done: homework3

homework3/.idea/MarsCodeWorkspaceAppSettings.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="com.codeverse.userSettings.MarscodeWorkspaceAppSettingsState">
+    <option name="ckgOperationStatus" value="SUCCESS" />
+  </component>
+</project>

homework3/.idea/homework3.iml

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+<?xml version="1.0" encoding="UTF-8"?>
+<module type="PYTHON_MODULE" version="4">
+  <component name="NewModuleRootManager">
+    <content url="file://$MODULE_DIR$" />
+    <orderEntry type="jdk" jdkName="ai-homework" jdkType="Python SDK" />
+    <orderEntry type="sourceFolder" forTests="false" />
+  </component>
+</module>

homework3/.idea/inspectionProfiles/profiles_settings.xml

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+<component name="InspectionProjectProfileManager">
+  <settings>
+    <option name="USE_PROJECT_PROFILE" value="false" />
+    <version value="1.0" />
+  </settings>
+</component>

homework3/.idea/misc.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="Black">
+    <option name="sdkName" value="ai-homework" />
+  </component>
+</project>

homework3/.idea/modules.xml

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+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="ProjectModuleManager">
+    <modules>
+      <module fileurl="file://$PROJECT_DIR$/.idea/homework3.iml" filepath="$PROJECT_DIR$/.idea/homework3.iml" />
+    </modules>
+  </component>
+</project>

homework3/.idea/vcs.xml

@@ -1,4 +1,6 @@
 <?xml version="1.0" encoding="UTF-8"?>
 <project version="4">
-  <component name="VcsDirectoryMappings" defaultProject="true" />
+  <component name="VcsDirectoryMappings">
+    <mapping directory="$PROJECT_DIR$/.." vcs="Git" />
+  </component>
 </project>

homework3/main.py

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+import numpy as np
+
+class State:
+    def __init__(self, state, directionFlag=None, parent=None, f=0):
+        """八数码问题状态类
+        Args:
+            state: 3x3 numpy数组，表示当前状态
+            directionFlag: 禁止的移动方向（用于防止走回头路）
+            parent: 父状态节点
+            f: 评估函数值（f = g + h）
+        """
+        self.state = state  # 当前状态矩阵
+        self.direction = ['up', 'down', 'right', 'left']  # 可移动方向
+        if directionFlag:  # 移除来源方向防止回退
+            self.direction.remove(directionFlag)
+        self.parent = parent  # 父节点指针
+        self.f = f  # 评估函数值
+
+    def getDirection(self):
+        """获取当前允许的移动方向列表"""
+        return self.direction
+
+    def setF(self, f):
+        """设置评估函数值"""
+        self.f = f
+        return
+
+    # 打印结果
+    def showInfo(self):
+        """打印当前状态矩阵"""
+        for i in range(len(self.state)):
+            for j in range(len(self.state)):
+                print(self.state[i, j], end='  ')
+            print("\n")
+        print('->')
+        return
+
+    # 获取0点
+    def getZeroPos(self):
+        """获取空白格（0）的位置坐标
+        Returns:
+            tuple: 包含空白格的行列坐标(x, y)
+        """
+        postion = np.where(self.state == 0)
+        return postion
+
+    # 曼哈顿距离  f = g + h，g=1，如果用宽度优先的评估函数可以不调用该函数
+    def getFunctionValue(self):
+        """计算曼哈顿距离评估值
+        Returns:
+            int: 当前状态到目标状态的评估值（f = 移动步数 + 启发函数值）
+        """
+        cur_node = self.state.copy()
+        fin_node = self.answer.copy()
+        dist = 0  # 曼哈顿距离总和
+        N = len(cur_node)  # 矩阵维度（3）
+
+        # 遍历每个格子计算距离
+        for i in range(N):
+            for j in range(N):
+                if cur_node[i][j] != fin_node[i][j]:
+                    index = np.argwhere(fin_node == cur_node[i][j])  # 找到对应数字在目标状态的位置
+                    x = index[0][0]  # 目标x坐标
+                    y = index[0][1]  # 目标y坐标
+                    dist += (abs(x - i) + abs(y - j))  # 累加曼哈顿距离
+        return dist + 1  # 总距离+当前步数（g值固定为1）
+
+    def nextStep(self):
+        """生成所有可能的下一个合法状态
+        Returns:
+            State: 评估函数值最小的下一个状态
+        """
+        if not self.direction:  # 无可用移动方向
+            return []
+        subStates = []  # 子状态列表
+        boarder = len(self.state) - 1  # 矩阵边界索引
+
+        # 获取0点位置
+        x, y = self.getZeroPos()
+        x, y = x[0], y[0]  # 转换为标量值
+
+        # 向左移动
+        if 'left' in self.direction and y > 0:
+            s = self.state.copy()
+            tmp = s[x, y - 1]
+            s[x, y - 1] = s[x, y]
+            s[x, y] = tmp
+            news = State(s, directionFlag='right', parent=self)
+            news.setF(news.getFunctionValue())
+            subStates.append(news)
+
+        # 向上移动
+        if 'up' in self.direction and x > 0:
+            s = self.state.copy()
+            tmp = s[x - 1, y]
+            s[x - 1, y] = s[x, y]
+            s[x, y] = tmp
+            news = State(s, directionFlag='down', parent=self)
+            news.setF(news.getFunctionValue())
+            subStates.append(news)
+
+        # 向下移动
+        if 'down' in self.direction and x < boarder:
+            s = self.state.copy()
+            tmp = s[x + 1, y]
+            s[x + 1, y] = s[x, y]
+            s[x, y] = tmp
+            news = State(s, directionFlag='up', parent=self)
+            news.setF(news.getFunctionValue())
+            subStates.append(news)
+
+        # 向右移动
+        if 'right' in self.direction and y < boarder:
+            s = self.state.copy()
+            tmp = s[x, y + 1]
+            s[x, y + 1] = s[x, y]
+            s[x, y] = tmp
+            news = State(s, directionFlag='left', parent=self)
+            news.setF(news.getFunctionValue())
+            subStates.append(news)
+
+        # 返回F值最小的下一个点
+        subStates.sort(key=compareNum)
+        return subStates[0]
+
+    # A* 迭代
+    def solve(self):
+        """执行A*算法求解路径
+        Returns:
+            list: 从初始状态到目标状态的路径节点列表
+        """
+        # openList（待访问节点列表）
+        openTable = []
+        # closeList（已访问节点列表）
+        closeTable = []
+        openTable.append(self)  # 初始节点加入open表
+
+        while len(openTable) > 0:  # 当存在待访问节点时
+            # 取出评估值最小的节点
+            n = openTable.pop(0)
+            # 加入已访问列表
+            closeTable.append(n)
+            # 生成子节点
+            subStates = n.nextStep()
+            path = []
+
+            # 判断是否到达目标状态
+            if (subStates.state == subStates.answer).all():
+                # 回溯路径
+                while subStates.parent and subStates.parent != originState:
+                    path.append(subStates.parent)
+                    subStates = subStates.parent
+                path.reverse()  # 反转得到正序路径
+                return path
+
+            # 将子节点加入open表
+            openTable.append(subStates)
+        else:
+            return None, None
+
+def compareNum(state):
+    """状态比较函数（用于排序）"""
+    return state.f
+
+if __name__ == '__main__':
+    # 初始化起始状态（0代表空格）
+    originState = State(np.array([[1, 5, 3], [2, 4, 6], [7, 0, 8]]))
+    # 设置类属性：目标状态
+    State.answer = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 0]])
+
+    # 创建初始状态对象
+    s1 = State(state=originState.state)
+    # 求解路径
+    path = s1.solve()
+
+    # 输出结果
+    if path:
+        print("解决方案路径：")
+        for node in path:
+            node.showInfo()
+        print("目标状态：")
+        print(State.answer)
+        print("总步数：%d" % len(path))