n-Queens Problem using Backtracking | 4-Queens & 8-Queens Algorithm Explained
In this video, we dive deep into the n-Queens problem, a classic challenge in computer science and the Design and Analysis of Algorithms (DAA). We explore how to place "n" queens on an n×n chessboard such that no two queens attack each other—meaning no two queens share the same row, column, or diagonal.
What you will learn:
Problem Definition: Understanding the constraints of the 8-Queens and n-Queens problems [00:08].
Solution Representation: How to represent solutions as n-element tuples [00:47].
State Space Trees: Calculating the number of nodes for 4-Queens (65 nodes) and 8-Queens (69,781 nodes) [02:48].
Step-by-Step Walkthrough: Watch the backtracking strategy in action for a 4-Queens problem [05:46].
Diagonal Math: The logic behind checking diagonal attacks using row and column indices [23:07].
Algorithm & Complexity: A detailed look at the Place and N-Queens recursive algorithms and their time complexity [26:45].
This tutorial is perfect for students preparing for university exams or anyone interested in competitive programming and algorithm design.
Key Solutions Found in Video:
Solution 1: [2, 4, 1, 3] [01:12:59]
Solution 2: [3, 1, 4, 2] [01:16:08]
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