Largest Subarray with 0 Sum

In computer science and algorithms, finding the largest subarray with a sum of 0 is a classic problem. Given an array of integers, our task is to identify the longest contiguous subarray whose elements sum up to 0. This problem finds applications in various domains, including data analysis, finance, and gaming. In this article, we will discuss an efficient approach to solve this problem, accompanied by the code, time complexity, and space complexity analysis.

Approach

To solve the “Largest Subarray with 0 Sum” problem, we can utilize the concept of prefix sums. We maintain a running sum of the elements in the array while traversing it from left to right. If we encounter the same sum again during traversal, it implies that the subarray between the previous occurrence and the current occurrence has a sum of 0.

Implementation

Below is the Python code demonstrating the implementation of the above approach:

def largest_subarray_with_zero_sum(arr):
 sum_map = {0: -1} # Store sum and its index as key-value pairs
 max_length = 0
 curr_sum = 0
for idx, num in enumerate(arr):
 curr_sum += num
if curr_sum in sum_map:
 # Calculate the length of the subarray with zero sum
 max_length = max(max_length, idx - sum_map[curr_sum])
else:
 # If the sum is not in the map, store it with the current…