8 Queen Problem Algorithm Explained

The 8 queen problem algorithm is a classic example of backtracking in computer science. This page explains the algorithm step by step, provides Python code, and visualizes the solution process. Mastering this algorithm will help you understand recursion, constraint satisfaction, and problem-solving strategies.

What is the 8 Queen Problem?

The 8 Queen Problem asks: How can you place eight queens on a standard chessboard so that no two queens threaten each other? This means no two queens share the same row, column, or diagonal. The problem is famous for its elegant solution and is often used to teach algorithmic thinking.

Step-by-Step Algorithm

1. Start with an empty chessboard.
2. Place a queen in the first row, first column.
3. Move to the next row and try to place a queen in a safe column (no threats from previous queens).
4. If a safe spot is found, place the queen and move to the next row.
5. If no safe spot is found, backtrack to the previous row and move the queen to the next available column.
6. Repeat until all eight queens are placed or all possibilities are exhausted.

Python Implementation

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

print(solve_nqueens(8))

This code uses recursion and backtracking to find all valid solutions for the 8 queen problem. Each solution is a list of column indices for each row.

Visualizing the Solution

Visualizing the backtracking process helps understand how the algorithm explores possibilities and backtracks when conflicts arise. Try our interactive 8 queens puzzle game to see the algorithm in action!

FAQ