Tree Game Problem

A “tree game” needs rules before an algorithm: ask where players start, whether moves only go downward, whether nodes can be revisited, what score is collected, and whether both play optimally. For an impartial win/lose game on a rooted acyclic tree, define win(node) as whether the player to move can force a win; it is true exactly when some legal child is losing. For score games, use minimax: current player maximizes their payoff while the opponent minimizes it, carrying turn and collected-state information when necessary. Because a tree has no cycles, a postorder recurrence often evaluates each state once, typically O(n) time and O(h) stack space; extra game state may increase complexity. Test leaves, one legal move, ties, and turn order. Do not claim a solution until the payoff semantics are explicit.