Solution: N-Queens II
Explore how to solve the N-Queens II problem using an optimized backtracking approach in C++. Understand how to safely place queens row by row by tracking columns and diagonals, backtrack when necessary, and count all valid configurations efficiently. This lesson equips you to handle combinatorial problems with backtracking and analyze the time and space complexity for this classical problem.
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:
n
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 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 queens on a ...