52. N-Queens II

题目描述

52. N-Queens II

回溯法 

这道题与第51题是一样的。51. N-Queens-优快云博客

class Solution {
    int columns;  //从低位到高位起算，第i位为0表示棋盘第i列可以放置皇后，第i位为1表示棋盘第i列不能放置皇后
    //边长为n的棋盘分别有2n-1条正斜线和反斜线。
    int diagnals1;//反斜线（从右上角到左下角）。第i位表示第i条反斜线能否放置皇后
    int diagnals2;//正斜线（从左上角到右下角）。含义同上
    int res = 0;
public:
    int totalNQueens(int n) {
        columns = 0;
        diagnals1 = 0;
        diagnals2 = 0;
        backtrack(n,0);
        return res;
    }

    void backtrack(int n,int row){
        if(row==n)
        {
            res++;
            return;
        }
        for(int col = 0;col <n;col++){
            if(columns &(1<<col))
                continue;
            int diag1 = row+col;
            if(diagnals1 &(1<<diag1))
                continue;
            int diag2 = row-col+(n-1);
            if(diagnals2 &(1<<diag2))
                continue;
            columns |= (1<<col);
            diagnals1 |= (1<<diag1);
            diagnals2 |= (1<<diag2);
            backtrack(n,row+1);
            columns &= (~(1<<col));
            diagnals1 &= (~(1<<diag1));
            diagnals2 &= (~(1<<diag2)); 
        }
    }
};