N QUEENS

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#include <stdio.h>

#include <math.h>


// This array stores the column position of queens

int queenPositions[20]; 

int solutionCount = 0; // To count the number of solutions


// Function to print the board for one solution

void printSolution(int n) {

    printf("\nSolution %d:\n\n", ++solutionCount);

    for (int row = 1; row <= n; row++) {

        for (int col = 1; col <= n; col++) {

            // Print 'Q' if a queen is placed, else print '-'

            if (queenPositions[row] == col) {

                printf(" Q ");

            } else {

                printf(" - ");

            }

        }

        printf("\n");

    }

    printf("\n");

}


// Function to check if a queen can be placed in the given row and column

int isSafe(int currentRow, int currentCol) {

    for (int previousRow = 1; previousRow < currentRow; previousRow++) {

        // Check if another queen is in the same column or diagonal

        if (queenPositions[previousRow] == currentCol || 

            abs(queenPositions[previousRow] - currentCol) == abs(previousRow - currentRow)) {

            return 0; // Not safe

        }

    }

    return 1; // Safe

}


// Function to solve the N-Queens problem

void solveNQueens(int currentRow, int n) {

    // If all queens are placed, print the solution

    if (currentRow > n) {

        printSolution(n);

        return;

    }


    // Try placing a queen in each column of the current row

    for (int col = 1; col <= n; col++) {

        if (isSafe(currentRow, col)) {

            queenPositions[currentRow] = col; // Place the queen

            solveNQueens(currentRow + 1, n); // Solve for the next row

        }

    }

}


int main() {

    int n;

    printf("Enter the number of queens: ");

    scanf("%d", &n);

    solveNQueens(1, n); // Start solving from the first row

    return 0;

}

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