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Create n_queen_prob.cpp #737

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80 changes: 80 additions & 0 deletions n_queen_prob.cpp
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#include <iostream>
#include <vector>

using namespace std;

bool isSafe(vector<vector<int>>& board, int row, int col, int n) {
// Check if there is a queen in the same column
for (int i = 0; i < row; ++i) {
if (board[i][col] == 1) {
return false;
}
}

// Check upper-left diagonal
for (int i = row, j = col; i >= 0 && j >= 0; --i, --j) {
if (board[i][j] == 1) {
return false;
}
}

// Check upper-right diagonal
for (int i = row, j = col; i >= 0 && j < n; --i, ++j) {
if (board[i][j] == 1) {
return false;
}
}

return true;
}

bool solveNQueens(vector<vector<int>>& board, int row, int n) {
if (row == n) {
// All queens have been placed successfully
return true;
}

for (int col = 0; col < n; ++col) {
if (isSafe(board, row, col, n)) {
board[row][col] = 1; // Place the queen

if (solveNQueens(board, row + 1, n)) {
return true;
}

board[row][col] = 0; // Backtrack if no solution found
}
}

return false; // No safe placement in this row
}

void printBoard(vector<vector<int>>& board, int n) {
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
if (board[i][j] == 1) {
cout << "Q ";
} else {
cout << ". ";
}
}
cout << endl;
}
}

int main() {
int n;
cout << "Enter the value of N for N-Queens: ";
cin >> n;

vector<vector<int>> board(n, vector<int>(n, 0));

if (solveNQueens(board, 0, n)) {
cout << "Solution exists. Here is the board:\n";
printBoard(board, n);
} else {
cout << "No solution exists for N = " << n << endl;
}

return 0;
}