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Min and max heap

Difference between min-heap and max-heap.

Min and max heap

In a min-heap each node is smaller than or equal to its children; the root is the smallest. In a max-heap each node is larger than or equal to its children; the root is the largest.

A heap is stored as a complete binary tree in an array. Parent (i-1)//2, left child 2i+1, right child 2i+2.

Min-heap is used to get the smallest element quickly in a priority queue; max-heap for the largest.

Parent-child

In the array representation, the parent of node at index i is (i-1)//2, left child 2i+1, right child 2i+2.

The root is arr[0] and has no parent. Leaves are in the second half of the array (i ≥ n//2).

These formulas give parent-child relations in O(1); no pointers needed.

Practice Check min-heap

Write is_min_heap(arr). Each child must be >= parent. Print True with print(is_min_heap([1, 3, 2, 5, 4])).

Starter code

solution.py
def is_min_heap(arr):
    # Check min-heap

Sample solution

solution.py
def is_min_heap(arr):
    # Check min-heap
    for i in range(1, len(arr)):
        if arr[(i - 1) // 2] > arr[i]:
            return False
    return True
print(is_min_heap([1, 3, 2, 5, 4]))

Expected output

True

Questions and answers

Review the lesson questions together with their answers. To test yourself, solve the lesson interactively.

1 What is the root in a min-heap?

  • The largest
  • The smallest element Correct answer
  • The median
  • Random

Explanation: The smallest element

2 Parent

Question 
parent = (i - 1) // ____
Answer 
parent = (i - 1) // 2

Explanation: 2 is right.

3 Min and max heap: match the terms

Term Meaning
Min-heap Root smallest
Max-heap Root largest
Parent (i-1)//2
Left child 2i+1

All lessons in Intermediate

1 Merge sort

  1. Divide and conquer
  2. Merge operation
  3. Full merge sort
  4. Summary - Merge sort

2 Quick sort

  1. Pivot selection
  2. Partitioning
  3. Recursive quick sort
  4. Summary - Quick sort

3 Heap sort

  1. What is a heap?
  2. Heapify
  3. Build heap and sort
  4. Summary - Heap sort

4 Counting sort

  1. Counting idea
  2. Count array
  3. Output array
  4. Summary - Counting sort

5 Radix sort

  1. Radix idea
  2. Digit pass
  3. Stable sub-sort
  4. Summary - Radix sort

6 Sorting project

  1. Project: Overview
  2. Score array
  3. Apply merge sort
  4. Print statistics

7 Tree

  1. What is a tree?
  2. Node and edge
  3. Binary tree
  4. Summary - Trees

8 Binary search tree

  1. BST rule
  2. BST insert
  3. BST search
  4. Summary - BST

9 AVL tree

  1. Balanced tree
  2. Rotation
  3. Balance after insert
  4. Summary - AVL tree

10 Heap

  1. Min and max heap
  2. Insert
  3. Extract
  4. Summary - Heap

11 Priority queue

  1. What is a priority queue?
  2. Heap-based implementation
  3. Push and pop
  4. Summary - Priority queue

12 Data structures project

  1. Project: Overview
  2. Undo stack
  3. Pending queue
  4. Print the state

13 Graph basics

  1. What is a graph?
  2. Adjacency list
  3. Adjacency matrix
  4. Summary - Graph

14 Breadth-first search

  1. BFS idea
  2. Using a queue
  3. Marking visited
  4. Summary - BFS

15 Depth-first search

  1. DFS idea
  2. Stack or recursion
  3. Backtracking
  4. Summary - DFS

16 Greedy algorithms

  1. Greedy approach
  2. Coin change
  3. Greedy limits
  4. Summary - Greedy

17 Divide and conquer

  1. Three steps
  2. Recursive structure
  3. Master theorem
  4. Summary - Divide and conquer

18 Backtracking

  1. What is backtracking?
  2. State tree
  3. Pruning
  4. Summary - Backtracking

19 Graph project

  1. Project: Overview
  2. City graph
  3. BFS for reachability
  4. Print the result

20 Intermediate final

  1. Challenge 1
  2. Challenge 2
  3. Challenge 3
  4. Challenge 4