(* Helper function to check if a queen can be placed at (row, col) *)
isSafe[board_, row_, col_] := 
  And @@ (And[# != row, # + board[[#]] != row + col, # - board[[#]] != row - col] & /@ Range[col - 1]);

(* Recursive function to solve the 9-queens problem *)
solveQueens[board_, col_] := 
  If[col > 9, (* If all queens are placed, return the solution *)
     Print[board];,
     (* Else, try placing the queen in each row of the current column *)
     Do[
       If[isSafe[board, row, col],
          solveQueens[ReplacePart[board, col -> row], col + 1]; (* Recur for the next column *)
       ],
       {row, 1, 9}
     ]
  ];

#include <stdio.h>

#define N 9  // Board size for the 9-queens problem

// Function to check if a queen can be placed at board[row][col]
int isSafe(int board[N], int row, int col) {
    int i;
    for(i = 0; i < col; i++) {
        if(board[i] == row || 
           board[i] - i == row - col || 
           board[i] + i == row + col)
            return 0;  // Not safe
    }
    return 1;  // Safe position
}

// Recursive function to solve the 9-queens problem
void solveQueens(int board[N], int col) {
    if(col >= N) {  // If all queens are placed, print the solution
        printf("\nSolution: ");
        int i;
        for(i = 0; i < N; i++) 
            printf("%d ", board[i] + 1);  // Convert 0-based to 1-based
        printf("\n");
        return;
    }

    // Try placing a queen in each row of the current column
    int row;
    for(row = 0; row < N; row++) {
        if(isSafe(board, row, col)) {
            board[col] = row;  // Place queen
            solveQueens(board, col + 1);  // Recur for the next column
            board[col] = 0;  // Backtrack
        }
    }
}

// Main function to initialize the board and start solving
void main() {
    int board[N] = {0};  // Initialize board with all zeroes
    solveQueens(board, 0);  // Start recursion from column 0
}

#include <stdio.h>

#define N 9  // Board size for the 9-queens problem

// Function to check if a queen can be placed at board[row][col]
int isSafe(int board[N], int row, int col) {
    int i;
    for (i = 0; i < col; i++) {
        if (board[i] == row || 
            board[i] - i == row - col || 
            board[i] + i == row + col) 
            return 0;  // Not safe
    }
    return 1;  // Safe position
}

// Function in `f(x) = f(x - 1)` form
int solveQueens(int board[N], int col) {
    if (col == 0) return 1;  // Base case: when col reaches 0, return success

    int prev = solveQueens(board, col - 1);  // Recursive call f(x) = f(x - 1)
    
    if (prev == 0) return 0;  // If previous step failed, return failure

    int row;
    for (row = 0; row < N; row++) {
        if (isSafe(board, row, col - 1)) {  // Check previous column
            board[col - 1] = row;
            return 1;  // Solution found
        }
    }

    return 0;  // No solution found, return failure
}

// Main function to initialize the board and start solving
void main() {
    int board[N] = {0};  // Initialize board with all zeroes
    solveQueens(board, N);  // Start recursion from column N (reverse order)
}