AlgoViz: Interactive Algorithm Visualization Tool

Min-Heap

Category: Tree / Graph | Time: O(log n) Insert/Delete | Space: O(1)

Input Data

Visualization

Visual representation of the data structure

Enter tree data to start visualization.

About Min-Heap

A Min-Heap is a specialized tree-based data structure that satisfies the heap property: the value of each node is less than or equal to the value of its children. This means the smallest element is always at the root. It is commonly used to implement priority queues.

Code Editor

The code is for reference. Editing it won't affect the visualization.

// Heapify a subtree rooted with node i
function heapify(arr, n, i) {
    let smallest = i;
    const left = 2 * i + 1;
    const right = 2 * i + 2;

    if (left < n && arr[left] < arr[smallest]) {
        smallest = left;
    }

    if (right < n && arr[right] < arr[smallest]) {
        smallest = right;
    }

    if (smallest !== i) {
        [arr[i], arr[smallest]] = [arr[smallest], arr[i]];
        heapify(arr, n, smallest);
    }
}

// Build a min-heap from an array
function buildHeap(arr) {
    const n = arr.length;
    for (let i = Math.floor(n / 2) - 1; i >= 0; i--) {
        heapify(arr, n, i);
    }
}

// Extract the minimum element
function extractMin(arr) {
    const min = arr[0];
    arr[0] = arr.pop();
    heapify(arr, arr.length, 0);
    return min;
}

What is a Heap?

How is a Heap represented in memory?

What is 'heapify'?

What is the time complexity for heap operations?

What are the main applications of a Heap?

What is the difference between a Min-Heap and a Max-Heap?

How do you insert a new element into a Min-Heap?

Is a Heap a Binary Search Tree?

Where can I learn more?