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 exists in the hash table, that means we have subarray(s) present with 0 sum that ends at current index.
- Insert current sum into the hash table
Below are implementation of above idea –
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
This article is contributed by Aditya Goel. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to firstname.lastname@example.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
- Differences between number of increasing subarrays and decreasing subarrays in k sized windows
- Sum of XOR of all subarrays
- Sum of all Subarrays | Set 1
- Number of subarrays with odd sum
- Sum of bitwise OR of all subarrays
- Number of subarrays having sum less than K
- Maximize the number of subarrays with XOR as zero
- Find number of subarrays with even sum
- Maximum of all Subarrays of size k using set in C++ STL
- Generating subarrays using recursion
- Sum of minimum elements of all subarrays
- Number of subarrays with given product
- Number of subarrays having sum of the form k^m, m >= 0
- Sum of Bitwise-OR of all subarrays of a given Array | Set 2
- Queries on XOR of XORs of all subarrays
Improved By : rachana soma