N-Queens Problem


Description

LeetCode Problem 51.

The n-queens puzzle is the problem of placing n queens on an n x n chessboard such that no two queens attack each other.

Given an integer n, return all distinct solutions to the n-queens puzzle. You may return the answer in any order.

Each solution contains a distinct board configuration of the n-queens’ placement, where ‘Q’ and ‘.’ both indicate a queen and an empty space, respectively.

Example 1:

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Input: n = 4
Output: [[".Q..","...Q","Q...","..Q."],["..Q.","Q...","...Q",".Q.."]]
Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above

Example 2:

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Input: n = 1
Output: [["Q"]]

Constraints:

  • 1 <= n <= 9


Sample C++ Code

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class Solution {
public:
    vector<vector<string>> sols;
    int N;
    
    void dfs(vector<int>& col2row, int row) {
        if (row == N) {
            vector<string> sol;
            string s;
            for (int i = 0; i < N; i ++) {
                s = "";
                for (int j = 0; j < N; j ++) {
                    if (col2row[j] == i)
                        s += 'Q';
                    else
                        s += '.';
                }
                sol.push_back(s);
            }
            sols.push_back(sol);
            return;
        }
        
        vector<vector<int>> dir = { {-1,-1}, {1,1}, {-1,1}, {1,-1} };
        for (int i = 0; i < N; i ++) {
            if (col2row[i] == -1) {
                int r = row, c = i;
                bool place = true;
                for (int j = 0; j < 4; j ++) {
                    r = row+dir[j][0], c = i+dir[j][1];
                    while (r >= 0 && c >= 0 && r < N && c < N && place) {
                        if (col2row[c] == r) {
                            place = false; break;
                        }
                        r += dir[j][0], c += dir[j][1];
                    }
                    if (!place)
                        break;
                }

                
                if (place) {
                    col2row[i] = row;
                    dfs(col2row, row+1);
                    col2row[i] = -1;
                }
            }
        }
        
        
    }
    
    vector<vector<string>> solveNQueens(int n) {
        N = n;
        vector<int> col2row(n, -1);
        dfs(col2row, 0);
        return sols;
    }
};




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