Solution: N-Queens II
Understand how to solve the N-Queens II problem by exploring backtracking techniques. Learn to place n queens on an n x n chessboard without conflicts by tracking columns and diagonals, using recursion and backtracking. Gain skills in optimizing time and space complexity while finding all valid solutions.
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 ...