Eight Queens Problem Python Solutions

This page presents Python solutions for the eight queens problem. You'll find code, explanations, and sample output to help you understand and implement the solution.

Python Code for the Eight Queens Problem

def solve_nqueens(n):
    solutions = []
    board = []
    def is_safe(row, col):
        for r, c in enumerate(board):
            if c == col or abs(row - r) == abs(col - c):
                return False
        return True
    def backtrack(row=0):
        if row == n:
            solutions.append(list(board))
            return
        for col in range(n):
            if is_safe(row, col):
                board.append(col)
                backtrack(row + 1)
                board.pop()
    backtrack()
    return solutions

for sol in solve_nqueens(8):
    print(sol)

Sample Output

[0, 4, 7, 5, 2, 6, 1, 3]
[0, 5, 7, 2, 6, 3, 1, 4]
[0, 6, 3, 5, 7, 1, 4, 2]
... (total 92 solutions)

Explanation

Each solution is a list of column indices for each row. For example, [0, 4, 7, 5, 2, 6, 1, 3] means the queen in row 0 is in column 0, row 1 in column 4, and so on. This compact representation makes it easy to process and visualize solutions programmatically.

FAQ