My first instinct was BFS and that's correct, but I almost forgot to handle the boundary check inside the neighbor generation.
Model the chessboard as a graph where each square is a node and knight moves are edges, then use BFS to find the shortest path from start to target. BFS guarantees the minimum number of moves because all edges have equal weight. If the target is never reached, return -1.
Pro tip: Mention that BFS is optimal here because it explores level by level, and discuss how to optimize using bidirectional BFS or A* with a heuristic like Chebyshev distance for large boards. Also, handle edge cases like start equals target (return 0) and unreachable squares (e.g., on a 1x1 board).
Confirm the board size N, the starting and target coordinates, and that the knight moves in standard L-shapes (2,1) or (1,2). Ask about constraints like N up to 10^5 or if multiple queries are expected.
Select BFS for unweighted shortest path. Explain that BFS explores all squares reachable in k moves before k+1 moves, ensuring the first time we reach the target is the minimum.
Use a queue to store squares and a distance array or hash map to track visited squares and their distances. For each square, generate up to 8 valid knight moves within the board.
If start equals target, return 0. If the queue empties without reaching the target, return -1. Also consider N=1 (no moves possible) and N=2 (knight cannot move).
Time complexity is O(N^2) since each square is visited once, and space is O(N^2) for the visited set. For large N or multiple queries, discuss bidirectional BFS or precomputing distances.
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