Min Heap in Python

Last Updated : 08 Feb, 2025

A Min-Heap is a Data Structure with the following properties.

It is a complete Complete Binary Tree.
The value of the root node must be the smallest among all its descendant nodes and the same thing must be done for its left and right sub-tree also.

Table of Content

Example of Min Heap
Min Heap Representation as an Array
Operations on Min Heap
Implementation of Min Heap in Python
Implementation of Min Heap Using Python’s heapq Library
Implementation of Min Heap using Priority Queue

The elements of a heap can be mapped into an array using the following rules:

If a node is stored at index k:

Left child is stored at index 2k + 1 (for 0-based indexing) or 2k (for 1-based indexing).
Right child is stored at index 2k + 2 (for 0-based indexing) or 2k + 1 (for 1-based indexing).

Example of Min Heap

Tree Representation:

            5                      13
          /   \                  /    \  
        10     15              16      31
       /                      /  \     /  \
     30                     41    51  100  41

Array Representation:

For the first tree:

[5, 10, 15, 30]

For the second tree:

[13, 16, 31, 41, 51, 100, 41]

Min Heap Representation as an Array

Since a Min Heap is a Complete Binary Tree, it is commonly represented using an array. In an array representation:

The root element is stored at Arr[0].
For any i-th node (at Arr[i]):
- Parent Node → Arr[(i - 1) / 2]
- Left Child → Arr[(2 * i) + 1]
- Right Child → Arr[(2 * i) + 2]

Operations on Min Heap

getMin(): It returns the root element of Min Heap. Time Complexity of this operation is O(1).
extractMin(): Removes the minimum element from MinHeap. Time Complexity of this Operation is O(Log n) as this operation needs to maintain the heap property (by calling heapify()) after removing root.
insert(): Inserting a new key takes O(Log n) time. We add a new key at the end of the tree. If new key is larger than its parent, then we don’t need to do anything. Otherwise, we need to traverse up to fix the violated heap property.

Implementation of Min Heap in Python

Please refer Min-Heap for details.

Python

class MinHeap:
    def __init__(self):
        self.a = []

    """Insert a new element into the Min Heap."""
    def insert(self, val):
        self.a.append(val)
        i = len(self.a) - 1
        while i > 0 and self.a[(i - 1) // 2] > self.a[i]:
            self.a[i], self.a[(i - 1) // 2] = self.a[(i - 1) // 2], self.a[i]
            i = (i - 1) // 2

    """Delete a specific element from the Min Heap."""
    def delete(self, value):
        i = -1
        for j in range(len(self.a)):
            if self.a[j] == value:
                i = j
                break
        if i == -1:
            return
        self.a[i] = self.a[-1]
        self.a.pop()
        while True:
            left = 2 * i + 1
            right = 2 * i + 2
            smallest = i
            if left < len(self.a) and self.a[left] < self.a[smallest]:
                smallest = left
            if right < len(self.a) and self.a[right] < self.a[smallest]:
                smallest = right
            if smallest != i:
                self.a[i], self.a[smallest] = self.a[smallest], self.a[i]
                i = smallest
            else:
                break

    """Heapify function to maintain the heap property.""" 
    def minHeapify(self, i, n):
        smallest = i
        left = 2 * i + 1
        right = 2 * i + 2

        if left < n and self.a[left] < self.a[smallest]:
            smallest = left
        if right < n and self.a[right] < self.a[smallest]:
            smallest = right
        if smallest != i:
            self.a[i], self.a[smallest] = self.a[smallest], self.a[i]
            self.minHeapify(smallest, n)

    """Search for an element in the Min Heap."""
    def search(self, element):
        for j in self.a:
            if j == element:
                return True
        return False

    def getMin(self):
        return self.a[0] if self.a else None

    def printHeap(self):
        print("Min Heap:", self.a)

# Example Usage
if __name__ == "__main__":
    h = MinHeap()
    values = [10, 7, 11, 5, 4, 13]
    for value in values:
        h.insert(value)
    h.printHeap()
    
    h.delete(7)
    print("Heap after deleting 7:", h.a)
    
    print("Searching for 10 in heap:", "Found" if h.search(10) else "Not Found")
    print("Minimum element in heap:", h.getMin())

Output

Min Heap: [4, 5, 11, 10, 7, 13]
Heap after deleting 7: [4, 5, 11, 10, 13]
Searching for 10 in heap: Found
Minimum element in heap: 4

Implementation of Min Heap Using Python’s heapq Library

Python’s heapq module implements a Min Heap by default.

Python

# Python3 program to demonstrate working of heapq

from heapq import heapify, heappush, heappop

# Creating empty heap
heap = []
heapify(heap)

# Adding items to the heap using heappush function
heappush(heap, 10)
heappush(heap, 30)
heappush(heap, 20)
heappush(heap, 400)

# printing the value of minimum element
print("Head value of heap : "+str(heap[0]))

# printing the elements of the heap
print("The heap elements : ")
for i in heap:
    print(i, end = ' ')
print("\n")

element = heappop(heap)

# printing the elements of the heap
print("The heap elements : ")
for i in heap:
    print(i, end = ' ')

Output

Head value of heap : 10
The heap elements : 
10 30 20 400 

The heap elements : 
20 30 400

Implementation of Min Heap using queue.PriorityQueue

Please refer queue.PriorityQueue for details.

Python

from queue import PriorityQueue 

q = PriorityQueue() 

# insert into queue 
q.put(10)
q.put(20) 
q.put(5) 

# remove and return 
# lowest priority item 
print(q.get()) 
print(q.get()) 

# check queue size 
print('Items in queue :', q.qsize()) 

# check if queue is empty 
print('Is queue empty :', q.empty()) 

# check if queue is full 
print('Is queue full :', q.full())

Output

5
10
Items in queue : 1
Is queue empty : False
Is queue full : False

Max Heap in Python

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Article Tags :

Practice Tags :

Min Heap in Python

Example of Min Heap

Tree Representation:

Array Representation:

Min Heap Representation as an Array

Operations on Min Heap

Implementation of Min Heap in Python

Implementation of Min Heap Using Python’s heapq Library

Implementation of Min Heap using queue.PriorityQueue

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