Binary TreesBinary Trees36

  1. 1Preorder Traversal of a Binary Tree using Recursion
  2. 2Preorder Traversal of a Binary Tree using Iteration
  3. 3Postorder Traversal of a Binary Tree Using Recursion
  4. 4Postorder Traversal of a Binary Tree using Iteration
  5. 5Level Order Traversal of a Binary Tree using Recursion
  6. 6Level Order Traversal of a Binary Tree using Iteration
  7. 7Reverse Level Order Traversal of a Binary Tree using Iteration
  8. 8Reverse Level Order Traversal of a Binary Tree using Recursion
  9. 9Find Height of a Binary Tree
  10. 10Find Diameter of a Binary Tree
  11. 11Find Mirror of a Binary Tree - Todo
  12. 12Inorder Traversal of a Binary Tree using Recursion
  13. 13Inorder Traversal of a Binary Tree using Iteration
  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

Find Longest Subarray with Given Sum using HashMap - Optimal Solution



Problem Statement

Given an array of integers (which may include positive numbers, negative numbers, or zeros) and a target sum k, your task is to find the length of the longest contiguous subarray that adds up exactly to k.

The subarray must be continuous, and if multiple such subarrays exist, return the length of the longest one.

If no such subarray exists, return 0.

Examples

Input ArrayTarget Sum (k)Longest Subarray LengthDescription
[1, 2, 3, -2, 5]54The subarray [2, 3, -2, 2] or [1, 2, 3, -1] gives sum 5
[10, -10, 10, -10, 10]04The subarray [10, -10, 10, -10] gives sum 0
[5, 1, -1, 2, 3]105The entire array sums to 10
[1, 2, 3]70No subarray has sum 7
[0, 0, 0, 0]04All elements are 0, entire array sums to 0
[3, 4, -7, 1, 2]03The subarray [3, 4, -7] gives sum 0
[]00Empty array, so no subarray exists
[-2, -1, 2, 1]03The subarray [-1, 2, -1] or [-2, -1, 2, 1] gives sum 0

Solution

To find the longest subarray with a given sum k, especially when the array can have both positive and negative integers, we use a strategy based on prefix sums and a hash map.

Here’s the idea: As we traverse the array, we keep track of the cumulative sum (also called prefix sum) up to the current index. For each prefix sum, we store the first index where it occurred in a hash map.

Understanding the Intuition

Suppose at index i, the prefix sum is curr_sum. If there exists a prefix sum at an earlier index j such that:

curr_sum - prefix_sum[j] = k

then the subarray from index j+1 to i has a sum of k. By storing the first occurrence of each prefix sum in a map, we can look this up quickly and determine the length of such subarrays.

What Happens in Different Cases?

  • Exact match from the start: If the prefix sum itself becomes k, then the subarray from index 0 to i is valid. We track this using i + 1.
  • Zero sum cases: When the target sum is 0, the logic still works because the prefix sum might repeat, and the difference is 0.
  • All elements are zeros: If the entire array is zeros and the target is also zero, the whole array is the valid longest subarray.
  • No matching sum found: If we go through the array and never find a prefix sum that helps us build a valid subarray with sum = k, we return 0.
  • Empty array: If the array is empty, there’s no subarray at all, so the answer is 0.

Using this method ensures that we consider all possible subarrays without checking each one manually, and we do so efficiently with a time complexity of O(n).

This solution works great even with negative numbers, unlike sliding window techniques that require non-negative elements.

Visualization

Algorithm Steps

  1. Given an array arr of integers (positive, negative, or zero) and a target sum k.
  2. Initialize prefix_sum = 0, max_len = 0, and an empty hash_map to store the first occurrence of each prefix sum.
  3. Iterate through the array with index i:
  4. → Add arr[i] to prefix_sum.
  5. → If prefix_sum == k, update max_len = i + 1.
  6. → If prefix_sum - k exists in hash_map, calculate the length and update max_len accordingly.
  7. → If prefix_sum is not in hash_map, store prefix_sum with index i.
  8. Return max_len after the loop ends.

Code

Python
JavaScript
Java
C++
C
def longest_subarray_with_sum_k(arr, k):
    prefix_sum = 0
    max_len = 0
    prefix_map = {}

    for i in range(len(arr)):
        prefix_sum += arr[i]

        if prefix_sum == k:
            max_len = i + 1

        if (prefix_sum - k) in prefix_map:
            max_len = max(max_len, i - prefix_map[prefix_sum - k])

        if prefix_sum not in prefix_map:
            prefix_map[prefix_sum] = i

    return max_len

# Sample Input
arr = [1, -1, 5, -2, 3]
k = 3
print("Length of Longest Subarray:", longest_subarray_with_sum_k(arr, k))

Time Complexity

CaseTime ComplexityExplanation
Best CaseO(n)Each element is processed once, and HashMap lookups and insertions are O(1) on average. In the best case, the prefix sum quickly matches the target early in the array.
Average CaseO(n)The algorithm traverses the entire array once, using a HashMap for fast prefix sum lookups and updates.
Average CaseO(n)Even in the worst case, the algorithm completes a single pass over the array, with constant-time operations per element.

Space Complexity

O(n)

Explanation: In the worst case, each prefix sum is unique and stored in the HashMap, resulting in O(n) additional space.



Welcome to ProgramGuru

Sign up to start your journey with us

Support ProgramGuru.org

Mention your name, and programguru.org in the message. Your name shall be displayed in the sponsers list.

PayPal

UPI

PhonePe QR

MALLIKARJUNA M