N-Queens 題解

題目

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.

Difficulty: Hard

分析

跟上一道題 N-Queens II實際上是一模一樣的，只是多了一個需要保存解的要求，詳細分析見我的上篇博客：N-Queens II 經典問題：8皇后問題 題解
這裏直接給出代碼：

class Solution {
private:
    vector<vector<string>> ret;
    vector<int> queen;
public:
    bool CheckPlace(int Checkline, int Checkrow) {
        for (int i = 0; i < Checkline; i++) {
            if (queen[i] == Checkrow || abs(Checkline - i) == abs(Checkrow - queen[i])) {
                return false;
            }
        }
        return true;
    }
    void PlaceQueen(int Checkline, int n) {
        if (Checkline == n) {
            vector<string> curr(n, string(n, '.'));
            for (int i = 0; i < queen.size(); i++) {
                curr[i][queen[i]] = 'Q';
            }
            ret.push_back(curr);
            return;
        }
        else {
            for (int i = 0; i < n; i++) {
                if (CheckPlace(Checkline, i)) {
                    queen[Checkline] = i;
                    PlaceQueen(Checkline + 1, n);
                }
            }
        }
    }
    vector<vector<string>> solveNQueens(int n) {
        queen.resize(n);
        PlaceQueen(0, n);
        return ret;
    }
};