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Solution: N-Queens II

Explore the N-Queens II problem solution by applying backtracking to place queens safely on an n x n chessboard. Understand how to track columns and diagonals, use recursion to explore placements, and backtrack when conflicts arise. This lesson helps you implement a systematic approach to count all valid queen configurations efficiently.

Statement

Given an integer, n, representing the size of an n x n chessboard, return the number of distinct ways to place n queens so that no two queens attack each other. A queen can attack another queen if they are in the same row, column, or diagonal.

Constraints:

  • 11 \leq n 9\leq 9

Solution

So far, you’ve probably brainstormed some approaches and have an idea of how to solve this problem. Let’s explore some of these approaches and figure out which one to follow based on considerations such as time complexity and any implementation constraints.

Naive solution

In order to find the optimal placement of the queens on a chessboard, we could find all configurations with all possible placements of nn queens and then determine for every configuration if it is valid or not.

However, this would be very expensive, since there would be a very large number of possible placements and only a handful of valid ones. For example, when trying to place 66 queens on a 6×66 \times 6 ...