添加（0051.N皇后.md）Scala版本

problems/0051.N皇后.md

@@ -455,7 +455,7 @@ var solveNQueens = function(n) {
 };
 ```
 
-## TypeScript
+### TypeScript
 
 ```typescript
 function solveNQueens(n: number): string[][] {
@@ -683,5 +683,77 @@ char *** solveNQueens(int n, int* returnSize, int** returnColumnSizes){
 }
 ```
 
+### Scala
+
+```scala
+object Solution {
+  import scala.collection.mutable
+  def solveNQueens(n: Int): List[List[String]] = {
+    var result = mutable.ListBuffer[List[String]]()
+
+    def judge(x: Int, y: Int, maze: Array[Array[Boolean]]): Boolean = {
+      // 正上方
+      var xx = x
+      while (xx >= 0) {
+        if (maze(xx)(y)) return false
+        xx -= 1
+      }
+      // 左边
+      var yy = y
+      while (yy >= 0) {
+        if (maze(x)(yy)) return false
+        yy -= 1
+      }
+      // 左上方
+      xx = x
+      yy = y
+      while (xx >= 0 && yy >= 0) {
+        if (maze(xx)(yy)) return false
+        xx -= 1
+        yy -= 1
+      }
+      xx = x
+      yy = y
+      // 右上方
+      while (xx >= 0 && yy < n) {
+        if (maze(xx)(yy)) return false
+        xx -= 1
+        yy += 1
+      }
+      true
+    }
+
+    def backtracking(row: Int, maze: Array[Array[Boolean]]): Unit = {
+      if (row == n) {
+        // 将结果转换为题目所需要的形式
+        var path = mutable.ListBuffer[String]()
+        for (x <- maze) {
+          var tmp = mutable.ListBuffer[String]()
+          for (y <- x) {
+            if (y == true) tmp.append("Q")
+            else tmp.append(".")
+          }
+          path.append(tmp.mkString)
+        }
+        result.append(path.toList)
+        return
+      }
+
+      for (j <- 0 until n) {
+        // 判断这个位置是否可以放置皇后
+        if (judge(row, j, maze)) {
+          maze(row)(j) = true
+          backtracking(row + 1, maze)
+          maze(row)(j) = false
+        }
+      }
+    }
+
+    backtracking(0, Array.ofDim[Boolean](n, n))
+    result.toList
+  }
+}
+```
+
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