Minimum knight moves on a grid

Problem Find the minimum number of knight moves from a start cell to a target cell on an N x N board (standard 8 knight moves; stay on the board).

Input / Output

• Input: N, start (x1,y1), target (x2,y2). Output: minimum move count (-1 if unreachable on tiny boards).

Constraints

• N up to 10^3 → O(N^2) BFS is fine; the infinite-board variant needs pruning/bidirectional BFS — mention if asked.

Example

• N=8, (0,0) → (7,7) → 6 moves; (0,0) → (2,1) → 1.