add 051-N-Queens

Author: zongyanqi

051-N-Queens.js

@@ -0,0 +1,67 @@
+/**
+ * https://leetcode.com/problems/n-queens/description/
+ * Difficulty:Hard
+ * 
+ * The n-queens puzzle is the problem of placing n queens on an n×n chessboard
+ * such that no two queens attack each other.
+ *
+ * Given an integer n, return all distinct solutions to the n-queens puzzle.
+ * Each solution contains a distinct board configuration of the n-queens' placement, where 'Q' and '.' both indicate a queen and an empty space respectively.
+ *
+ * For example,
+ * There exist two distinct solutions to the 4-queens puzzle:
+ * [
+ *  [".Q..",  // Solution 1
+ *   "...Q",
+ *   "Q...",
+ *   "..Q."],
+ *
+ *  ["..Q.",  // Solution 2
+ *   "Q...",
+ *   "...Q",
+ *   ".Q.."]
+ * ]
+ * 2,1 3,2
+ */
+
+/**
+ * @param {number} n
+ * @return {string[][]}
+ */
+var solveNQueens = function (n) {
+    var ret = [];
+    var board = [];
+    for (var i = 0; i < n; i++) {
+        board.push(new Array(n).fill('.'));
+    }
+    helper(board, 0, ret);
+    return ret;
+};
+
+function helper(board, col, ret) {
+    if (col === board.length) {
+        ret.push(construct(board));
+    } else {
+        for (var i = 0; i < board.length; i++) {
+            if (check(board, i, col)) {
+                board[i][col] = 'Q';
+                helper(board, col + 1, ret);
+                board[i][col] = '.';
+            }
+        }
+    }
+}
+
+function check(board, x, y) {
+    for (var i = 0; i < board.length; i++) {
+        for (var j = 0; j < y; j++) {
+            if (board[i][j] === 'Q' &&
+                (i === x || i + j === x + y || i + y === j + x)) return false;
+        }
+    }
+    return true;
+}
+function construct(board) {
+    return board.map(arr => arr.join(''));
+}
+console.log(solveNQueens(4));