Find if there is a subarray with 0 sum
Mon Feb 07 2022 15:44:47 GMT+0000 (Coordinated Universal Time)
Saved by @Uttam #java #gfg #geeksforgeeks #lecture #arrays #prefixsum #subarrays #splitarray
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 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. Input: {-3, 2, 3, 1, 6} Output: false --------------------------------------------------------------------------------------------------------- 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). The 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 the sum of elements from 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. Example : arr[] = {1, 4, -2, -2, 5, -4, 3} If we consider all prefix sums, we can notice that there is a subarray with 0 sum when : 1) Either a prefix sum repeats or 2) Or prefix sum becomes 0. Prefix sums for above array are: 1, 5, 3, 1, 6, 2, 5 Since prefix sum 1 repeats, we have a subarray with 0 sum. --------------------------------------------------------------------------------------------------------- Time Complexity of this solution can be considered as O(n) under the assumption that we have good hashing function that allows insertion and retrieval operations in O(1) time. Space Complexity: O(n) .Here we required extra space for unordered_set to insert array elements. ---------------------------------------------------------------------------------------------------------
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