Zero Sum Subarrays is the famous Data Structure and Algorithm problem asked in different interviews.
A component or section of an array is frequently referred to as a subarray. An array is a collection of variables defined by a programmer. Rather than generating several variables, the programmer might define a single array with multiple labels. Zero Sum Subarrays is the famous Data Structure and Algorithm problem asked in different interviews.
You have given an array, you have to find all the subarrays whose sum is equal to zero (0).
For Example:
Input: { 3, 4, 7, 3, 1, 3, 1, 4, 2} Output: Subarray starts from index 1 to 3. Subarray starts from index 2 to 4. Subarray starts from index 3 to 6. Subarray starts from index 6 to 8. 
A naive solution is to consider all subarrays and find their sum. If the subarray sum is equal to 0, print it.
Following code is implemented in C++.

Output:
Time Complexity: O(n3)
Space Complexity: O(1)
We can use multimap to display all subarrays in the supplied array that have a zerosum. The idea is to create an empty multimap to record the ending index of all subarrays with a certain amount. Traverse the array, keeping track of the total number of elements viewed so far. If the sum has been seen before, at least one subarray with zerosum ends at the current index. Finally, print all subarrays of this kind.
Following is a C++ code implementation.
#include <bits/stdc++.h> using namespace std;
// Function to print all subarrays with a zerosum in a given array void printAllSubarrays(int nums[ ], int n) { unordered_multimap<int, int> map;
// insert (0, 1) pair into the map to handle the case when // subarray with zerosum starts from index 0 map.insert(pair<int, int>(0, 1));
int sum = 0;
for (int i = 0; i < n; i++) { sum += nums[i];
// if the sum is seen before, there exists at least one subarray with sum zero. if (map.find(sum) != map.end()) { auto it = map.find(sum);
// find all subarrays with the same sum while (it != map.end() && it>first == sum) { cout << "Subarray starts from index " << it>second + 1 << " to " << i << ".\"; it++; } }
// insert (sum so far, current index) pair into multimap map.insert(pair<int, int>(sum, i)); } }
int main() { int nums[ ] = { 6, 3, 1, 3, 4, 2, 2, 4, 6, 12, 7 }; int n = sizeof(nums)/sizeof(nums[0]);
printAllSubarrays(nums, n);
return 0; } 
Output:
Time Complexity: O(n2)
Space Complexity: O(n)
A contiguous subsequence of a list S is one that consists of S's consecutive entries. 15 30, 10 is a continuous subsequence if S is {5, 15, 30, 10, 5, 40, 10}.
A component or section of an array is frequently referred to as a subarray. An array is a collection of variables defined by a programmer.
A subarray or substring must be contiguous, while a subsequence does not have to be. That is, subsequences do not have to appear in the same order as the main sequences.
The full array itself is a subarray of itself. An empty array is a subarray of any array.
In this article we had discussed the entire detailed explanation of Zero Sum Subarray. We had solved the problem in 2 different approaches. We also learnt the time and space complexity of both the approaches.
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