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

Find Length of Largest Subarray with 0 Sum using Hash Map Optimal Solution

Arrays

Contents

ProblemExamplesVisualizationSolutionAlgorithmCodeTimeSpace

Problem Statement❯

Given an array of integers (which may contain both positive and negative numbers), your task is to find the length of the longest contiguous subarray whose elements sum up to 0.

  • The subarray must consist of consecutive elements.
  • The array may contain positive numbers, negative numbers, and zeros.
  • If no such subarray exists, return 0.

Examples❯

Input Array Output Description
[1, 2, -3, 3, -1, -2] 6 The entire array sums to 0
[15, -2, 2, -8, 1, 7, 10, 23] 5 Subarray [-2, 2, -8, 1, 7] has sum 0
[1, 2, 3] 0 No subarray has 0 sum
[0, 0, 0, 0] 4 All elements are 0, full array is valid
[4, -1, -3, 1, 2] 5 Entire array has sum 0
[1] 0 Single element not equal to 0
[0] 1 Single 0 is a valid subarray
[] 0 Empty array, no subarrays

Visualization Player

Solution❯

To find the longest subarray with sum 0, we need to understand how the prefix sum (running total) can help us track when a subarray cancels itself out.

We traverse the array from left to right and calculate the sum of elements up to each index—this is called the prefix sum. At any point, if the same prefix sum appears again, it means the subarray between those two indices has a sum of 0.

Let’s understand this with different situations:

  • Case 1: Prefix sum becomes 0 at index i
    This means the subarray from index 0 to i itself has a sum of 0. So we update the maximum length to i + 1.
  • Case 2: Prefix sum repeats
    If the current prefix sum was seen before at index j, it means the elements between index j+1 and the current index cancel out to 0. The length of this subarray is i - j.
  • Case 3: Prefix sum is seen for the first time
    We store it in a map with its index, so that if it repeats later, we can calculate the subarray length.
  • Case 4: No 0 sum subarray exists
    In this case, no prefix sum ever repeats, and the sum is never 0. So the answer remains 0.
  • Case 5: Entire array has sum 0
    This happens when the prefix sum is 0 at the last index. Then the whole array is the longest valid subarray.
  • Case 6: Array with all zeros
    Every prefix sum is 0 here, so we always get subarrays with 0 sum. The longest one is the entire array.

This approach works well because we don’t have to check every possible subarray. Instead, we use a Hash Map to remember where each prefix sum first appeared and use that to quickly calculate lengths of potential zero-sum subarrays. This gives us a very efficient O(n) time solution.

Algorithm Steps❯

  1. Given an array arr of size n.
  2. Initialize an empty Hash Map to store prefix sums and their first occurrence index.
  3. Initialize variables: max_len = 0 and prefix_sum = 0.
  4. Traverse the array:
  5. → Add the current element to prefix_sum.
  6. → If prefix_sum == 0, update max_len = current index + 1.
  7. → If prefix_sum already exists in the map, update max_len as the maximum of current max_len and current index - first occurrence index.
  8. → Else, store prefix_sum with the current index in the map.
  9. Return max_len.

Code

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

    for i, num in enumerate(arr):
        prefix_sum += num

        if prefix_sum == 0:
            max_len = i + 1
        elif prefix_sum in prefix_map:
            max_len = max(max_len, i - prefix_map[prefix_sum])
        else:
            prefix_map[prefix_sum] = i

    return max_len

# Sample Input
arr = [15, -2, 2, -8, 1, 7, 10, 23]
print("Length of Largest Subarray with 0 Sum:", max_len_zero_sum_subarray(arr))

Time Complexity❯

CaseTime ComplexityExplanation
Best CaseO(n)In the best case, we traverse the array once and find subarrays summing to 0 early, updating the maximum length efficiently.
Average CaseO(n)The algorithm runs in linear time by computing the prefix sum and checking/recording it in the hash map in constant time for each element.
Worst CaseO(n)Even in the worst case, we perform a single pass through the array, and all hash map operations (insertion, lookup) are constant time on average.

Space Complexity❯

O(n)

Explanation: In the worst case, all prefix sums may be unique, requiring storage of each sum and its index in the hash map.