**Problem:** Given an array (positive and negative) and an integer, find the subarray with sum is equal to the given integer.** **

**Note: **This problem is an extension of – find the subarray with sum to a Given Value, in which arrays with negative numbers are not handled.

**Example:**

Given input: [25, 12, -14, 22, -19, 15, -10, 23] K = -11. Subarray with sum = -11 Output: [-14 22 -19 ] Given input: [10, 0, -1, 20, 25, 30] K = 45 Subarray with sum = 45 Output: [20 25]

**Approach: **

Given : input[] and K

**Idea:** We need to find subarray input[a, b] – sum of elements from index a to b = K.

input[a, b] = input[0, b] – input[0, a-1]

**Steps:**

- Initialize a
**map**which will store the sum up to element at the current index and current index as a value. - Initialize i = 0, j = -1.
- Initialize curr_sum = 0, keep adding elements during iteration.
- Iterate through array and for currenct index
**n**,- curr_sum = curr_sum + input[
**n**]. - Check if curr_sum = K, we have found a subarray and means all the elements till the current element are included, do
**j = n**, and break the loop. - Check if the map contains
**curr_sum – K**, if yes then we have found a subarray, get the**index**from the map for key curr_sum – K and do**i = index + 1**and**j = n**, the elements from index**i**to**j**will have sum = K.

- curr_sum = curr_sum + input[
- Check if j!=-1, means we have found the subarray during iteration. Print the elements from index
to index*i*. (*j*), else if j==-1 then no subarray exists with sum = K.*input[i, j]*

Time Complexity: O(N), Space Complexity: O(N)

**Complete Code:**

**Output:**

Given input: [25, 12, 14, 22, 19, 15, 10, 23] Subarray with sum = 55 14 22 19 -------------------------------- Given input: [25, 12, -14, 22, -19, 15, -10, 23] Subarray with sum = -11 -14 22 -19 -------------------------------- Given input: [10, 0, -1, 20, 25, 30] Subarray with sum = 45 20 25