LeetCode-52.N-Queen II

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 the number of distinct solutions to the n-queens puzzle.

Example:

Input: 4
Output: 2
Explanation: There are two distinct solutions to the 4-queens puzzle as shown below.
[
 [".Q..",  // Solution 1
  "...Q",
  "Q...",
  "..Q."],

 ["..Q.",  // Solution 2
  "Q...",
  "...Q",
  ".Q.."]
]

使用深度优先遍历，并剪枝
注意斜线上的规律，左斜线上的点 横纵坐标和相同，右斜线上的点 横纵坐标差相同

 class Solution {
     int total = 0;
     public int totalNQueens(int n) {

         dfs(n,0,new ArrayList<Integer>(),new ArrayList<Integer>(),new ArrayList<Integer>());
         return total;
     }
     private void dfs( int n, int level, List<Integer> cols, List<Integer> sum, List<Integer> dif) {
         if (level == n) {
             total++;
             return;
         }
         for (int i = 0; i < n; i++) {
             if (cols.contains(i) || sum.contains(i + level) || dif.contains(i - level))
                 continue;
             cols.add(i);
             sum.add(i + level);
             dif.add(i - level);
             dfs(n, level + 1, cols, sum, dif);
             cols.remove(cols.size() - 1);
             sum.remove(sum.size() - 1);
             dif.remove(dif.size() - 1);
         }
     }
 }

使用位运算（最优解）

 class Solution {//DFS 位运算 mytip
     public int totalNQueens(int n) {
         int total=0;
         return dfs(total,n,0,0,0,0);
         //return total;
     }
     private int dfs(int total, int n, int level, int cols, int pie, int na) {
         if (level == n) {
             total++;
             return total;
         }
         int bits = (~(cols|pie|na))&((1<<n)-1);//得到可能放的空位
         while(0!=bits){//遍历可能放的空位
             int cur = bits&(-bits);//得到最后一个1
             total= dfs(total,n,level+1,cols|cur,(pie|cur)<<1,(na|cur)>>1);
             bits= bits&(bits-1);//清楚最后一个1
         }
         return total;
     }
 }

相关题

n皇后 LeetCode51 https://www.cnblogs.com/zhacai/p/10621300.html