Zero-sum at the start
Input
arr = [1, -1, 3, -3, 5]
Output
4
Prefix sum becomes 0 at index 3, so subarray from index 0 to 3 has sum 0 and length 4.
Full lesson preview
Find the largest zero-sum subarray
Find the length of the longest contiguous subarray whose elements sum to zero using prefix sums and a map.
Python practice30 minHashing & SetsAdvancedLast updated March 26, 2026
Problem statement
Given an integer array arr, return the length of the longest contiguous subarray whose sum is 0. Implement an O(n) approach using a dictionary that maps prefix sums to their earliest index.
Task
Use prefix sums and a hash map to locate repeated prefix sums and compute the maximum zero-sum subarray length in O(n).
Examples
Input format
Function input: largest_zero_sum_subarray(arr) where arr is a list of integers.
Output format
Return an integer: the length of the longest contiguous subarray with sum zero. Return 0 if none exist.
Constraints
0 <= len(arr) <= 10^5, elements between -10^9 and 10^9. Aim for O(n) time and O(n) space.
Samples
Sample 1
Input
arr = [1, 2, -3, 3]
Output
3
Subarray [1,2,-3] sums to 0 and has length 3.