Binary Heap Simulator

Binary Heap Simulator

A binary heap is a complete binary tree stored in an array. In a max-heap no parent is smaller than its children (in a min-heap, no parent is larger), so the largest (smallest) value sits at the root.

Controls

• Heap type switches between max-heap and min-heap.
• Insert adds a value; Remove Root deletes the root; Peek just reads it.
• Build Heap builds a heap from the comma-separated values; Random fills the heap with random values; Heap Sort sorts the array in place.
• Reset empties the heap; Cancel stops the animation and puts the heap back the way it was.

Index arithmetic (0-based)

parent(i) = ⌊(i − 1) / 2⌋, left(i) = 2i + 1, right(i) = 2i + 2.

Operations

• Insert: the value goes into the first free slot at the end and moves up while it beats its parent (up-heap).
• Remove: the last element moves to the root, then sinks by swapping with the better child (down-heap).
• Building a heap (bottom-up): every internal node from ⌊n/2⌋ − 1 down to 0 is sunk in turn.
• Heap sort: swap the root with the last heap element, shrink the heap by one, sink the new root; repeat.

Complexity