From 95c2f4d52be4ff434435772aca134a177054e080 Mon Sep 17 00:00:00 2001
From: golitter_wsl2 <1981971524@qq.com>
Date: Wed, 1 May 2024 22:27:36 +0800
Subject: [PATCH] =?UTF-8?q?add=20=E5=BA=B7=E6=89=98=E5=B1=95=E5=BC=80?=
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---
 CMakeLists.txt             |  2 +-
 README.md                  | 23 +++++++++++++++++++++++
 auto_build.sh              | 19 +++++++++++++++++++
 include/cantor_expansion.h | 22 ++++++++++++++++++++++
 main.cpp                   |  6 +++++-
 src/cantor_expansion.cpp   | 27 +++++++++++++++++++++++++++
 6 files changed, 97 insertions(+), 2 deletions(-)
 create mode 100644 auto_build.sh
 create mode 100644 include/cantor_expansion.h
 create mode 100644 src/cantor_expansion.cpp

diff --git a/CMakeLists.txt b/CMakeLists.txt
index f6b7a4f..416565c 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -5,7 +5,7 @@ include(CTest)
 enable_testing()
 include_directories(include)
 
-add_executable(EightPuzzle-AStar-IDDFS main.cpp src/A_star.cpp)
+add_executable(EightPuzzle-AStar-IDDFS main.cpp src/A_star.cpp src/cantor_expansion.cpp)
 
 set(CPACK_PROJECT_NAME ${PROJECT_NAME})
 set(CPACK_PROJECT_VERSION ${PROJECT_VERSION})
diff --git a/README.md b/README.md
index cd5ddca..6b537ad 100644
--- a/README.md
+++ b/README.md
@@ -1,3 +1,26 @@
 # EightPuzzle-AStar-IDDFS
+
 人工智能大作业：基于迭代加深的A*算法求解八数码问题
 
+
+
+基于迭代加深的A*算法（IA\*)本质是对dfs算法剪枝。
+
+剪枝：
+
+- 最优性剪枝：曼哈顿距离剪枝
+- 记忆化剪枝：康托展开优化的哈希映射
+
+评估函数：当前深度 + 到达目标状态所需的最小步骤
+
+### 康托展开
+
+
+
+
+
+[【数论系列】 康托展开-CSDN博客](https://blog.csdn.net/qq_40772692/article/details/80549303?ops_request_misc=&request_id=&biz_id=102&utm_term=康托展开&utm_medium=distribute.pc_search_result.none-task-blog-2~all~sobaiduweb~default-0-80549303.nonecase&spm=1018.2226.3001.4187)
+
+[C++ 八数码问题理解 `IDA*` 算法原则：及时止损，缘尽即散-CSDN博客](https://blog.csdn.net/y6123236/article/details/136210573)
+
+[康托展开 - OI Wiki (oi-wiki.org)](https://oi-wiki.org/math/combinatorics/cantor/)
\ No newline at end of file
diff --git a/auto_build.sh b/auto_build.sh
new file mode 100644
index 0000000..e6cd60d
--- /dev/null
+++ b/auto_build.sh
@@ -0,0 +1,19 @@
+#!/bin/bash
+
+# 任何命令返回非零退出码时立即停止执行，并输出相应的错误信息
+set -e
+
+mkdir -p build
+cd build
+
+# 生成MakeFile文件
+cmake ..
+
+# 构建可执行文件
+make -j8
+
+# 执行可执行文件
+./EightPuzzle-AStar-IDDFS
+
+# 退回到原来目录下
+cd ..
\ No newline at end of file
diff --git a/include/cantor_expansion.h b/include/cantor_expansion.h
new file mode 100644
index 0000000..92dedd8
--- /dev/null
+++ b/include/cantor_expansion.h
@@ -0,0 +1,22 @@
+#include <iostream>
+#include <vector>
+
+namespace Cantor {
+
+typedef long long LL;
+
+const int MaxSize = 12;
+// ***** 由于八数码问题是小于等于9个元素的，因此这里固定了n的大小
+const int n = 10; // 0~9 共十个数字
+
+/**
+* @idx: 元素在数组中的下标
+* @count: 在数组后面有多少个比当前元素小的元素个数
+*/
+LL get_fact(int idx, int count);
+
+/**
+* @vec: vec数组
+*/
+LL cantor_value(std::vector<int> vec);
+}
\ No newline at end of file
diff --git a/main.cpp b/main.cpp
index f571c3b..6e0a8d5 100644
--- a/main.cpp
+++ b/main.cpp
@@ -1,5 +1,9 @@
 #include <iostream>
-
+#include "include/cantor_expansion.h"
+void test_Cantor() {
+    std::cout<<Cantor::get_fact(3, 4)<<std::endl;
+}
 int main(int, char**){
     std::cout << "Hello, from EightPuzzle-AStar-IDDFS!\n";
+    test_Cantor();
 }
diff --git a/src/cantor_expansion.cpp b/src/cantor_expansion.cpp
new file mode 100644
index 0000000..55cf8e8
--- /dev/null
+++ b/src/cantor_expansion.cpp
@@ -0,0 +1,27 @@
+#include "../include/cantor_expansion.h"
+
+namespace Cantor {
+
+LL fact[MaxSize] = {1,1,2,6,24,120,720,5040,40320,362880}; // 定义0~9的阶乘表
+
+LL get_fact(int idx, int count) {
+    if(n - idx - 1 < 0) {
+        std::cerr<<"ERROR!!!"<<std::endl;
+        exit(0);
+    }
+    return fact[n - idx - 1] * count;
+}
+
+LL cantor_value(std::vector<int> vec) {
+    LL sum = 0; //记录总的在s之前数目
+    int len = vec.size();
+    for(int i = 0; i < len; ++i) {
+        int cnt = 0;
+        for(int j = i + 1; j < len; ++j) {
+            if(vec[j] < vec[i]) ++cnt;
+        }
+        sum += get_fact(i, cnt);
+    }
+    return sum + 1;
+}
+}
\ No newline at end of file