Find if there is a subarray with 0 sum

Given an array of positive and negative numbers, find if there is a subarray (of size at-least one) with 0 sum.

Examples:

Input: {4, 2, -3, 1, 6}
Output: true 
There is a subarray with zero sum from index 1 to 3.

Input: {4, 2, 0, 1, 6}
Output: true 
There is a subarray with zero sum from index 2 to 2.

Input: {-3, 2, 3, 1, 6}
Output: false
There is no subarray with zero sum.

We strongly recommend to minimize the browser and try this yourself first.

A simple solution is to consider all subarrays one by one and check the sum of every subarray. We can run two loops: the outer loop picks a starting point i and the inner loop tries all subarrays starting from i (See this for implementation). Time complexity of this method is O(n2).

We can also use hashing. The idea is to iterate through the array and for every element arr[i], calculate sum of elements form 0 to i (this can simply be done as sum += arr[i]). If the current sum has been seen before, then there is a zero sum array. Hashing is used to store the sum values, so that we can quickly store sum and find out whether the current sum is seen before or not.

Following is Java implementation of the above approach.

// A Java program to find if there is a zero sum subarray import java.util.HashMap;    class ZeroSumSubarray {           // Returns true if arr[] has a subarray with sero sum     static Boolean printZeroSumSubarray(int arr[])     {         // Creates an empty hashMap hM         HashMap<Integer, Integer> hM = new HashMap<Integer, Integer>();                   // Initialize sum of elements         int sum = 0;                          // Traverse through the given array         for (int i = 0; i < arr.length; i++)         {               // Add current element to sum             sum += arr[i];                           // Return true in following cases             // a) Current element is 0             // b) sum of elements from 0 to i is 0             // c) sum is already present in hash map             if (arr[i] == 0 || sum == 0 || hM.get(sum) != null)                                           return true;                           // Add sum to hash map             hM.put(sum, i);         }                      // We reach here only when there is no subarray with 0 sum         return false;     }                  public static void main(String arg[])     {         int arr[] = {4, 2, -3, 1, 6};         if (printZeroSumSubarray(arr))             System.out.println("Found a subarray with 0 sum");         else             System.out.println("No Subarray with 0 sum");                }            }

Output:

Found a subarray with 0 sum