[leetcode] N-Queenes

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.

Example:

Input: 4
Output: [
 [".Q..",  // Solution 1
  "...Q",
  "Q...",
  "..Q."],

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

Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above.

Solution

class Solution {
 public:
  vector<vector<string>> solveNQueens(int n) {
    vector<vector<string>> vvs;
    vector<string> vs(n, std::string(n, '.'));
    solveNQueensHelper(vvs, vs, 0);
    return vvs;
  }
private:
  void solveNQueensHelper(vector<vector<string>> &vvs, vector<string> &vs, int row) {
    if (row != vs.size()) {
      for (int i = 0; i < vs.size(); ++i) {
        if (valid(vs, row, i)) {
          vs[row][i] = 'Q';
          solveNQueensHelper(vvs, vs, row + 1);
          vs[row][i] = '.';
        }
      }
    } else {
      vvs.push_back(vs);
    }
  }
  int valid(vector<string> &vs, int row, int col) {
    for (int i = 0; i < vs.size(); ++i) {
      if (vs[i][col] == 'Q') {
        return 0;
      }
    }
    for (int i = row - 1, j = col - 1; i > -1 && j > -1; --i, --j) {
      if (vs[i][j] == 'Q') {
        return 0;
      }
    }
    for (int i = row - 1, j = col + 1; i > -1 && j < vs.size(); --i, ++j) {
      if (vs[i][j] == 'Q') {
        return 0;
      }
    }
    return 1;
  }
};