Solving the N Queen Problem with C

Solving the N-Queen Problem with C. The N-Queen Problem is a classic algorithmic challenge that involves placing N queens on an N*N chessboard so that no two queens can threaten each other. This means two queens can be in the same row, column, or diagonal. This article provides a step-by-step guide to solving the n queen problem with C language, focusing on a backtracking approach, which is a form of recursive algorithm.

Understanding the N Queen Problem

Before jumping into coding, it is crucial to thoroughly understand what the n queen problem is and what it entails. the goal is to find all the problem arrangments of n queen on an n*n chessboard where no two queens attack each other.

Solving N Queen Problem with C

Defining the Chessboard

The chessboard can be represented as a 2D array of integers, where 0 indicates a space and 1 represents a queen.

Initializing the Chessboard

Before starting ensure that the chessboard is empty. this can be done with the simple nested loop

Check if the Queen can be Placed

We need a function to check if a queen can be placed on the board at the [row][col] position without being attacked by another queen.

Solve the N Queen Problem

Use backtracking to solve the problem recursively. the function tries to place a queen on every row. if placing a queen in a certain column leads to the solution, it proceeds to place another queen in the next row. If it does not lead to a solution, it backtracks and tries a different column.

Implement the Main Function

This function initializes the board and calls the utility function to solve the problem.

Implement a function to print the chessboard with a Queen place.

Compelet C Program for N Queen Problem

Output of N Queen Solution

n = 8

n queen problem


n queen problem using backtracking

N Queen Problem Time Complexity

The backtracking approach for solving the n queen problem, as demonstrated in this article by using C language, does not have a straightforward time complexity due to its recursive nature and the fact that it explores multiple branches of execution, backtracking when a potential solution does not lead to success. The worst-case time complexity for the n queen problem using backtracking can be roughly estimated as O(n!) where n is the number of queens(or the size of the chessboard). This factorail time complexity arises because, in the worst case, the algorithm might need to try all possible arrangements of n queens on the board.

Happy Coding & Learning

See Also

2 thoughts on “Solving the N Queen Problem with C”

Leave a Comment