Binary TreesBinary Trees36
  1. 1Preorder Traversal of a Binary Tree using Recursion
  2. 2Preorder Traversal of a Binary Tree using Iteration
  3. 3Inorder Traversal of a Binary Tree using Recursion
  4. 4Inorder Traversal of a Binary Tree using Iteration
  5. 5Postorder Traversal of a Binary Tree Using Recursion
  6. 6Postorder Traversal of a Binary Tree using Iteration
  7. 7Level Order Traversal of a Binary Tree using Recursion
  8. 8Level Order Traversal of a Binary Tree using Iteration
  9. 9Reverse Level Order Traversal of a Binary Tree using Iteration
  10. 10Reverse Level Order Traversal of a Binary Tree using Recursion
  11. 11Find Height of a Binary Tree
  12. 12Find Diameter of a Binary Tree
  13. 13Find Mirror of a Binary Tree
  14. 14Left View of a Binary Tree
  15. 15Right View of a Binary Tree
  16. 16Top View of a Binary Tree
  17. 17Bottom View of a Binary Tree
  18. 18Zigzag Traversal of a Binary Tree
  19. 19Check if a Binary Tree is Balanced
  20. 20Diagonal Traversal of a Binary Tree
  21. 21Boundary Traversal of a Binary Tree
  22. 22Construct a Binary Tree from a String with Bracket Representation
  23. 23Convert a Binary Tree into a Doubly Linked List
  24. 24Convert a Binary Tree into a Sum Tree
  25. 25Find Minimum Swaps Required to Convert a Binary Tree into a BST
  26. 26Check if a Binary Tree is a Sum Tree
  27. 27Check if All Leaf Nodes are at the Same Level in a Binary Tree
  28. 28Lowest Common Ancestor (LCA) in a Binary Tree
  29. 29Solve the Tree Isomorphism Problem
  30. 30Check if a Binary Tree Contains Duplicate Subtrees of Size 2 or More
  31. 31Check if Two Binary Trees are Mirror Images
  32. 32Calculate the Sum of Nodes on the Longest Path from Root to Leaf in a Binary Tree
  33. 33Print All Paths in a Binary Tree with a Given Sum
  34. 34Find the Distance Between Two Nodes in a Binary Tree
  35. 35Find the kth Ancestor of a Node in a Binary Tree
  36. 36Find All Duplicate Subtrees in a Binary Tree
GraphsGraphs46
  1. 1Breadth-First Search in Graphs
  2. 2Depth-First Search in Graphs
  3. 3Number of Provinces in an Undirected Graph
  4. 4Connected Components in a Matrix
  5. 5Rotten Oranges Problem - BFS in Matrix
  6. 6Flood Fill Algorithm - Graph Based
  7. 7Detect Cycle in an Undirected Graph using DFS
  8. 8Detect Cycle in an Undirected Graph using BFS
  9. 9Distance of Nearest Cell Having 1 - Grid BFS
  10. 10Surrounded Regions in Matrix using Graph Traversal
  11. 11Number of Enclaves in Grid
  12. 12Word Ladder - Shortest Transformation using Graph
  13. 13Word Ladder II - All Shortest Transformation Sequences
  14. 14Number of Distinct Islands using DFS
  15. 15Check if a Graph is Bipartite using DFS
  16. 16Topological Sort Using DFS
  17. 17Topological Sort using Kahn's Algorithm
  18. 18Cycle Detection in Directed Graph using BFS
  19. 19Course Schedule - Task Ordering with Prerequisites
  20. 20Course Schedule 2 - Task Ordering Using Topological Sort
  21. 21Find Eventual Safe States in a Directed Graph
  22. 22Alien Dictionary Character Order
  23. 23Shortest Path in Undirected Graph with Unit Distance
  24. 24Shortest Path in DAG using Topological Sort
  25. 25Dijkstra's Algorithm Using Set - Shortest Path in Graph
  26. 26Dijkstra’s Algorithm Using Priority Queue
  27. 27Shortest Distance in a Binary Maze using BFS
  28. 28Path With Minimum Effort in Grid using Graphs
  29. 29Cheapest Flights Within K Stops - Graph Problem
  30. 30Number of Ways to Reach Destination in Shortest Time - Graph Problem
  31. 31Minimum Multiplications to Reach End - Graph BFS
  32. 32Bellman-Ford Algorithm for Shortest Paths
  33. 33Floyd Warshall Algorithm for All-Pairs Shortest Path
  34. 34Find the City With the Fewest Reachable Neighbours
  35. 35Minimum Spanning Tree in Graphs
  36. 36Prim's Algorithm for Minimum Spanning Tree
  37. 37Disjoint Set (Union-Find) with Union by Rank and Path Compression
  38. 38Kruskal's Algorithm - Minimum Spanning Tree
  39. 39Minimum Operations to Make Network Connected
  40. 40Most Stones Removed with Same Row or Column
  41. 41Accounts Merge Problem using Disjoint Set Union
  42. 42Number of Islands II - Online Queries using DSU
  43. 43Making a Large Island Using DSU
  44. 44Bridges in Graph using Tarjan's Algorithm
  45. 45Articulation Points in Graphs
  46. 46Strongly Connected Components using Kosaraju's Algorithm

Heaps Technique in DSA | Max Heap, Min Heap, and Applications

Heaps in a Nutshell

  • A complete binary tree where each parent satisfies a specific property compared to its children.
  • Supports efficient insertion, deletion, and extraction of minimum or maximum element.
  • Commonly used in priority queues and algorithms like Dijkstra and Heapsort.

What is the Heap Technique?

The Heap Technique is a method of organizing elements in a binary tree structure where the parent node always maintains a relationship with its children based on either:

  • Max Heap: Parent ≥ Children
  • Min Heap: Parent ≤ Children

Heaps are typically implemented as arrays and are ideal for scenarios requiring repeated access to the largest or smallest element.

Types of Heaps

  • Max Heap: The root is the maximum. Every parent is greater than or equal to its children.
  • Min Heap: The root is the minimum. Every parent is less than or equal to its children.

Common Heap Operations

  • Insert: Add a new element while maintaining the heap property.
  • Delete: Remove the top element (max or min), then re-heapify.
  • Heapify: Convert an array into a valid heap.

Pseudocode: Inserting into a Heap

// Insert value into heap and bubble it up
function insert(heap, value):
    heap.append(value)
    index = heap.length - 1

    while index > 0:
        parent = floor((index - 1) / 2)
        if heap[parent] < heap[index]:  // Max Heap
            swap(heap[parent], heap[index])
            index = parent
        else:
            break

Pseudocode: Heapify an Array

// Heapify subtree rooted at index 'i' for Max Heap
function heapify(arr, n, i):
    largest = i
    left = 2 * i + 1
    right = 2 * i + 2

    if left < n and arr[left] > arr[largest]:
        largest = left
    if right < n and arr[right] > arr[largest]:
        largest = right

    if largest != i:
        swap(arr[i], arr[largest])
        heapify(arr, n, largest)

Pseudocode: Build Max Heap from Unordered Array

function buildMaxHeap(arr):
    n = arr.length
    for i from floor(n/2) - 1 down to 0:
        heapify(arr, n, i)

Applications of Heap Technique

  • Priority Queue: Heaps allow you to always access the highest or lowest priority item in O(1) and insert/delete in O(log n).
  • Heapsort: A sorting algorithm using the heap property to sort in O(n log n) time.
  • Top-K Elements: Min heap (for top K largest) or Max heap (for top K smallest).
  • Dijkstra’s Shortest Path: Uses a min heap (priority queue) to efficiently fetch the closest node.
  • Median in a Stream: Maintain a max heap and min heap to find running median in O(log n).

Example: Find K Largest Elements

Problem: Given an array, return the K largest elements in sorted order.

Solution: Use a Min Heap of size K. Iterate through the array, and:

  • If heap size < K, insert element.
  • If element > min of heap, replace min and re-heapify.

Pseudocode

function kLargestElements(arr, K):
    minHeap = new MinHeap()

    for num in arr:
        if minHeap.size() < K:
            minHeap.insert(num)
        else if num > minHeap.peek():
            minHeap.pop()
            minHeap.insert(num)

    return minHeap.toSortedArray()

Time and Space Complexity

  • Insert/Delete: O(log n)
  • Access Top: O(1)
  • Build Heap: O(n)

When to Use Heap Technique

  • You need to repeatedly access the max/min element.
  • Maintaining a dynamic dataset with changing priorities.
  • Solving problems involving scheduling, ranking, or optimization.

Advantages and Disadvantages

Advantages

  • Efficient priority access with log-time updates.
  • Simple array-based implementation.
  • Supports partial sorting (top-k elements).

Disadvantages

  • Does not support fast arbitrary search (like a HashMap).
  • Limited to scenarios where order is based on priority comparisons only.

Conclusion

The Heap Technique is vital in DSA for building efficient solutions to problems that require order-based access. Whether you're sorting, managing priorities, or scheduling, heaps offer a structured and performant approach to maintaining maximum or minimum values dynamically.