Update 0051.N皇后.md

problems/0051.N皇后.md

@@ -348,48 +348,47 @@ class Solution {
 ```python
 class Solution:
     def solveNQueens(self, n: int) -> List[List[str]]:
-        if not n: return []
-        board = [['.'] * n for _ in range(n)]
-        res = []
-        def isVaild(board,row, col):
-            #判断同一列是否冲突
-            for i in range(len(board)):
-                if board[i][col] == 'Q':
-                    return False
-            # 判断左上角是否冲突
-            i = row -1
-            j = col -1
-            while i>=0 and j>=0:
-                if board[i][j] == 'Q':
-                    return False
+        result = []  # 存储最终结果的二维字符串数组
+
+        chessboard = ['.' * n for _ in range(n)]  # 初始化棋盘
+        self.backtracking(n, 0, chessboard, result)  # 回溯求解
+        return [[''.join(row) for row in solution] for solution in result]  # 返回结果集
+
+    def backtracking(self, n: int, row: int, chessboard: List[str], result: List[List[str]]) -> None:
+        if row == n:
+            result.append(chessboard[:])  # 棋盘填满，将当前解加入结果集
+            return
+
+        for col in range(n):
+            if self.isValid(row, col, chessboard):
+                chessboard[row] = chessboard[row][:col] + 'Q' + chessboard[row][col+1:]  # 放置皇后
+                self.backtracking(n, row + 1, chessboard, result)  # 递归到下一行
+                chessboard[row] = chessboard[row][:col] + '.' + chessboard[row][col+1:]  # 回溯，撤销当前位置的皇后
+
+    def isValid(self, row: int, col: int, chessboard: List[str]) -> bool:
+        # 检查列
+        for i in range(row):
+            if chessboard[i][col] == 'Q':
+                return False  # 当前列已经存在皇后，不合法
+
+        # 检查 45 度角是否有皇后
+        i, j = row - 1, col - 1
+        while i >= 0 and j >= 0:
+            if chessboard[i][j] == 'Q':
+                return False  # 左上方向已经存在皇后，不合法
             i -= 1
             j -= 1
-            # 判断右上角是否冲突
-            i = row - 1
-            j = col + 1
-            while i>=0 and j < len(board):
-                if board[i][j] == 'Q':
-                    return False
+
+        # 检查 135 度角是否有皇后
+        i, j = row - 1, col + 1
+        while i >= 0 and j < len(chessboard):
+            if chessboard[i][j] == 'Q':
+                return False  # 右上方向已经存在皇后，不合法
             i -= 1
             j += 1
-            return True
 
-        def backtracking(board, row, n):
-            # 如果走到最后一行，说明已经找到一个解
-            if row == n:
-                temp_res = []
-                for temp in board:
-                    temp_str = "".join(temp)
-                    temp_res.append(temp_str)
-                res.append(temp_res)
-            for col in range(n):
-                if not isVaild(board, row, col):
-                    continue
-                board[row][col] = 'Q'
-                backtracking(board, row+1, n)
-                board[row][col] = '.'
-        backtracking(board, 0, n)
-        return res
+        return True  # 当前位置合法
+
 ```