A binary heap is a complete binary tree stored in an array that maintains the heap property: in a min-heap, every parent is ≤ its children, so the minimum is always at the root. This makes it the standard implementation of a priority queue.
1 index: 0 1 2 3 4
/ \ array: [1, 3, 5, 8, 4]
3 5 parent(i) = (i-1)//2
/ \ left(i) = 2i+1
8 4 right(i) = 2i+2
import heapq
h = []
heapq.heappush(h, 5) # O(log n) — bubble up
heapq.heappush(h, 1)
heapq.heappush(h, 3)
smallest = h[0] # peek min -> O(1)
heapq.heappop(h) # O(log n) — remove root, sift down -> 1
| Operation | Time |
|---|---|
| peek min/max | O(1) |
| push (insert) | O(log n) |
| pop (extract) | O(log n) |
| build heap from n items | O(n) |
A heap gives you the next-most-important item instantly without keeping everything fully sorted, which is far cheaper than re-sorting.
It is the backbone of priority-driven algorithms and a frequent interview tool for "k largest/smallest" questions.