 Solution

Depth-first search computes minimax search values with much less live storage and naturally supports alpha-beta pruning. A parent's value needs only its current best child value and the next child to visit. Once a child subtree has been evaluated, its internal search nodes can be discarded; a final value cannot usually be computed from a nonterminal frontier alone.

With branching factor $b$ and horizon $d$, breadth-first search stores a frontier of order $b^d$. A depth-first search implementation storing sibling lists uses $O(bd)$ space complexity; lazy successor generation can reduce this to $O(d)$ frames plus game-state storage. Both unpruned traversals have $O(b^d)$ time complexity for $b>1$. Depth-first search also supplies a completed sibling outcome early, allowing alpha-beta pruning to reject later subtrees before generating them.