 | 0000 | 0 | |
|
||||
| 1 | 0001 | 1 | |
|
||||
| 2 | 0010 | 2 | |
|
||||
| 3 | 0011 | 3 | |
|
||||
| 4 | 0100 | 4 | |
|
||||
| 5 | 0101 | 5 | |
|
||||
| 6 | 0110 | 6 | |
|
||||
| 7 | 0111 | 7 | |
|
||||
| 8 | 1000 | 8 | |
|
||||
| 9 | 1001 | 9 | |
|
||||
| A | 1010 | 10 | |
|
||||
| B | 1011 | 11 | |
|
||||
| C | 1100 | 12 | |
|
||||
| D | 1101 | 13 | |
|
||||
| E | 1110 | 14 | |
|
||||
| F | 1111 | 15 | |
|
||||
|
|
||||
8个十六进制位相当于32个二进制位，由于每个棋子占用2个二进制位，因此最多储存16个棋子信息；将其依次填入，若有空余则补0填；按此操作即可将布局转化为编码，规定编码最后的0可以省略。 |
|
||||
|
|
||||
**编码举例** |
|
||||
|
|
||||
|
|
||||
**例1：** |
|
||||
|
|
||||
<img src="/images/code_exp_1.png" alt="exp-1A9BF0C00" style="zoom: 60%;" /> |
|
||||
|
|
||||
<table style="text-align: center"> |
|
||||
<tr> |
|
||||
<td>2 x 2</td> |
|
||||
<td>1</td> |
|
||||
<td>2</td> |
|
||||
<td>3</td> |
|
||||
<td>4</td> |
|
||||
<td>5</td> |
|
||||
<td>6</td> |
|
||||
<td>7</td> |
|
||||
<td>8</td> |
|
||||
<td>9</td> |
|
||||
<td>10</td> |
|
||||
<td>11</td> |
|
||||
<td colspan="5">补0</td> |
|
||||
</tr> |
|
||||
<tr> |
|
||||
<td>0001</td> |
|
||||
<td>10</td> |
|
||||
<td>10</td> |
|
||||
<td>10</td> |
|
||||
<td>01</td> |
|
||||
<td>10</td> |
|
||||
<td>11</td> |
|
||||
<td>11</td> |
|
||||
<td>11</td> |
|
||||
<td>00</td> |
|
||||
<td>00</td> |
|
||||
<td>11</td> |
|
||||
<td>00</td> |
|
||||
<td>00</td> |
|
||||
<td>00</td> |
|
||||
<td>00</td> |
|
||||
<td>00</td> |
|
||||
</tr> |
|
||||
<tr> |
|
||||
<td><b>1</b></td> |
|
||||
<td colspan="2"><b>A</b></td> |
|
||||
<td colspan="2"><b>9</b></td> |
|
||||
<td colspan="2"><b>B</b></td> |
|
||||
<td colspan="2"><b>F</b></td> |
|
||||
<td colspan="2"><b>0</b></td> |
|
||||
<td colspan="2"><b>C</b></td> |
|
||||
<td colspan="2"><b>0</b></td> |
|
||||
<td colspan="2"><b>0</b></td> |
|
||||
</tr> |
|
||||
</table> |
|
||||
因此，布局编码为<b>1A9BF0C00</b>，可简写为<b>1A9BF0C</b> |
|
||||
|
|
||||
|
|
||||
**例2：** |
|
||||
|
|
||||
<img src="/images/code_exp_2.png" alt="exp-4FEA13400" style="zoom: 60%;" /> |
|
||||
|
|
||||
<table style="text-align: center"> |
|
||||
<tr> |
|
||||
<td>2 x 2</td> |
|
||||
<td>1</td> |
|
||||
<td>2</td> |
|
||||
<td>3</td> |
|
||||
<td>4</td> |
|
||||
<td>5</td> |
|
||||
<td>6</td> |
|
||||
<td>7</td> |
|
||||
<td>8</td> |
|
||||
<td>9</td> |
|
||||
<td>10</td> |
|
||||
<td>11</td> |
|
||||
<td colspan="5">补0</td> |
|
||||
</tr> |
|
||||
<tr> |
|
||||
<td>0100</td> |
|
||||
<td>11</td> |
|
||||
<td>11</td> |
|
||||
<td>11</td> |
|
||||
<td>10</td> |
|
||||
<td>10</td> |
|
||||
<td>10</td> |
|
||||
<td>00</td> |
|
||||
<td>01</td> |
|
||||
<td>00</td> |
|
||||
<td>11</td> |
|
||||
<td>01</td> |
|
||||
<td>00</td> |
|
||||
<td>00</td> |
|
||||
<td>00</td> |
|
||||
<td>00</td> |
|
||||
<td>00</td> |
|
||||
</tr> |
|
||||
<tr> |
|
||||
<td><b>4</b></td> |
|
||||
<td colspan="2"><b>F</b></td> |
|
||||
<td colspan="2"><b>E</b></td> |
|
||||
<td colspan="2"><b>A</b></td> |
|
||||
<td colspan="2"><b>1</b></td> |
|
||||
<td colspan="2"><b>3</b></td> |
|
||||
<td colspan="2"><b>4</b></td> |
|
||||
<td colspan="2"><b>0</b></td> |
|
||||
<td colspan="2"><b>0</b></td> |
|
||||
</tr> |
|
||||
</table> |
|
||||
因此，布局编码为<b>4FEA13400</b>，可简写为<b>4FEA134</b> |
|
||||
|
|
||||
**例3：** |
|
||||
|
|
||||
<img src="/images/code_exp_3.png" alt="exp-5DC02F800" style="zoom: 60%;" /> |
|
||||
|
|
||||
<table style="text-align: center"> |
|
||||
<tr> |
|
||||
<td>2 x 2</td> |
|
||||
<td>1</td> |
|
||||
<td>2</td> |
|
||||
<td>3</td> |
|
||||
<td>4</td> |
|
||||
<td>5</td> |
|
||||
<td>6</td> |
|
||||
<td>7</td> |
|
||||
<td>8</td> |
|
||||
<td>9</td> |
|
||||
<td>10</td> |
|
||||
<td>11</td> |
|
||||
<td>12</td> |
|
||||
<td>13</td> |
|
||||
<td colspan="3">补0</td> |
|
||||
</tr> |
|
||||
<tr> |
|
||||
<td>0101</td> |
|
||||
<td>11</td> |
|
||||
<td>01</td> |
|
||||
<td>11</td> |
|
||||
<td>00</td> |
|
||||
<td>00</td> |
|
||||
<td>00</td> |
|
||||
<td>00</td> |
|
||||
<td>10</td> |
|
||||
<td>11</td> |
|
||||
<td>11</td> |
|
||||
<td>10</td> |
|
||||
<td>00</td> |
|
||||
<td>00</td> |
|
||||
<td>00</td> |
|
||||
<td>00</td> |
|
||||
<td>00</td> |
|
||||
</tr> |
|
||||
<tr> |
|
||||
<td><b>5</b></td> |
|
||||
<td colspan="2"><b>D</b></td> |
|
||||
<td colspan="2"><b>C</b></td> |
|
||||
<td colspan="2"><b>0</b></td> |
|
||||
<td colspan="2"><b>2</b></td> |
|
||||
<td colspan="2"><b>F</b></td> |
|
||||
<td colspan="2"><b>8</b></td> |
|
||||
<td colspan="2"><b>0</b></td> |
|
||||
<td colspan="2"><b>0</b></td> |
|
||||
</tr> |
|
||||
</table> |
|
||||
因此，布局编码为<b>5DC02F800</b>，可简写为<b>5DC02F8</b> |
|
||||
|
|
||||
|
|
||||
|
|
||||
## 分类 |
|
||||
|
|
||||
由于共有29334498种布局，将它们从小到大排列，进而得到唯一的id(0 ~ 29334497)； |
|
||||
|
|
||||
|
|
||||
|
|
||||
### 摆列方式分类 |
|
||||
|
|
||||
将2 x 1（1 x 2）的数量称为jiang_num，1 x 1的数量称为bing_num； |
|
||||
|
|
||||
据此可分为64种情况，统计如下： |
|
||||
|
|
||||
| jiang_num | bing_num | 数量 | |
|
||||
| :-: | :-: | :-: | |
|
||||
| 0 | 0 | 12 | |
|
||||
| 0 | 1 | 192 | |
|
||||
| 0 | 2 | 1440 | |
|
||||
| 0 | 3 | 6720 | |
|
||||
| 0 | 4 | 21840 | |
|
||||
| 0 | 5 | 52416 | |
|
||||
| 0 | 6 | 96096 | |
|
||||
| 0 | 7 | 137280 | |
|
||||
| 0 | 8 | 154440 | |
|
||||
| 0 | 9 | 137280 | |
|
||||
| 0 | 10 | 96096 | |
|
||||
| 0 | 11 | 52416 | |
|
||||
| 0 | 12 | 21840 | |
|
||||
| 0 | 13 | 6720 | |
|
||||
| 0 | 14 | 1440 | |
|
||||
| 1 | 0 | 256 | |
|
||||
| 1 | 1 | 3584 | |
|
||||
| 1 | 2 | 23296 | |
|
||||
| 1 | 3 | 93184 | |
|
||||
| 1 | 4 | 256256 | |
|
||||
| 1 | 5 | 512512 | |
|
||||
| 1 | 6 | 768768 | |
|
||||
| 1 | 7 | 878592 | |
|
||||
| 1 | 8 | 768768 | |
|
||||
| 1 | 9 | 512512 | |
|
||||
| 1 | 10 | 256256 | |
|
||||
| 1 | 11 | 93184 | |
|
||||
| 1 | 12 | 23296 | |
|
||||
| 2 | 0 | 2138 | |
|
||||
| 2 | 1 | 25656 | |
|
||||
| 2 | 2 | 141108 | |
|
||||
| 2 | 3 | 470360 | |
|
||||
| 2 | 4 | 1058310 | |
|
||||
| 2 | 5 | 1693296 | |
|
||||
| 2 | 6 | 1975512 | |
|
||||
| 2 | 7 | 1693296 | |
|
||||
| 2 | 8 | 1058310 | |
|
||||
| 2 | 9 | 470360 | |
|
||||
| 2 | 10 | 141108 | |
|
||||
| 3 | 0 | 8974 | |
|
||||
| 3 | 1 | 89740 | |
|
||||
| 3 | 2 | 403830 | |
|
||||
| 3 | 3 | 1076880 | |
|
||||
| 3 | 4 | 1884540 | |
|
||||
| 3 | 5 | 2261448 | |
|
||||
| 3 | 6 | 1884540 | |
|
||||
| 3 | 7 | 1076880 | |
|
||||
| 3 | 8 | 403830 | |
|
||||
| 4 | 0 | 20224 | |
|
||||
| 4 | 1 | 161792 | |
|
||||
| 4 | 2 | 566272 | |
|
||||
| 4 | 3 | 1132544 | |
|
||||
| 4 | 4 | 1415680 | |
|
||||
| 4 | 5 | 1132544 | |
|
||||
| 4 | 6 | 566272 | |
|
||||
| 5 | 0 | 24232 | |
|
||||
| 5 | 1 | 145392 | |
|
||||
| 5 | 2 | 363480 | |
|
||||
| 5 | 3 | 484640 | |
|
||||
| 5 | 4 | 363480 | |
|
||||
| 6 | 0 | 14330 | |
|
||||
| 6 | 1 | 57320 | |
|
||||
| 6 | 2 | 85980 | |
|
||||
| 7 | 0 | 3508 | |
|
||||
|
|
||||
进而，将2 x 1的数量称为style_num，于是有style_num恒小于或等于jiang_num； |
|
||||
|
|
||||
此时可分出203种情况（注意不存在 *jiang_num-bing_num-style_num = 7-0-0* 的情况）： |
|
||||
|
|
||||
[203种分类的元素数量](./style_count.md) |
|
||||
|
|
||||
|
|
||||
|
|
||||
### 群 |
|
||||
|
|
||||
定义：群是有限个不同布局的集合，该集合中全部布局都可以由其中任一布局经过有限次移动得到； |
|
||||
|
|
||||
性质：任意一个布局无论如何移动，其结果仍在该群内； |
|
||||
|
|
||||
构造：群是封闭的，群中所有元素无序且互异，同时构成一个关系网； |
|
||||
|
|
||||
最简性：只需群中任意一个布局，即可复原出群中的所有元素； |
|
||||
|
|
||||
|
|
||||
|
|
||||
### 按群继续分类 |
|
||||
|
|
||||
对于一个特定的 *jiang_num-bing_num-style_num* 分组，可拆分出n个群；将分出的群按元素数量从大到小排列，若存在元素数量相同的群，则取其中的最小元素排序；对这些群进行编号得0 ~ (n - 1) 共n个群，编号记为group_num； |
|
||||
|
|
||||
因而对于某一群，存在一个唯一编号 *jiang_num-bing_num-style_num-group_num* ；由于群中的元素个数是确定的，将其中的元素按编码从小到大排列，其中的元素可得唯一编号group_index； |
|
||||
|
|
||||
所以，对于任意布局，可得唯一编号 *jiang_num-bing_num-style_num-group_num-group_index*； |
|
||||
|
|
||||
|
|
||||
|
|
||||
## 层级关系 |
|
||||
|
|
||||
**最少步数**：当布局A和布局B处于同一个群时，从布局A移动到B所需最少的步数，该数值存在且是确定的； |
|
||||
|
|
||||
性质：布局A到B的最少步数与布局B到A的最少步数必定相同； |
|
||||
|
|
||||
**最短路径**：从布局A到布局B，所有满足最少步数的路径（最少路径可能不止一条）； |
|
||||
|
|
||||
**最远步数**：布局A到它所在群中任一布局均存在一最少步数，其中最大的最少步数称为最远步数； |
|
||||
|
|
||||
**最远布局**：布局A到布局B的最少步数为最远步数时，称布局B为布局A的最远布局（一般情况下不止一个）； |
|
||||
|
|
||||
（标准华容道中不存在最远布局退化的情况，即最远步数至少为1） |
|
||||
|
|
||||
**最少步解**：布局A所在群中存在一布局S，满足2 x 2方块在棋盘的最下方中间（即2 x 2块所在位置编号为13，亦或编码以D开头），记A到S的最少步数为n，此时不存在其他任何满足以上条件的S‘使得最少步数小于n，则称S为布局A的最少步解，n为最少步解的步数（亦简称为最少步）； |
|
||||
|
|
||||
**解**：布局A所在群中存在一布局S满足2 x 2方块在棋盘的最下方中间，且有A到S的任意最短路径中均不存在符合2 x 2方块在棋盘的最下方中间的布局，此时称S为布局A的解； |
|
||||
|
|
||||
性质：布局的解可能是空集；最少步解属于解的子集（特定条件下两者可以相同）； |
|
||||
|
|
||||
|
|
||||
|
|
||||
**层模型** |
|
||||
|
|
||||
表述：存在一起始布局A，从它开始衍生出有限个布局，每个布局抽象为一个节点，同时称A为根节点；由于任一由A衍生出布局到根节点存在一个确定的最少步数，将其称之为到根节点的距离；将所有距离相同的布局称为一个层，层内元素无序且互异，根节点所在层称为第0层，之后依次排列可得有限个层； |
|
||||
|
|
||||
记排列的最后一层为第n层，则共有n + 1个层（包括第0层）； |
|
||||
|
|
||||
性质1：所有层中的元素集合即为根节点所在的群； |
|
||||
|
|
||||
性质2：某一节点所在层数为其到根节点的最少步数； |
|
||||
|
|
||||
性质3：若最后一层为第n层，则最远步数为n，且第n层的所有元素均为最远布局； |
|
||||
|
|
||||
|
引擎封装了多个类实现不同功能，这里是它库函数的[使用演示](./docs/class.md)； |
||||
|
|
||||
|
为了方便解析/获取编码，这里提供了一个图形化的[绘制工具](./docs/visual.md)； |
||||
|
|
||||
|
在计算完所有布局后，数据将以csv格式保存，这里是[建立与使用数据库](./docs/database.md)的讲解； |
||||
|
|
||||
|
本项目所有源码以[MIT协议](./LICENSE)开源，你可以不受任何限制地使用，但保留作者版权； |
||||
|
|
||||
|
*by Dnomd343* |
||||
|
*2020.7.6* |
||||
@ -1,22 +0,0 @@ |
|||||
dim jiang_num, bing_num, style_num |
|
||||
dim fso, file |
|
||||
dim cmd, dat |
|
||||
set fso = CreateObject("Scripting.FileSystemObject") |
|
||||
fso.CreateFolder("./cal_sh") |
|
||||
|
|
||||
for jiang_num = 0 to 7 |
|
||||
for bing_num = 0 to 14 - jiang_num * 2 |
|
||||
set file = fso.CreateTextFile("./cal_sh/" & jiang_num & "-" & bing_num & ".sh", true) |
|
||||
cmd = "" |
|
||||
for style_num = 0 to jiang_num |
|
||||
if jiang_num = 7 and bing_num = 0 and style_num = 0 then style_num = 1 |
|
||||
dat = jiang_num & "-" & bing_num & "-" & style_num |
|
||||
cmd = cmd & "../engine --analy-multi-group ../seed/" & dat & ".txt " |
|
||||
cmd = cmd & "../farthest/farthest_" & dat & ".csv ../solution/solution_" & dat & ".csv" & chr(10) |
|
||||
next |
|
||||
cmd = cmd & "touch " & jiang_num & "-" & bing_num & "_OK" |
|
||||
file.Write(cmd) |
|
||||
file.Close() |
|
||||
next |
|
||||
next |
|
||||
msgbox "OK" |
|
||||
@ -0,0 +1,253 @@ |
|||||
|
## 库的调用 |
||||
|
|
||||
|
代码已封装为四个类 |
||||
|
|
||||
|
+ HRD_cal: 华容道快速计算器 |
||||
|
|
||||
|
+ HRD_analy: 华容道分析器 |
||||
|
|
||||
|
+ HRD_group: 华容道群组批量分析器 |
||||
|
|
||||
|
+ HRD_statistic: 华容道统计工具 |
||||
|
|
||||
|
以上可根据需要调用，包含对应头文件即可 |
||||
|
|
||||
|
|
||||
|
### HRD_cal |
||||
|
|
||||
|
描述：华容道快速计算器 |
||||
|
|
||||
|
+ 判断编码正确性 |
||||
|
|
||||
|
+ 对起始布局求解（仅返回搜索到的第一个最少步解的一个解法） |
||||
|
|
||||
|
+ 找到两布局间最短路径（仅返回搜索到的第一条最短路径） |
||||
|
|
||||
|
+ 找到起始布局衍生出的所有情况 |
||||
|
|
||||
|
使用：包含头文件"HRD_cal.h"，类名为HRD_cal； |
||||
|
|
||||
|
示例： |
||||
|
|
||||
|
```c++ |
||||
|
#include <iostream> |
||||
|
#include <vector> |
||||
|
#include "HRD_cal.h" |
||||
|
using namespace std; |
||||
|
|
||||
|
int main() { |
||||
|
cout << "Klotski fast calculator by Dnomd343" << endl; |
||||
|
vector <unsigned long long> dat; |
||||
|
HRD_cal demo; |
||||
|
|
||||
|
// 将编码转为文本(参数为unsigned long long 返回string类) |
||||
|
cout << "4FEA13400 is " << demo.Change_str(0x4FEA13400) << endl; |
||||
|
cout << "----------------" << endl; |
||||
|
|
||||
|
// 将文本转为编码(参数为*char 返回unsigned long long) |
||||
|
cout << "1a9bf0c00 is " << hex << demo.Change_int("1A9BF0C00") << dec << endl; |
||||
|
cout << "----------------" << endl; |
||||
|
|
||||
|
// 检测编码的正确性 |
||||
|
if (demo.Check_Code(0x123456789) == false) { |
||||
|
cout << "Code error!" << endl; |
||||
|
} |
||||
|
|
||||
|
// 计算最少步数(参数为unsigned long long 返回vector类) |
||||
|
dat = demo.Calculate(0x1A9BF0C00); |
||||
|
cout << demo.Change_str(0x1A9BF0C00) << "'s solution"; |
||||
|
cout << " need at least " << dat.size() - 1 << " steps" << endl; |
||||
|
for (unsigned int i = 0; i < dat.size(); i++) { |
||||
|
cout << i << ": " << demo.Change_str(dat[i]) << endl; |
||||
|
} |
||||
|
cout << "----------------" << endl; |
||||
|
|
||||
|
// 计算到某一布局的最短路径(参数均为unsigned long long 分别为起始编码和目标编码 返回vector类) |
||||
|
dat = demo.Calculate(0x1A9BF0C00, 0x1ABE70C00); |
||||
|
cout << demo.Change_str(0x1A9BF0C00) << " to " << demo.Change_str(0x1ABE70C00); |
||||
|
cout << " need at least " << dat.size() - 1 << " steps" << endl; |
||||
|
for (unsigned int i = 0; i < dat.size(); i++) { |
||||
|
cout << i << ": " << demo.Change_str(dat[i]) << endl; |
||||
|
} |
||||
|
cout << "----------------" << endl; |
||||
|
|
||||
|
// 计算某一布局衍生出的所有布局 |
||||
|
dat = demo.Calculate_All(0x1A9BF0C00); |
||||
|
cout << demo.Change_str(0x1A9BF0C00) << " can derive " << dat.size() << " cases" << endl; |
||||
|
cout << "----------------" << endl; |
||||
|
|
||||
|
return 0; |
||||
|
} |
||||
|
``` |
||||
|
|
||||
|
### HRD_analy |
||||
|
|
||||
|
描述：华容道分析器 |
||||
|
|
||||
|
+ 编码解析为具体排列 |
||||
|
|
||||
|
+ 检查编码是否合法 |
||||
|
|
||||
|
+ 根据起始布局分析出层级结构，包括各层间的链接关系 |
||||
|
|
||||
|
+ 得到布局的具体参数，包括全部最远布局、全部最少步解、全部合法解及其步数 |
||||
|
|
||||
|
+ 将分析结果导出到文件 |
||||
|
|
||||
|
使用：包含头文件"HRD_analy.h"，类名为HRD_analy； |
||||
|
|
||||
|
示例： |
||||
|
|
||||
|
```c++ |
||||
|
#include <iostream> |
||||
|
#include "HRD_analy.h" |
||||
|
using namespace std; |
||||
|
|
||||
|
int main() { |
||||
|
cout << "Klotski Analyser by Dnomd343" << endl; |
||||
|
HRD_analy demo; |
||||
|
|
||||
|
// 显示编码的实际布局样式 |
||||
|
demo.Output_Graph(0x1A9BF0C00, 4, 1, "&%"); |
||||
|
|
||||
|
// 解译编码 |
||||
|
demo.Parse_Code(0x1A9BF0C00); |
||||
|
cout << "code: " << demo.Change_str(demo.Parse_dat.code) << endl; |
||||
|
cout << "status" << endl; |
||||
|
for (int y = 0; y < 5; y++) { |
||||
|
for (int x = 0; x < 4; x++) { |
||||
|
if (demo.Parse_dat.status[x][y] <= 9) { // 0 ~ 9 |
||||
|
cout << int(demo.Parse_dat.status[x][y]) << " "; |
||||
|
} else if (demo.Parse_dat.status[x][y] <= 0xE) { // A ~ E |
||||
|
cout << char(demo.Parse_dat.status[x][y] + 55) << " "; |
||||
|
} else if (demo.Parse_dat.status[x][y] == 0xFE) { // space |
||||
|
cout << ". "; |
||||
|
} else if (demo.Parse_dat.status[x][y] == 0xFF) { // undefined |
||||
|
cout << "* "; |
||||
|
} else { // error |
||||
|
cout << "! "; |
||||
|
} |
||||
|
} |
||||
|
cout << endl; |
||||
|
} |
||||
|
cout << "type" << endl; |
||||
|
for (int i = 0; i < 15; i++) { |
||||
|
if (i < 10) { |
||||
|
cout << i; |
||||
|
} else { |
||||
|
cout << char(i + 55); |
||||
|
} |
||||
|
cout << " -> "; |
||||
|
switch (demo.Parse_dat.type[i]) { |
||||
|
case 0: |
||||
|
cout << "2 * 2" << endl; |
||||
|
break; |
||||
|
case 1: |
||||
|
cout << "2 * 1" << endl; |
||||
|
break; |
||||
|
case 2: |
||||
|
cout << "1 * 2" << endl; |
||||
|
break; |
||||
|
case 3: |
||||
|
cout << "1 * 1" << endl; |
||||
|
break; |
||||
|
default: |
||||
|
cout << "undefined" << endl; |
||||
|
break; |
||||
|
} |
||||
|
} |
||||
|
cout << "---------------------------" << endl; |
||||
|
|
||||
|
// 分析布局 |
||||
|
demo.quiet = false; // 输出分析状态 |
||||
|
demo.Analyse_Case(0x1A9BF0C00); |
||||
|
demo.Output_Detail("demo-1A9BF0C00.txt"); // 输出分析结果到文件 |
||||
|
cout << "---------------------------" << endl; |
||||
|
|
||||
|
// 查看某布局的前后情况 |
||||
|
int layer_num = 29, layer_index = 190; |
||||
|
// 得到全部父节点 |
||||
|
for (int k = 0; k < (*(*demo.Layer[layer_num][layer_index]).adjacent).source_case.size(); k++) { |
||||
|
cout << " (" << (*(*(*demo.Layer[layer_num][layer_index]).adjacent).source_case[k]).layer_num; |
||||
|
cout << "," << (*(*(*demo.Layer[layer_num][layer_index]).adjacent).source_case[k]).layer_index << "):"; |
||||
|
cout << demo.Change_str((*(*(*demo.Layer[layer_num][layer_index]).adjacent).source_case[k]).code); |
||||
|
} |
||||
|
cout << " ->"; |
||||
|
cout << " (" << layer_num << "," << layer_index << "):" << demo.Change_str((*demo.Layer[layer_num][layer_index]).code); |
||||
|
cout << " ->"; |
||||
|
// 得到全部子节点 |
||||
|
for (int k = 0; k < (*(*demo.Layer[layer_num][layer_index]).adjacent).next_case.size(); k++) { |
||||
|
cout << " (" << (*(*(*demo.Layer[layer_num][layer_index]).adjacent).next_case[k]).layer_num; |
||||
|
cout << "," << (*(*(*demo.Layer[layer_num][layer_index]).adjacent).next_case[k]).layer_index << "):"; |
||||
|
cout << demo.Change_str((*(*(*demo.Layer[layer_num][layer_index]).adjacent).next_case[k]).code); |
||||
|
} |
||||
|
cout << endl; |
||||
|
cout << "---------------------------" << endl; |
||||
|
|
||||
|
return 0; |
||||
|
} |
||||
|
``` |
||||
|
|
||||
|
### HRD_group |
||||
|
|
||||
|
描述：华容道群组批量分析器 |
||||
|
|
||||
|
+ 搜索某一群组全部元素的具体参数（输入群组中任一布局编码） |
||||
|
|
||||
|
+ 排列分析多个群组（输入储存种子编码的文件名） |
||||
|
|
||||
|
使用：包含头文件"HRD_group.h"，类名为HRD_group（依赖HRD_cal）； |
||||
|
|
||||
|
示例： |
||||
|
|
||||
|
```c++ |
||||
|
#include <iostream> |
||||
|
#include "HRD_group.h" |
||||
|
using namespace std; |
||||
|
|
||||
|
int main() { |
||||
|
cout << "Klotski batch analyser by Dnomd343" << endl; |
||||
|
HRD_group demo; |
||||
|
|
||||
|
// 计算群组中所有元素的具体参数并输出到文件（此处即计算1A9BF0C00所在群的数据） |
||||
|
demo.Batch_Analyse(0x1A9BF0C00, "farthest.csv", "solution.csv", true); |
||||
|
|
||||
|
// 计算多个群组的分析信息，同时合并输出到文件（编码储存于5-4-0.txt中，最后一行切不可为空） |
||||
|
demo.Multi_Analyse("5-4-0.txt", "farthest_5-4-0.csv", "solution_5-4-0.csv", true); |
||||
|
|
||||
|
return 0; |
||||
|
} |
||||
|
``` |
||||
|
|
||||
|
### HRD_statistic |
||||
|
|
||||
|
描述：华容道统计工具 |
||||
|
|
||||
|
+ 搜索全部合法的华容道布局编码 |
||||
|
|
||||
|
+ 计算搜索到编码分类，即各布局的jiang_num-bing_num-style_num-group_num-group_index信息 |
||||
|
|
||||
|
+ 取各群组的种子编码输出到文件 |
||||
|
|
||||
|
使用：包含头文件"HRD_statistic.h"，类名为HRD_statistic（依赖HRD_cal与HRD_analy）； |
||||
|
|
||||
|
示例： |
||||
|
|
||||
|
```c++ |
||||
|
#include <iostream> |
||||
|
#include "HRD_statistic.h" |
||||
|
using namespace std; |
||||
|
|
||||
|
int main() { |
||||
|
cout << "Klotski statistician by Dnomd343" << endl; |
||||
|
HRD_statistic demo; |
||||
|
|
||||
|
// 找到全部合法的编码 |
||||
|
demo.Find_All_Case("Output-All_Case.txt"); |
||||
|
|
||||
|
// 找到全部合法的编码并进行分类输出 |
||||
|
demo.All_Statistic(); |
||||
|
|
||||
|
return 0; |
||||
|
} |
||||
|
``` |
||||
@ -0,0 +1 @@ |
|||||
|
未完待续... |
||||
@ -0,0 +1 @@ |
|||||
|
未完待续... |
||||
@ -0,0 +1,205 @@ |
|||||
|
| jiang_num | bing_num | style_num | 群的数量 | |
||||
|
| :-: | :-: | :-: | :-: | |
||||
|
| 0 | 0 | 0 | 1 | |
||||
|
| 0 | 1 | 0 | 1 | |
||||
|
| 0 | 2 | 0 | 1 | |
||||
|
| 0 | 3 | 0 | 1 | |
||||
|
| 0 | 4 | 0 | 1 | |
||||
|
| 0 | 5 | 0 | 1 | |
||||
|
| 0 | 6 | 0 | 1 | |
||||
|
| 0 | 7 | 0 | 1 | |
||||
|
| 0 | 8 | 0 | 1 | |
||||
|
| 0 | 9 | 0 | 1 | |
||||
|
| 0 | 10 | 0 | 1 | |
||||
|
| 0 | 11 | 0 | 1 | |
||||
|
| 0 | 12 | 0 | 1 | |
||||
|
| 0 | 13 | 0 | 1 | |
||||
|
| 0 | 14 | 0 | 1 | |
||||
|
| 1 | 0 | 0 | 1 | |
||||
|
| 1 | 0 | 1 | 1 | |
||||
|
| 1 | 1 | 0 | 1 | |
||||
|
| 1 | 1 | 1 | 1 | |
||||
|
| 1 | 2 | 0 | 1 | |
||||
|
| 1 | 2 | 1 | 1 | |
||||
|
| 1 | 3 | 0 | 1 | |
||||
|
| 1 | 3 | 1 | 1 | |
||||
|
| 1 | 4 | 0 | 1 | |
||||
|
| 1 | 4 | 1 | 1 | |
||||
|
| 1 | 5 | 0 | 1 | |
||||
|
| 1 | 5 | 1 | 1 | |
||||
|
| 1 | 6 | 0 | 1 | |
||||
|
| 1 | 6 | 1 | 1 | |
||||
|
| 1 | 7 | 0 | 1 | |
||||
|
| 1 | 7 | 1 | 1 | |
||||
|
| 1 | 8 | 0 | 1 | |
||||
|
| 1 | 8 | 1 | 1 | |
||||
|
| 1 | 9 | 0 | 1 | |
||||
|
| 1 | 9 | 1 | 1 | |
||||
|
| 1 | 10 | 0 | 1 | |
||||
|
| 1 | 10 | 1 | 1 | |
||||
|
| 1 | 11 | 0 | 1 | |
||||
|
| 1 | 11 | 1 | 1 | |
||||
|
| 1 | 12 | 0 | 5 | |
||||
|
| 1 | 12 | 1 | 13 | |
||||
|
| 2 | 0 | 0 | 1 | |
||||
|
| 2 | 0 | 1 | 1 | |
||||
|
| 2 | 0 | 2 | 1 | |
||||
|
| 2 | 1 | 0 | 1 | |
||||
|
| 2 | 1 | 1 | 1 | |
||||
|
| 2 | 1 | 2 | 1 | |
||||
|
| 2 | 2 | 0 | 1 | |
||||
|
| 2 | 2 | 1 | 1 | |
||||
|
| 2 | 2 | 2 | 1 | |
||||
|
| 2 | 3 | 0 | 1 | |
||||
|
| 2 | 3 | 1 | 1 | |
||||
|
| 2 | 3 | 2 | 1 | |
||||
|
| 2 | 4 | 0 | 1 | |
||||
|
| 2 | 4 | 1 | 1 | |
||||
|
| 2 | 4 | 2 | 1 | |
||||
|
| 2 | 5 | 0 | 1 | |
||||
|
| 2 | 5 | 1 | 1 | |
||||
|
| 2 | 5 | 2 | 1 | |
||||
|
| 2 | 6 | 0 | 1 | |
||||
|
| 2 | 6 | 1 | 1 | |
||||
|
| 2 | 6 | 2 | 1 | |
||||
|
| 2 | 7 | 0 | 1 | |
||||
|
| 2 | 7 | 1 | 1 | |
||||
|
| 2 | 7 | 2 | 1 | |
||||
|
| 2 | 8 | 0 | 1 | |
||||
|
| 2 | 8 | 1 | 1 | |
||||
|
| 2 | 8 | 2 | 1 | |
||||
|
| 2 | 9 | 0 | 1 | |
||||
|
| 2 | 9 | 1 | 21 | |
||||
|
| 2 | 9 | 2 | 3 | |
||||
|
| 2 | 10 | 0 | 17 | |
||||
|
| 2 | 10 | 1 | 141 | |
||||
|
| 2 | 10 | 2 | 79 | |
||||
|
| 3 | 0 | 0 | 1 | |
||||
|
| 3 | 0 | 1 | 1 | |
||||
|
| 3 | 0 | 2 | 1 | |
||||
|
| 3 | 0 | 3 | 1 | |
||||
|
| 3 | 1 | 0 | 1 | |
||||
|
| 3 | 1 | 1 | 1 | |
||||
|
| 3 | 1 | 2 | 1 | |
||||
|
| 3 | 1 | 3 | 1 | |
||||
|
| 3 | 2 | 0 | 1 | |
||||
|
| 3 | 2 | 1 | 1 | |
||||
|
| 3 | 2 | 2 | 1 | |
||||
|
| 3 | 2 | 3 | 1 | |
||||
|
| 3 | 3 | 0 | 1 | |
||||
|
| 3 | 3 | 1 | 1 | |
||||
|
| 3 | 3 | 2 | 1 | |
||||
|
| 3 | 3 | 3 | 1 | |
||||
|
| 3 | 4 | 0 | 1 | |
||||
|
| 3 | 4 | 1 | 1 | |
||||
|
| 3 | 4 | 2 | 1 | |
||||
|
| 3 | 4 | 3 | 1 | |
||||
|
| 3 | 5 | 0 | 1 | |
||||
|
| 3 | 5 | 1 | 1 | |
||||
|
| 3 | 5 | 2 | 1 | |
||||
|
| 3 | 5 | 3 | 1 | |
||||
|
| 3 | 6 | 0 | 1 | |
||||
|
| 3 | 6 | 1 | 15 | |
||||
|
| 3 | 6 | 2 | 9 | |
||||
|
| 3 | 6 | 3 | 1 | |
||||
|
| 3 | 7 | 0 | 5 | |
||||
|
| 3 | 7 | 1 | 97 | |
||||
|
| 3 | 7 | 2 | 145 | |
||||
|
| 3 | 7 | 3 | 17 | |
||||
|
| 3 | 8 | 0 | 91 | |
||||
|
| 3 | 8 | 1 | 517 | |
||||
|
| 3 | 8 | 2 | 841 | |
||||
|
| 3 | 8 | 3 | 273 | |
||||
|
| 4 | 0 | 0 | 1 | |
||||
|
| 4 | 0 | 1 | 1 | |
||||
|
| 4 | 0 | 2 | 1 | |
||||
|
| 4 | 0 | 3 | 1 | |
||||
|
| 4 | 0 | 4 | 1 | |
||||
|
| 4 | 1 | 0 | 1 | |
||||
|
| 4 | 1 | 1 | 1 | |
||||
|
| 4 | 1 | 2 | 1 | |
||||
|
| 4 | 1 | 3 | 1 | |
||||
|
| 4 | 1 | 4 | 1 | |
||||
|
| 4 | 2 | 0 | 1 | |
||||
|
| 4 | 2 | 1 | 1 | |
||||
|
| 4 | 2 | 2 | 1 | |
||||
|
| 4 | 2 | 3 | 1 | |
||||
|
| 4 | 2 | 4 | 1 | |
||||
|
| 4 | 3 | 0 | 1 | |
||||
|
| 4 | 3 | 1 | 5 | |
||||
|
| 4 | 3 | 2 | 7 | |
||||
|
| 4 | 3 | 3 | 1 | |
||||
|
| 4 | 3 | 4 | 1 | |
||||
|
| 4 | 4 | 0 | 1 | |
||||
|
| 4 | 4 | 1 | 33 | |
||||
|
| 4 | 4 | 2 | 81 | |
||||
|
| 4 | 4 | 3 | 21 | |
||||
|
| 4 | 4 | 4 | 1 | |
||||
|
| 4 | 5 | 0 | 9 | |
||||
|
| 4 | 5 | 1 | 165 | |
||||
|
| 4 | 5 | 2 | 479 | |
||||
|
| 4 | 5 | 3 | 353 | |
||||
|
| 4 | 5 | 4 | 59 | |
||||
|
| 4 | 6 | 0 | 157 | |
||||
|
| 4 | 6 | 1 | 1053 | |
||||
|
| 4 | 6 | 2 | 2327 | |
||||
|
| 4 | 6 | 3 | 1741 | |
||||
|
| 4 | 6 | 4 | 587 | |
||||
|
| 5 | 0 | 0 | 2 | |
||||
|
| 5 | 0 | 1 | 1 | |
||||
|
| 5 | 0 | 2 | 1 | |
||||
|
| 5 | 0 | 3 | 3 | |
||||
|
| 5 | 0 | 4 | 1 | |
||||
|
| 5 | 0 | 5 | 1 | |
||||
|
| 5 | 1 | 0 | 2 | |
||||
|
| 5 | 1 | 1 | 1 | |
||||
|
| 5 | 1 | 2 | 17 | |
||||
|
| 5 | 1 | 3 | 9 | |
||||
|
| 5 | 1 | 4 | 1 | |
||||
|
| 5 | 1 | 5 | 1 | |
||||
|
| 5 | 2 | 0 | 2 | |
||||
|
| 5 | 2 | 1 | 11 | |
||||
|
| 5 | 2 | 2 | 91 | |
||||
|
| 5 | 2 | 3 | 99 | |
||||
|
| 5 | 2 | 4 | 13 | |
||||
|
| 5 | 2 | 5 | 1 | |
||||
|
| 5 | 3 | 0 | 2 | |
||||
|
| 5 | 3 | 1 | 75 | |
||||
|
| 5 | 3 | 2 | 487 | |
||||
|
| 5 | 3 | 3 | 631 | |
||||
|
| 5 | 3 | 4 | 325 | |
||||
|
| 5 | 3 | 5 | 57 | |
||||
|
| 5 | 4 | 0 | 80 | |
||||
|
| 5 | 4 | 1 | 898 | |
||||
|
| 5 | 4 | 2 | 2653 | |
||||
|
| 5 | 4 | 3 | 2609 | |
||||
|
| 5 | 4 | 4 | 1729 | |
||||
|
| 5 | 4 | 5 | 505 | |
||||
|
| 6 | 0 | 0 | 6 | |
||||
|
| 6 | 0 | 1 | 6 | |
||||
|
| 6 | 0 | 2 | 13 | |
||||
|
| 6 | 0 | 3 | 33 | |
||||
|
| 6 | 0 | 4 | 22 | |
||||
|
| 6 | 0 | 5 | 14 | |
||||
|
| 6 | 0 | 6 | 1 | |
||||
|
| 6 | 1 | 0 | 18 | |
||||
|
| 6 | 1 | 1 | 16 | |
||||
|
| 6 | 1 | 2 | 171 | |
||||
|
| 6 | 1 | 3 | 209 | |
||||
|
| 6 | 1 | 4 | 183 | |
||||
|
| 6 | 1 | 5 | 126 | |
||||
|
| 6 | 1 | 6 | 2 | |
||||
|
| 6 | 2 | 0 | 54 | |
||||
|
| 6 | 2 | 1 | 214 | |
||||
|
| 6 | 2 | 2 | 1185 | |
||||
|
| 6 | 2 | 3 | 1178 | |
||||
|
| 6 | 2 | 4 | 1074 | |
||||
|
| 6 | 2 | 5 | 590 | |
||||
|
| 6 | 2 | 6 | 138 | |
||||
|
| 7 | 0 | 1 | 18 | |
||||
|
| 7 | 0 | 2 | 70 | |
||||
|
| 7 | 0 | 3 | 84 | |
||||
|
| 7 | 0 | 4 | 124 | |
||||
|
| 7 | 0 | 5 | 40 | |
||||
|
| 7 | 0 | 6 | 44 | |
||||
|
| 7 | 0 | 7 | 2 | |
||||
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@ -0,0 +1,66 @@ |
|||||
|
| jiang_num | bing_num | COUNT | |
||||
|
| :-: | :-: | :-: | |
||||
|
| 0 | 0 | 12 | |
||||
|
| 0 | 1 | 192 | |
||||
|
| 0 | 2 | 1440 | |
||||
|
| 0 | 3 | 6720 | |
||||
|
| 0 | 4 | 21840 | |
||||
|
| 0 | 5 | 52416 | |
||||
|
| 0 | 6 | 96096 | |
||||
|
| 0 | 7 | 137280 | |
||||
|
| 0 | 8 | 154440 | |
||||
|
| 0 | 9 | 137280 | |
||||
|
| 0 | 10 | 96096 | |
||||
|
| 0 | 11 | 52416 | |
||||
|
| 0 | 12 | 21840 | |
||||
|
| 0 | 13 | 6720 | |
||||
|
| 0 | 14 | 1440 | |
||||
|
| 1 | 0 | 256 | |
||||
|
| 1 | 1 | 3584 | |
||||
|
| 1 | 2 | 23296 | |
||||
|
| 1 | 3 | 93184 | |
||||
|
| 1 | 4 | 256256 | |
||||
|
| 1 | 5 | 512512 | |
||||
|
| 1 | 6 | 768768 | |
||||
|
| 1 | 7 | 878592 | |
||||
|
| 1 | 8 | 768768 | |
||||
|
| 1 | 9 | 512512 | |
||||
|
| 1 | 10 | 256256 | |
||||
|
| 1 | 11 | 93184 | |
||||
|
| 1 | 12 | 23296 | |
||||
|
| 2 | 0 | 2138 | |
||||
|
| 2 | 1 | 25656 | |
||||
|
| 2 | 2 | 141108 | |
||||
|
| 2 | 3 | 470360 | |
||||
|
| 2 | 4 | 1058310 | |
||||
|
| 2 | 5 | 1693296 | |
||||
|
| 2 | 6 | 1975512 | |
||||
|
| 2 | 7 | 1693296 | |
||||
|
| 2 | 8 | 1058310 | |
||||
|
| 2 | 9 | 470360 | |
||||
|
| 2 | 10 | 141108 | |
||||
|
| 3 | 0 | 8974 | |
||||
|
| 3 | 1 | 89740 | |
||||
|
| 3 | 2 | 403830 | |
||||
|
| 3 | 3 | 1076880 | |
||||
|
| 3 | 4 | 1884540 | |
||||
|
| 3 | 5 | 2261448 | |
||||
|
| 3 | 6 | 1884540 | |
||||
|
| 3 | 7 | 1076880 | |
||||
|
| 3 | 8 | 403830 | |
||||
|
| 4 | 0 | 20224 | |
||||
|
| 4 | 1 | 161792 | |
||||
|
| 4 | 2 | 566272 | |
||||
|
| 4 | 3 | 1132544 | |
||||
|
| 4 | 4 | 1415680 | |
||||
|
| 4 | 5 | 1132544 | |
||||
|
| 4 | 6 | 566272 | |
||||
|
| 5 | 0 | 24232 | |
||||
|
| 5 | 1 | 145392 | |
||||
|
| 5 | 2 | 363480 | |
||||
|
| 5 | 3 | 484640 | |
||||
|
| 5 | 4 | 363480 | |
||||
|
| 6 | 0 | 14330 | |
||||
|
| 6 | 1 | 57320 | |
||||
|
| 6 | 2 | 85980 | |
||||
|
| 7 | 0 | 3508 | |
||||
@ -0,0 +1,188 @@ |
|||||
|
## 华容道布局 |
||||
|
|
||||
|
### 合法布局定义 |
||||
|
|
||||
|
+ 棋盘大小为4 x 5 |
||||
|
|
||||
|
+ 棋子为2 x 2，2 x 1（1 x 2），1 x 1三种 |
||||
|
|
||||
|
+ 棋子间不能重叠，且至少存在两个空格 |
||||
|
|
||||
|
+ 有且仅有一个2 x 2块，其他类型不限定 |
||||
|
|
||||
|
*（合法的布局必须满足以上四点）* |
||||
|
|
||||
|
合法华容道布局共有29334498种 |
||||
|
|
||||
|
|
||||
|
### 标准情况与非标准情况 |
||||
|
|
||||
|
标准布局：存在5个2 x 1（或1 x 2）和4个1 x 1棋子的合法华容道布局（363480种） |
||||
|
|
||||
|
非标准布局：除标准布局外的全部合法华容道布局（28971018种） |
||||
|
|
||||
|
|
||||
|
### 合法布局举例： |
||||
|
|
||||
|
<img src="/images/legal_1+2.png" alt="legal_1+2" style="zoom: 40%;" /> |
||||
|
|
||||
|
<img src="/images/legal_3+4.png" alt="legal_3+4" style="zoom: 40%;" /> |
||||
|
|
||||
|
|
||||
|
### 非法布局举例： |
||||
|
|
||||
|
<img src="/images/illegal_1+2.png" alt="illegal_1+2" style="zoom: 40%;" /> |
||||
|
|
||||
|
<img src="/images/illegal_3+4.png" alt="illegal_3+4" style="zoom: 40%;" /> |
||||
|
|
||||
|
**错误原因：** |
||||
|
|
||||
|
+ 缺少2 x 2块 |
||||
|
|
||||
|
+ 仅有一个空格 |
||||
|
|
||||
|
+ 存在两个2 x 2块 |
||||
|
|
||||
|
+ 存在3 x 1块 |
||||
|
|
||||
|
|
||||
|
|
||||
|
## 布局间的关系 |
||||
|
|
||||
|
+ 移动原则：棋子只能平行移动，不能进行旋转； |
||||
|
|
||||
|
+ **一步**：某一棋子做任意次移动的过程（或结果）； |
||||
|
|
||||
|
+ **子布局**：某一布局通过一步移动可以得到的布局称为子布局； |
||||
|
|
||||
|
+ **相邻布局**：两布局互为对方子布局时，两者为相邻布局； |
||||
|
|
||||
|
性质：若布局A是布局B的子布局，则同时必有布局B是布局A的子布局； |
||||
|
|
||||
|
|
||||
|
### 步的举例 |
||||
|
<img src="/images/step_exp_1.png" alt="step_exp_1" style="zoom: 40%;" /> |
||||
|
|
||||
|
<img src="/images/step_exp_2.png" alt="step_exp_2" style="zoom:40%;" /> |
||||
|
|
||||
|
<img src="/images/step_exp_3.png" alt="step_exp_3" style="zoom:40%;" /> |
||||
|
|
||||
|
|
||||
|
|
||||
|
## 分类 |
||||
|
|
||||
|
### 布局id |
||||
|
|
||||
|
合法布局共有29334498种，将它们从小到大排列，进而得到唯一的id(0 ~ 29334497)； |
||||
|
|
||||
|
|
||||
|
### 摆列方式分类 |
||||
|
|
||||
|
**2 x 1 与 1 x 2的数量** |
||||
|
|
||||
|
将2 x 1（1 x 2）的数量称为jiang_num； |
||||
|
|
||||
|
由于至少存在两个空格，于是有`0 ≤ jiang_num ≤ 7` |
||||
|
|
||||
|
可分为七种情况： |
||||
|
|
||||
|
| jiang_num | COUNT | |
||||
|
| :-: | :-: | |
||||
|
| 0 | 786228 | |
||||
|
| 1 | 4190464 | |
||||
|
| 2 | 8729454 | |
||||
|
| 3 | 9090662 | |
||||
|
| 4 | 4995328 | |
||||
|
| 5 | 1381224 | |
||||
|
| 6 | 157630 | |
||||
|
| 7 | 3508 | |
||||
|
|
||||
|
|
||||
|
**1 x 1块的数量** |
||||
|
|
||||
|
将1 x 1的数量称为bing_num，结合jiang_num进行分类； |
||||
|
|
||||
|
由于至少存在两个空格，于是有`0 ≤ bing_num ≤ (14 - jiang_num * 2)` |
||||
|
|
||||
|
据此可分为64种情况： |
||||
|
|
||||
|
[64种分类的元素数量](./jiang_bing_count.md) |
||||
|
|
||||
|
|
||||
|
**2 x 1与1 x 2块的方向** |
||||
|
|
||||
|
进而，将2 x 1块的数量称为style_num，则1 x 2块的数量为(jiang_num - style_num)，于是有`0 ≤ style_num ≤ jiang_num` |
||||
|
|
||||
|
此时可分出203种情况： |
||||
|
|
||||
|
[203种分类的元素数量](./style_count.md) |
||||
|
|
||||
|
（注意不存在 *jiang_num-bing_num-style_num = 7-0-0* ，即七竖将的情况） |
||||
|
|
||||
|
|
||||
|
### 群 |
||||
|
|
||||
|
定义：群是有限个不同布局的集合，该集合中全部布局都可以由其中任一布局经过有限次移动得到； |
||||
|
|
||||
|
性质1：任意一个布局无论如何移动，其结果仍在该群内； |
||||
|
|
||||
|
性质2：只需群中任意一个布局，即可复原出群中的所有元素； |
||||
|
|
||||
|
性质3：群是封闭的，群中所有元素无序且互异，同时构成一个关系网； |
||||
|
|
||||
|
统计：29334498种布局可拆分出25422个群，其中元素数量存在两极分化现象；一般情况下，布局的空格增加，其所在群的数量会急剧上升； |
||||
|
|
||||
|
[群的数量统计](./group_num.md) |
||||
|
|
||||
|
|
||||
|
### 按群继续分类 |
||||
|
|
||||
|
对于一个特定的 *jiang_num-bing_num-style_num* 分组，可拆分出n个群；将分出的群按元素数量从大到小排列，若存在元素数量相同的群，则取其中的最小元素排序；对这些群进行编号得0 ~ (n - 1) 共n个群，编号记为group_num； |
||||
|
|
||||
|
因而对于某一群，存在一个唯一编号 *jiang_num-bing_num-style_num-group_num* ；由于群中的元素个数是确定的，将其中的元素按编码从小到大排列，其中的元素可得唯一编号group_index； |
||||
|
|
||||
|
所以，对于任意布局，可得唯一编号 *jiang_num-bing_num-style_num-group_num-group_index*； |
||||
|
|
||||
|
[群包含的元素数量统计](./group_size.md) |
||||
|
|
||||
|
|
||||
|
|
||||
|
## 层级关系 |
||||
|
|
||||
|
### 基本定义 |
||||
|
|
||||
|
**最少步数**：当布局A和布局B处于同一个群时，从布局A移动到B所需最少的步数，该数值存在且是确定的； |
||||
|
|
||||
|
性质：布局A到B的最少步数与布局B到A的最少步数必定相同； |
||||
|
|
||||
|
**最短路径**：从布局A到布局B，所有满足最少步数的路径（最少路径可能不止一条）； |
||||
|
|
||||
|
**最远步数**：布局A到它所在群中任一布局均存在一最少步数，其中最大的最少步数称为最远步数； |
||||
|
|
||||
|
**最远布局**：布局A到布局B的最少步数为最远步数时，称布局B为布局A的最远布局（一般情况下不止一个）； |
||||
|
|
||||
|
（标准华容道中不存在最远布局退化的情况，即最远步数至少为1） |
||||
|
|
||||
|
**最少步解**：布局A所在群中存在一布局S，满足2 x 2方块在棋盘的最下方中间（即2 x 2块所在位置编号为13，亦或编码以D开头），记A到S的最少步数为n，此时不存在其他任何满足以上条件的S‘使得最少步数小于n，则称S为布局A的最少步解，n为最少步解的步数（亦简称为最少步）； |
||||
|
|
||||
|
**解**：布局A所在群中存在一布局S满足2 x 2方块在棋盘的最下方中间，且有A到S的任意最短路径中均不存在符合2 x 2方块在棋盘的最下方中间的布局，此时称S为布局A的解； |
||||
|
|
||||
|
性质：布局的解可能是空集；最少步解属于解的子集（特定条件下两者可以相同）； |
||||
|
|
||||
|
|
||||
|
### 层模型 |
||||
|
|
||||
|
表述：存在一起始布局A，从它开始衍生出有限个布局，每个布局抽象为一个节点，同时称A为根节点；由于任一由A衍生出布局到根节点存在一个确定的最少步数，将其称之为到根节点的距离；将所有距离相同的布局称为一个层，层内元素无序且互异，根节点所在层称为第0层，之后依次排列可得有限个层； |
||||
|
|
||||
|
记排列的最后一层为第n层，则共有n + 1个层（包括第0层）； |
||||
|
|
||||
|
性质1：所有层中的元素集合即为根节点所在的群； |
||||
|
|
||||
|
性质2：某一节点所在层数为其到根节点的最少步数； |
||||
|
|
||||
|
性质3：若最后一层为第n层，则最远步数为n，且第n层的所有元素均为最远布局； |
||||
|
|
||||
|
|
||||
|
### 网模型 |
||||
|
|
||||
|
未完待续... |
||||
@ -0,0 +1,206 @@ |
|||||
|
## 编码 |
||||
|
|
||||
|
合法华容道均有编码，长度9位，每一位是单个16进制数（0\~9与A\~F）；同一布局只能有唯一编码，同一编码亦对应唯一布局，即编码与布局一一对应； |
||||
|
|
||||
|
**位置编号** |
||||
|
|
||||
|
<img src="/images/address.png" alt="address" style="zoom: 40%;" /> |
||||
|
|
||||
|
2 x 2棋子的左上角在棋盘中的位置编号有12种情况，对应编码分别为：0、1、2、4、5、6、8、9、A(10)、C(12)、D(13)、E(14)，将其置于编码第一位；剩余8位十六进制位储存其他棋子信息。 |
||||
|
|
||||
|
其余棋子（空格此时暂时视为棋子）按从左到右，从上到下的顺序排列（取左上角排序） |
||||
|
|
||||
|
它们对应的代号（二进制）如下： |
||||
|
|
||||
|
| 棋子类型 | 代号 | |
||||
|
| :-: | :-: | |
||||
|
| 空格 | 00 | |
||||
|
| 2 x 1 | 01 | |
||||
|
| 1 x 2 | 10 | |
||||
|
| 1 x 1 | 11 | |
||||
|
|
||||
|
十六进制可按位转为二进制，对应关系如下： |
||||
|
|
||||
|
| 十六进制 | 二进制 | 十进制 | |
||||
|
| :-: | :-: | :-: | |
||||
|
| 0 | 0000 | 0 | |
||||
|
| 1 | 0001 | 1 | |
||||
|
| 2 | 0010 | 2 | |
||||
|
| 3 | 0011 | 3 | |
||||
|
| 4 | 0100 | 4 | |
||||
|
| 5 | 0101 | 5 | |
||||
|
| 6 | 0110 | 6 | |
||||
|
| 7 | 0111 | 7 | |
||||
|
| 8 | 1000 | 8 | |
||||
|
| 9 | 1001 | 9 | |
||||
|
| A | 1010 | 10 | |
||||
|
| B | 1011 | 11 | |
||||
|
| C | 1100 | 12 | |
||||
|
| D | 1101 | 13 | |
||||
|
| E | 1110 | 14 | |
||||
|
| F | 1111 | 15 | |
||||
|
|
||||
|
8个十六进制位相当于32个二进制位，由于每个棋子占用2个二进制位，因此最多储存16个棋子信息；将其依次填入，若有空余则补0填；按此操作即可将布局转化为编码，规定编码最后的0可以省略。 |
||||
|
|
||||
|
## 编码举例 |
||||
|
|
||||
|
**例1：** |
||||
|
|
||||
|
<img src="/images/code_exp_1.png" alt="exp-1A9BF0C00" style="zoom: 60%;" /> |
||||
|
|
||||
|
<table style="text-align: center"> |
||||
|
<tr> |
||||
|
<td>2 x 2</td> |
||||
|
<td>1</td> |
||||
|
<td>2</td> |
||||
|
<td>3</td> |
||||
|
<td>4</td> |
||||
|
<td>5</td> |
||||
|
<td>6</td> |
||||
|
<td>7</td> |
||||
|
<td>8</td> |
||||
|
<td>9</td> |
||||
|
<td>10</td> |
||||
|
<td>11</td> |
||||
|
<td colspan="5">补0</td> |
||||
|
</tr> |
||||
|
<tr> |
||||
|
<td>0001</td> |
||||
|
<td>10</td> |
||||
|
<td>10</td> |
||||
|
<td>10</td> |
||||
|
<td>01</td> |
||||
|
<td>10</td> |
||||
|
<td>11</td> |
||||
|
<td>11</td> |
||||
|
<td>11</td> |
||||
|
<td>00</td> |
||||
|
<td>00</td> |
||||
|
<td>11</td> |
||||
|
<td>00</td> |
||||
|
<td>00</td> |
||||
|
<td>00</td> |
||||
|
<td>00</td> |
||||
|
<td>00</td> |
||||
|
</tr> |
||||
|
<tr> |
||||
|
<td><b>1</b></td> |
||||
|
<td colspan="2"><b>A</b></td> |
||||
|
<td colspan="2"><b>9</b></td> |
||||
|
<td colspan="2"><b>B</b></td> |
||||
|
<td colspan="2"><b>F</b></td> |
||||
|
<td colspan="2"><b>0</b></td> |
||||
|
<td colspan="2"><b>C</b></td> |
||||
|
<td colspan="2"><b>0</b></td> |
||||
|
<td colspan="2"><b>0</b></td> |
||||
|
</tr> |
||||
|
</table> |
||||
|
因此，布局编码为<b>1A9BF0C00</b>，可简写为<b>1A9BF0C</b> |
||||
|
|
||||
|
**例2：** |
||||
|
|
||||
|
<img src="/images/code_exp_2.png" alt="exp-4FEA13400" style="zoom: 60%;" /> |
||||
|
|
||||
|
<table style="text-align: center"> |
||||
|
<tr> |
||||
|
<td>2 x 2</td> |
||||
|
<td>1</td> |
||||
|
<td>2</td> |
||||
|
<td>3</td> |
||||
|
<td>4</td> |
||||
|
<td>5</td> |
||||
|
<td>6</td> |
||||
|
<td>7</td> |
||||
|
<td>8</td> |
||||
|
<td>9</td> |
||||
|
<td>10</td> |
||||
|
<td>11</td> |
||||
|
<td colspan="5">补0</td> |
||||
|
</tr> |
||||
|
<tr> |
||||
|
<td>0100</td> |
||||
|
<td>11</td> |
||||
|
<td>11</td> |
||||
|
<td>11</td> |
||||
|
<td>10</td> |
||||
|
<td>10</td> |
||||
|
<td>10</td> |
||||
|
<td>00</td> |
||||
|
<td>01</td> |
||||
|
<td>00</td> |
||||
|
<td>11</td> |
||||
|
<td>01</td> |
||||
|
<td>00</td> |
||||
|
<td>00</td> |
||||
|
<td>00</td> |
||||
|
<td>00</td> |
||||
|
<td>00</td> |
||||
|
</tr> |
||||
|
<tr> |
||||
|
<td><b>4</b></td> |
||||
|
<td colspan="2"><b>F</b></td> |
||||
|
<td colspan="2"><b>E</b></td> |
||||
|
<td colspan="2"><b>A</b></td> |
||||
|
<td colspan="2"><b>1</b></td> |
||||
|
<td colspan="2"><b>3</b></td> |
||||
|
<td colspan="2"><b>4</b></td> |
||||
|
<td colspan="2"><b>0</b></td> |
||||
|
<td colspan="2"><b>0</b></td> |
||||
|
</tr> |
||||
|
</table> |
||||
|
因此，布局编码为<b>4FEA13400</b>，可简写为<b>4FEA134</b> |
||||
|
|
||||
|
**例3：** |
||||
|
|
||||
|
<img src="/images/code_exp_3.png" alt="exp-5DC02F800" style="zoom: 60%;" /> |
||||
|
|
||||
|
<table style="text-align: center"> |
||||
|
<tr> |
||||
|
<td>2 x 2</td> |
||||
|
<td>1</td> |
||||
|
<td>2</td> |
||||
|
<td>3</td> |
||||
|
<td>4</td> |
||||
|
<td>5</td> |
||||
|
<td>6</td> |
||||
|
<td>7</td> |
||||
|
<td>8</td> |
||||
|
<td>9</td> |
||||
|
<td>10</td> |
||||
|
<td>11</td> |
||||
|
<td>12</td> |
||||
|
<td>13</td> |
||||
|
<td colspan="3">补0</td> |
||||
|
</tr> |
||||
|
<tr> |
||||
|
<td>0101</td> |
||||
|
<td>11</td> |
||||
|
<td>01</td> |
||||
|
<td>11</td> |
||||
|
<td>00</td> |
||||
|
<td>00</td> |
||||
|
<td>00</td> |
||||
|
<td>00</td> |
||||
|
<td>10</td> |
||||
|
<td>11</td> |
||||
|
<td>11</td> |
||||
|
<td>10</td> |
||||
|
<td>00</td> |
||||
|
<td>00</td> |
||||
|
<td>00</td> |
||||
|
<td>00</td> |
||||
|
<td>00</td> |
||||
|
</tr> |
||||
|
<tr> |
||||
|
<td><b>5</b></td> |
||||
|
<td colspan="2"><b>D</b></td> |
||||
|
<td colspan="2"><b>C</b></td> |
||||
|
<td colspan="2"><b>0</b></td> |
||||
|
<td colspan="2"><b>2</b></td> |
||||
|
<td colspan="2"><b>F</b></td> |
||||
|
<td colspan="2"><b>8</b></td> |
||||
|
<td colspan="2"><b>0</b></td> |
||||
|
<td colspan="2"><b>0</b></td> |
||||
|
</tr> |
||||
|
</table> |
||||
|
因此，布局编码为<b>5DC02F800</b>，可简写为<b>5DC02F8</b> |
||||
@ -0,0 +1,121 @@ |
|||||
|
## 命令行参数 |
||||
|
|
||||
|
+ show命令：根据编码输出实际布局样式 |
||||
|
```bash |
||||
|
--show <code> [square_width] |
||||
|
Purpose: Visualize the <code> |
||||
|
exp: ./engine --show 1A9BF0C00 |
||||
|
./engine --show 1A9BF0C00 4 |
||||
|
``` |
||||
|
|
||||
|
+ cal命令：计算输入布局的最少步解法 |
||||
|
```bash |
||||
|
--cal <code> [file_name] |
||||
|
Purpose: Find the minimum step solution of <code> |
||||
|
exp: ./engine --cal 1A9BF0C00 |
||||
|
./engine --cal 1A9BF0C00 demo.txt |
||||
|
``` |
||||
|
|
||||
|
+ cal-target命令：计算两布局之间的最短路径 |
||||
|
```bash |
||||
|
--cal-target <code> <target> [file_name] |
||||
|
Purpose: Find the shortest path from <code> to <target> |
||||
|
exp: ./engine --cal-target 4FEA13400 43EA73400 |
||||
|
./engine --cal-target 4FEA13400 43EA73400 demo.txt |
||||
|
``` |
||||
|
|
||||
|
+ group命令：计算起始布局的所有衍生情况，即计算其所在群的全部元素 |
||||
|
```bash |
||||
|
--group <code> [file_name] |
||||
|
Purpose: Find all elements of the group where <code> located |
||||
|
exp: ./engine --group 4FEA13400 |
||||
|
./engine --group 4FEA13400 demo.txt |
||||
|
``` |
||||
|
|
||||
|
+ analy命令：分析布局的具体参数，包括层级结构，层间链接，解与最少步解，最远布局等 |
||||
|
```bash |
||||
|
--analy <code> [file_name] |
||||
|
Purpose: Detailed analysis of the <code> |
||||
|
exp: ./engine --analy 1A9BF0C00 |
||||
|
./engine --analy 1A9BF0C00 demo.txt |
||||
|
``` |
||||
|
|
||||
|
+ analy-quiet命令：同analy命令，但不输出计算过程 |
||||
|
```bash |
||||
|
--analy-quiet <code> <file_name> |
||||
|
Purpose: The same function as --analy, but doesn't show the specific process |
||||
|
exp: ./engine --analy-quiet 1A9BF0C00 demo.txt |
||||
|
``` |
||||
|
|
||||
|
+ analy-group命令：分析`code`衍生出的群中所有元素的具体参数，并输出到`最远布局信息`和`解的信息`两张csv表格中 |
||||
|
```bash |
||||
|
--analy-group <code> <file_name_farthest> <file_name_solution> |
||||
|
<file_name_farthest>: As the output file of "farthest" |
||||
|
<file_name_solution>: As the output file of "solution" |
||||
|
Purpose: Analyze the whole group where <code> located |
||||
|
exp: ./engine --analy-group 1A9BF0C00 farthest.csv solution.csv |
||||
|
``` |
||||
|
|
||||
|
+ analy-group-integral命令：同analy-group命令，但`解的信息`中将会输出全部解的编码及步数 |
||||
|
```bash |
||||
|
--analy-group-integral <code> <file_name_farthest> <file_name_farthest> |
||||
|
Purpose: The same function as --analy-group, but all solution case will be output |
||||
|
exp: ./engine --analy-group-integral 1A9BF0C00 farthest.csv solution.csv |
||||
|
``` |
||||
|
|
||||
|
+ analy-multi-group命令：多群组同时分析，相当于多次执行analy-group命令，结果合并输出到`最远布局信息`和`解的信息`两张csv表格中 |
||||
|
```bash |
||||
|
--analy-multi-group <input_file_name> <file_name_farthest> <file_name_farthest> |
||||
|
<input_file_name>: As the input file of seeds |
||||
|
<file_name_farthest>: As the output file of "farthest" |
||||
|
<file_name_farthest>: As the output file of "solution" |
||||
|
Purpose: Analyze the whole group where each seed located |
||||
|
exp: ./engine --analy-multi-group 5-4-0.txt farthest.csv solution.csv |
||||
|
``` |
||||
|
|
||||
|
+ analy-multi-group-integral命令：同analy-multi-group命令，但`解的信息`中将会输出全部解的编码及步数 |
||||
|
```bash |
||||
|
--analy-multi-group-integral <input_file_name> <file_name_farthest> <file_name_farthest> |
||||
|
Purpose: The same function as --analy-multi-group, but all solution case will be output |
||||
|
exp: ./engine --analy-multi-group-integral 5-4-0.txt farthest.csv solution.csv |
||||
|
``` |
||||
|
|
||||
|
+ all命令：找到所有可能的布局，同时得到其分类情况及群组关系，计算结果会输出到All_Case.txt（所有布局的编码），main.csv（所有布局的编码及其分类），\*-\*-\*.txt（各群组的第一个子布局集合） |
||||
|
```bash |
||||
|
--all |
||||
|
Purpose: Find all the cases of klotski with detail |
||||
|
exp: ./engine --all |
||||
|
``` |
||||
|
|
||||
|
+ all-code命令：简化版的all命令，仅输出全部布局的编码 |
||||
|
```bash |
||||
|
--all-code <file_name> |
||||
|
Purpose: Find all the code of klotski |
||||
|
exp: ./engine --all-code All_Case.txt |
||||
|
``` |
||||
|
|
||||
|
+ help命令：显示所有命令的使用方法 |
||||
|
```bash |
||||
|
--help |
||||
|
Purpose: Display instructions for use |
||||
|
exp: ./engine --help |
||||
|
``` |
||||
|
|
||||
|
## 编译 |
||||
|
|
||||
|
+ Windows下，要求计算机有mingw环境或其他C/C++编译器 |
||||
|
|
||||
|
+ Linux下，要求计算机有gcc编译器 |
||||
|
|
||||
|
+ Android下，可以在termux中安装clang编译器 |
||||
|
|
||||
|
使用make进行编译 |
||||
|
```bash |
||||
|
cd ./scr/engine |
||||
|
make |
||||
|
``` |
||||
|
|
||||
|
使用g++编译 |
||||
|
```bash |
||||
|
g++ -O3 ./src/engine/*.cpp -o ./engine |
||||
|
``` |
||||
@ -0,0 +1 @@ |
|||||
|
未完待续... |
||||
File diff suppressed because it is too large
@ -0,0 +1,25 @@ |
|||||
|
Option Explicit |
||||
|
dim fso, file |
||||
|
dim cmd, dat |
||||
|
dim jiang_num, bing_num, style_num |
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|
|
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set fso = CreateObject("Scripting.FileSystemObject") |
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|
If not fso.folderExists("../build/cal_sh") Then fso.CreateFolder("../build/cal_sh") |
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|
|
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|
for jiang_num = 0 to 7 |
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for bing_num = 0 to 14 - jiang_num * 2 |
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set file = fso.CreateTextFile("../build/cal_sh/" & jiang_num & "-" & bing_num & ".sh", true) |
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cmd = "" |
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for style_num = 0 to jiang_num |
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if jiang_num = 7 and bing_num = 0 and style_num = 0 then style_num = 1 |
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dat = jiang_num & "-" & bing_num & "-" & style_num |
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cmd = cmd & "../engine --analy-multi-group ../seed/" & dat & ".txt " |
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cmd = cmd & "../farthest/farthest_" & dat & ".csv ../solution/solution_" & dat & ".csv" & chr(10) |
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next |
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|
cmd = cmd & "touch " & jiang_num & "-" & bing_num & "_OK" |
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|
file.Write(cmd) |
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|
file.Close() |
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|
next |
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|
next |
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|
|
||||
|
msgbox "OK" |
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@ -0,0 +1,74 @@ |
|||||
|
' 使用以下SQL语句在main.csv导入的表中提取数据到文件 |
||||
|
' ------------------------------------------------------------------ |
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|
' SELECT jiang_num,bing_num,style_num,group_num,COUNT(*) FROM main |
||||
|
' GROUP BY jiang_num,bing_num,style_num,group_num |
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|
' ORDER BY jiang_num,bing_num,style_num,group_num |
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|
' INTO OUTFILE '(Path)/./res/group_size.data'; |
||||
|
' ------------------------------------------------------------------ |
||||
|
' |
||||
|
Option Explicit ' 强制要求声明变量 |
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|
dim fso, input, output |
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|
dim range, dat, num |
||||
|
dim start_group_num |
||||
|
dim jiang_num, bing_num, style_num, group_num, group_count |
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|
dim last_jiang_num, last_bing_num, last_style_num, last_group_num, last_group_count |
||||
|
dim input_file_name, output_file_name |
||||
|
|
||||
|
input_file_name = "../res/group_size.data" ' 数据库导出内容的文件名 |
||||
|
output_file_name = "../docs/group_size.md" ' 整理后输出的的文件名 |
||||
|
call init() ' 初始化数据并创建输出文件 |
||||
|
call sort() ' |
||||
|
msgbox "OK" |
||||
|
|
||||
|
function sort() |
||||
|
while input.atEndOfStream <> true ' 循环读到文件尾 |
||||
|
dat = input.ReadLine() ' 读入一行新数据 |
||||
|
range = split(dat, chr(9)) ' 根据tab进行切割 |
||||
|
jiang_num = range(0) ' 记录切割结果 |
||||
|
bing_num = range(1) |
||||
|
style_num = range(2) |
||||
|
group_num = range(3) |
||||
|
group_count = range(4) |
||||
|
if jiang_num = last_jiang_num and bing_num = last_bing_num and style_num = last_style_num and group_count = last_group_count then |
||||
|
last_group_num = group_num ' 备份group_num |
||||
|
else ' 如果另起一类 |
||||
|
if num <> 0 then call output_data(last_jiang_num, last_bing_num, last_style_num, start_group_num, last_group_num, last_group_count) ' 去除第一个空数据 |
||||
|
last_jiang_num = jiang_num ' 记录找到的新一类数据 |
||||
|
last_bing_num = bing_num |
||||
|
last_style_num = style_num |
||||
|
last_group_num = group_num |
||||
|
last_group_count = group_count |
||||
|
start_group_num = group_num |
||||
|
end if |
||||
|
num = num + 1 |
||||
|
wend |
||||
|
call output_data(jiang_num, bing_num, style_num, start_group_num, last_group_num, group_count) ' 补全最后一类 |
||||
|
end function |
||||
|
|
||||
|
function output_data(str_1, str_2, str_3, str_4_1, str_4_2, str_5) |
||||
|
dat = "|" & chr(9) & str_1 & chr(9) & "|" & chr(9) & str_2 |
||||
|
dat = dat & chr(9) & "|" & chr(9) & str_3 & chr(9) & "|" & chr(9) |
||||
|
if str_4_1 = str_4_2 then ' 如果该类中仅有一行数据 |
||||
|
dat = dat & str_4_1 |
||||
|
else |
||||
|
dat = dat & str_4_1 & " \~ " & str_4_2 |
||||
|
end if |
||||
|
dat = dat & chr(9) & "|" & chr(9) & str_5 & chr(9) & "|" |
||||
|
output.WriteLine(dat) ' 写入文件 |
||||
|
end function |
||||
|
|
||||
|
function init() |
||||
|
set fso = CreateObject("Scripting.FileSystemObject") |
||||
|
set input = fso.OpenTextFile(input_file_name, 1, false) ' 打开文件进行读取 |
||||
|
set output = fso.CreateTextFile(output_file_name, true) ' 打开文件进行写入 |
||||
|
|
||||
|
output.WriteLine("| jiang_num | bing_num | style_num | group_num | group_size |") ' 写入markdown表格头 |
||||
|
output.WriteLine("| :-: | :-: | :-: | :-: | :-: |") |
||||
|
|
||||
|
last_jiang_num = "" ' 初始化 |
||||
|
last_bing_num = "" |
||||
|
last_style_num = "" |
||||
|
last_group_num = "" |
||||
|
last_group_count = "" |
||||
|
start_group_num = "0" |
||||
|
end function |
||||
Loading…
Reference in new issue