Question

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

Examples:

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

Input: {4, 2, 0, 1, 6}
Output: true
Explanation: The third element is zero. A single element is also a sub-array.

Answer 1

The problem involves finding a subarray with a 0 sum in an array of positive and negative numbers, using rules of addition and subtraction and a cumulative sum approach.

Step-by-step explanation:

The question pertains to finding a subarray with a sum of zero within a given array of positive and negative numbers. To solve this, we apply simple rules of addition and subtraction, as described:

To find a subarray with zero sum, one commonly used approach is to calculate the cumulative sum of elements and use a hash table to track sums that have already been seen. If the cumulative sum repeats, it means that a subarray has summed to zero. This method works because if the cumulative sum up to two different indices is the same, the sum of the elements lying between those indices must be zero.