N-Queen II

Change-Id: I0cea47edcf32d09b399de1f4b946c67b17f69e17

Author: applewjg

N-QueensII.java

@@ -0,0 +1,79 @@
+/*
+ Author:     King, [email protected]
+ Date:       Aug 23, 2013
+ Problem:    N-Queens II
+ Difficulty: Medium
+ Source:     https://oj.leetcode.com/problems/n-queens-ii/
+ Notes:
+ 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.."]
+ ]
+
+ Solution: 1. Recursion.
+           2. Recursion + bit version. (fast)
+              The idea is from http://www.matrix67.com/blog/archives/266 (in chinese).
+*/
+
+public class Solution {
+    public int totalNQueens(int n) {
+        return totalNQueens_2(n);
+    }
+    public int totalNQueens_1(int n) {
+        int[] board = new int[n];
+        Arrays.fill(board,-1);
+        int[] res = new int[1];
+        totalNQueensRe(n, 0, board, res);
+        return res[0];
+    }
+    public void totalNQueensRe(int n, int row, int[] board, int[] res) {
+        if (n == row) {
+            res[0]++;
+            return;
+        }
+        for (int i = 0; i < n; ++i) {
+            if (isValid(board, row, i)) {
+                board[row] = i;
+                totalNQueensRe(n, row + 1, board, res);
+                board[row] = -1;
+            }
+        }
+    }
+    public boolean isValid(int[] board, int row, int col) {
+        for (int i = 0; i < row; ++i) {
+            if (board[i] == col || row - i == Math.abs(col - board[i]))
+                return false;
+        }
+        return true;
+    }
+    public int totalNQueens_2(int n) {
+        int[] res = new int[1];
+        totalNQueensRe2(n, 0, 0, 0, res);
+        return res[0];
+    }
+    public void totalNQueensRe2(int n, int row, int ld, int rd, int[] res) {
+        if (row == (1<<n) -1 ) {
+            res[0]++;
+            return;
+        }
+        int avail = ~(row | ld | rd);
+        for (int i = n - 1; i >= 0; --i) {
+            int pos = 1<<i;
+            if ((int)(avail&pos) != 0) {
+                totalNQueensRe2(n, row | pos, (ld|pos) << 1, (rd|pos) >>1, res);
+            }
+        }
+    }
+}