Given an array, print all subarrays in the array which has sum 0.
Input: arr = [6, 3, -1, -3, 4, -2, 2, 4, 6, -12, -7] Output: Subarray found from Index 2 to 4 Subarray found from Index 2 to 6 Subarray found from Index 5 to 6 Subarray found from Index 6 to 9 Subarray found from Index 0 to 10
Related posts: Find if there is a subarray with 0 sum
A simple solution is to consider all subarrays one by one and check if sum of every subarray is equal to 0 or not. The complexity of this solution would be O(n^2).
A better approach is to use Hashing.
Do following for each element in the array
- Maintain sum of elements encountered so far in a variable (say sum).
- If current sum is 0, we found a subarray starting from index 0 and ending at index current index
- Check if current sum exists in the hash table or not.
- If current sum already exists in the hash table then it indicates that this sum was the sum of some sub-array elements arr…arr[i] and now the same sum is obtained for the current sub-array arr…arr[j] which means that the sum of the sub-array arr[i+1]…arr[j] must be 0.
- Insert current sum into the hash table
Below is a dry run of the above approach:
Below is the implementation of the above approach:
Subarray found from Index 2 to 4 Subarray found from Index 2 to 6 Subarray found from Index 5 to 6 Subarray found from Index 6 to 9 Subarray found from Index 0 to 10
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