# Minimum number of array elements from either ends required to be subtracted from X to reduce X to 0

Minimum number of array elements from either ends required to be subtracted from X to reduce X to 0

Given an array nums[] and an integer X, the task is to reduce X to 0 by removing either the leftmost or the rightmost array elements and subtracting its value from X, minimum number of times. If it’s possible to reduce X to 0, print the count of operations required. Otherwise, return -1.

Examples:

Input: nums[] = {3,2,20,1,1,3}, X = 10Output: 5Explanation: X (= 10) – 3 – 1 – 1 – 3 – 2 = 0. Therefore, the number of operations required is 5.

Input: nums[] = {1, 1, 4, 2, 3}, X = 5Output: 2Explanation: X (= 5) – 3 – 2 = 0. Therefore, the number of operations required is 2.

Approach: The given problem can be solved using Two Pointers technique. Follow the steps below to solve the problem.

Maintain two pointers left and right, pointing to the ends of the left and right subarrays excluded from X.

Initialize left to consider the entire array, and right to include nothing.

Therefore, reduce X by the sum of the array.

Now, iterate until left reaches the front of the array.

If the sum of the left and the right subarrays exceeds X (i.e. X < 0), shift left by an index to the left and increase X that element.
If the sum of the left and the right subarrays is less than X (i.e. X > 0), shift right pointer by an index to the left and reduce X by that element.

If X is found to be 0 at any point, update the minimum number of operations required.

Print the minimum number of operations required.

Below is the implementation of the above approach:

Python3

import math

def minOperations(nums, x):

if sum(nums) < x:
return -1
ans = math.inf
l, r = len(nums)-1, len(nums)
x -= sum(nums)
while l >= 0:

if x 0:

r -= 1

x -= nums[r]

if x == 0:

ans = min(ans, (l+1) + (len(nums)-r))

return ans if ans < math.inf else -1
nums = [1, 1, 4, 2, 3]
x = 5
print(minOperations(nums, x))
Time Complexity: O(N)Auxiliary Space: O(1)
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