Match the following algorithms with the data structure it uses. Algorithm Data…

Concept: which support structure an algorithm needs is decided by its processing order — FIFO discovery order needs a Queue, LIFO backtracking order needs a Stack, and direct index-based access needs an Array.

• Breadth-first search (BFS) visits nodes in the exact order they were discovered, level by level — that FIFO behaviour requires a Queue.

• Heap sort maintains a binary heap where each node's parent/children are found by index arithmetic (2i+1, 2i+2) — that needs O(1) random access, so the heap is stored in an Array.

• Depth-first search (DFS) dives as far as possible along one branch, then backtracks to the most recently visited unfinished node — that LIFO behaviour requires a Stack (explicit, or the call stack via recursion).

Cross-check: this also matches known behaviour — BFS's queue-driven order is exactly what guarantees the shortest path in an unweighted graph, while DFS's stack-driven order lets it dive arbitrarily deep before backtracking, confirming the queue/stack split; heap sort's O(log n) sift-up/sift-down operations only work with direct array indexing, confirming the array.

So I (Breadth first search) - 2 (Queue), II (Heap sort) - 3 (Arrays), III (Depth first search) - 1 (Stacks).