Design BFS to detect forced win in Tic-Tac-Toe
Overview
This question evaluates algorithm design and search-space reasoning, focusing on BFS-based game-tree exploration, state representation, symmetry reduction and hashing, win/draw detection, pruning and move-ordering heuristics, and time/space complexity analysis in terms of n, k, t, and the branching factor within the Coding & Algorithms domain.
You are given an n×n Tic-Tac-Toe–like board and a target k (1 ≤ k ≤ n). From the current board state and the player to move, design an algorithm to determine whether the current player can force a win within at most t moves. Use a breadth-first search over game states: specify the state representation, successor generation, win/draw detection, and how you avoid revisiting equivalent states (e.g., hashing or symmetry reduction). Describe any pruning or move-ordering heuristics you would apply. Analyze the worst-case time and space complexity in terms of n, k, t, and the branching factor, and also provide the complexities for the standard 3×3, k=3 case.