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51 solution added #207

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64 changes: 64 additions & 0 deletions 51.N-Queens.cpp
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#include <bits/stdc++.h>
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@sourcery-ai sourcery-ai bot Oct 23, 2025

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suggestion: Avoid using <bits/stdc++.h> for portability.

This header is not part of the C++ standard and can cause compilation issues on non-GCC compilers. Please include only the specific headers you need.

Suggested implementation:

#include <vector>
#include <string>
using namespace std;

If your code uses input/output streams (e.g., cout, cin), you should also add #include <iostream>. If you use any algorithms (e.g., sort, find), add #include <algorithm>. Review the rest of your file and include only the headers you actually use.

using namespace std;

class Solution {
public:
// Function to check if placing a queen at (row, col) is safe
bool isSafe(int row, int col, vector<string> &temp, int n) {
int duprow = row;
int dupcol = col;
// Check all columns to the left in the same row
for (int j = 0; j < col; j++) {
if (temp[row][j] == 'Q') return false;
}

// Check upper-left diagonal
while(row >= 0 && col >= 0){
if(temp[row][col] == 'Q') return false;
Comment on lines +16 to +17
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@sourcery-ai sourcery-ai bot Oct 23, 2025

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suggestion (performance): Diagonal checks can be replaced with auxiliary arrays for efficiency.

Tracking diagonal occupancy with arrays enables constant-time checks, which is more efficient for large boards than iterating through each cell.

Suggested implementation:

    // Function to check if placing a queen at (row, col) is safe using auxiliary arrays
    bool isSafe(int row, int col, vector<int> &leftRow, vector<int> &upperDiagonal, vector<int> &lowerDiagonal, int n) {
        // Check if the column, upper diagonal, or lower diagonal is occupied
        if (leftRow[col] || lowerDiagonal[row + col] || upperDiagonal[n - 1 + col - row])
            return false;
        return true;
  1. You need to declare and initialize the auxiliary arrays in your main/backtracking function:
    • vector<int> leftRow(n, 0);
    • vector<int> upperDiagonal(2 * n - 1, 0);
    • vector<int> lowerDiagonal(2 * n - 1, 0);
  2. When placing a queen, set the corresponding entries to 1:
    • leftRow[col] = 1;
    • lowerDiagonal[row + col] = 1;
    • upperDiagonal[n - 1 + col - row] = 1;
  3. When removing a queen (backtracking), reset them to 0.
  4. Update all calls to isSafe to pass the new arrays.

row--;
col--;
}
row = duprow;
col = dupcol;
// Check lower-left diagonal
while(row < n && col >= 0){
if(temp[row][col] == 'Q') return false;
row++;
col--;
}

return true;
}

// Backtracking function to place queens column by column
void solve(int col, vector<string> temp, vector<vector<string>> &ans, int n) {
// If all columns are filled, add current board to answer
if (col == n) {
ans.push_back(temp);
return;
}

for (int row = 0; row < n; row++) {
if (isSafe(row, col, temp, n)) {
// Place queen
temp[row][col] = 'Q';
// Recurse for next column
solve(col + 1, temp, ans, n);
// Backtrack and remove queen
temp[row][col] = '.';
}
}
}

// Main function to call backtracking
vector<vector<string>> solveNQueens(int n) {
vector<vector<string>> ans;
vector<string> temp;
string s(n, '.');
for(int i = 0 ; i < n ; i++) temp.push_back(s); // FIXED

solve(0, temp, ans, n);
return ans;
}

};