Heap Data Structure

Data Structure and Algorithms Course
Practice Problems on Heap
Recent articles on Heap !

What is Heap Data Structure?

A Heap is a special Tree-based data structure in which the tree is a complete binary tree.

Operations of Heap Data Structure:

• Heapify: a process of creating a heap from an array.
• Insertion: process to insert an element in existing heap time complexity O(log N).
• Deletion: deleting the top element of the heap or the highest priority element, and then organizing the heap and returning the element with time complexity O(log N).
• Peek: to check or find the most prior element in the heap, (max or min element for max and min heap).

Types of Heap Data Structure

Generally, Heaps can be of two types:

1. Max-Heap: In a Max-Heap the key present at the root node must be greatest among the keys present at all of it’s children. The same property must be recursively true for all sub-trees in that Binary Tree.
2. Min-Heap: In a Min-Heap the key present at the root node must be minimum among the keys present at all of it’s children. The same property must be recursively true for all sub-trees in that Binary Tree.

Applications, Advantages and Disadvantages of Heap

Popular Articles on Heap :

1. Binary Heap
2. Time Complexity of building a heap
3. Applications of Heap Data Structure
4. Binomial Heap
5. Fibonacci Heap
6. Leftist Heap
7. K-ary Heap
8. Heap Sort
9. Iterative Heap Sort
10. K’th Largest Element in an array
11. K’th Smallest/Largest Element in Unsorted Array | Set 1
12. Sort an almost sorted array/
13. Tournament Tree (Winner Tree) and Binary Heap
14. Check if a given Binary Tree is Heap
15. How to check if a given array represents a Binary Heap?
16. Connect n ropes with minimum cost
17. Design an efficient data structure for given operations
18. Merge k sorted arrays | Set 1
19. Merge Sort Tree for Range Order Statistics
20. Sort numbers stored on different machines
21. Smallest Derangement of Sequence
22. Largest Derangement of a Sequence
23. K maximum sum combinations from two arrays
24. Maximum distinct elements after removing k elements
25. Maximum difference between two subsets of m elements
26. Height of a complete binary tree (or Heap) with N nodes
27. Heap Sort for decreasing order using min heap
28. Print all nodes less than a value x in a Min Heap.
29. Median of Stream of Running Integers using STL
30. Largest triplet product in a stream
31. Find k numbers with most occurrences in the given array
32. Convert BST to Min Heap
33. Merge two binary Max Heaps
34. K-th Largest Sum Contiguous Subarray
35. Minimum product of k integers in an array of positive Integers
36. Leaf starting point in a Binary Heap data structure
37. Why is Binary Heap Preferred over BST for Priority Queue?
38. Convert min Heap to max Heap
39. Given level order traversal of a Binary Tree, check if the Tree is a Min-Heap
40. Rearrange characters in a string such that no two adjacent are same
41. Implementation of Binomial Heap
42. Array Representation Of Binary Heap
43. Sum of all elements between k1’th and k2’th smallest elements
44. Minimum sum of two numbers formed from digits of an array
45. K’th largest element in a stream
46. k largest(or smallest) elements in an array | added Min Heap method
47. Median in a stream of integers (running integers)
48. Sort a nearly sorted (or K sorted) array

Misc :

• Why is Binary Heap Preferred over BST for Priority Queue?
• Heap in C++ STL | make_heap(), push_heap(), pop_heap(), sort_heap(), is_heap, is_heap_until()
  
• Heap in Python (Using Heapq module)
• Where is Heap Sort used practically?

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