N-Queens
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# LeetCode #51: N-Queens (C/C++).

hard

source: https://leetcode.com/problems/n-queens/
C/C++ Solution to LeetCode problem 51. N-Queens.

## Problem

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.

## Examples

### Example 1:

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.

Input: n = 1
Output: [[“Q”]]

## Constraints

• 1 <= n <= 9

## Solution

I will use the backtracking technique, I propose two solutions, same algorithm, but different implementation.

1. First solution, uses a set to keep tracking only of the Queens positions. The problem with this solution is that, once a solution is found, then we need to generate the strings to represent the board.
2. Second solution uses directly strings to represent the whole board at all times.

### Solution 1:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 class Solution { private: vector<vector<string>> result; bool isValid(int n, int r, int c, set<pair<int, int>>& tmpSol) { for (const auto& pair: tmpSol) { if (pair.first == r || pair.second == c) return false; if (abs(pair.first - r) == abs(pair.second - c)) return false; } return true; } void addSolution(int n, set<pair<int, int>>& tmpSol) { vector<string> tmp; for (int r=0; r<n; r++) { string sol = ""s; for (int c=0; c<n; c++) { if (tmpSol.find({r,c}) == tmpSol.end()) sol = sol + "."; else sol = sol + "Q"; } tmp.push_back(sol); } result.push_back(tmp); } void solve(int n, set<pair<int, int>>& tmpSol, int r) { if (r == n) { addSolution(n, tmpSol); return; } for (int c=0; c<n; c++) { if (!isValid(n, r, c, tmpSol)) continue; tmpSol.insert({r, c}); solve(n, tmpSol, r+1); tmpSol.erase({r, c}); } } public: vector<vector<string>> solveNQueens(int n) { set<pair<int,int>> tmpSol; solve(n, tmpSol, 0); return result; } }; 

### Solution 2:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 class Solution { private: vector<vector<string>> result; bool isValid(int n, vector<string>& tmpSol, int row, int col){ for (int i=0; i<n; i++){ if (tmpSol[i][col] == 'Q') return false; } for(int i=row-1, j=col-1; i>=0 && j>=0; i--, j--){ if(tmpSol[i][j] == 'Q') return false; } for (int i=row-1, j=col+1; i>=0 && j<n; i--, j++) { if(tmpSol[i][j] == 'Q') return false; } return true; } void solve(int n, vector<string>& tmpSol, int r){ if (r == n) { result.push_back(tmpSol); return; } for (int c=0; c<n; c++) { if (isValid(n, tmpSol, r, c)) { tmpSol[r][c] = 'Q'; solve(n, tmpSol, r+1); tmpSol[r][c] = '.'; } } } public: vector<vector<string>> solveNQueens(int n) { vector<string> tmpSol(n , string(n, '.')); solve(n, tmpSol, 0); return result; } };