 # 724. Find Pivot Index

Updated: 2023-09-01 LeetCode problem

## Problem Statement

Given an array of integers nums, the task is to calculate the pivot index of this array. The pivot index is defined as the index where the sum of all the numbers strictly to the left of the index is equal to the sum of all the numbers strictly to the index’s right. If no such index exists, return -1.

## Naive Solution

A naive approach would be to iterate over each index and for each index, calculate the sum of elements to the left and right of the index. If the sums are equal, return the index. However, this approach has a time complexity of O(n^2) which makes it inefficient for larger inputs.

## Hints & Tips

A more optimized solution would use the prefix and suffix sum concept. Prefix sum is the sum of all elements to the left of the index, and suffix sum is the sum of all elements to the right of the index. We can calculate these sums in O(n) time and use them to find the pivot index.

## Approach

We will calculate the total sum of the array first.

Then, we will initialize a variable left_sum to keep track of the sum of elements to the left of the current index.

As we iterate over each index, we will update the total sum by subtracting the current element, which will give us the right sum. We will then check if left_sum is equal to the right sum (total sum - left_sum - current element).

If they are equal, we return the index.

After checking, we will update the left_sum by adding the current element.

## Steps

1. Calculate the total sum of the array.
2. Initialize a variable left_sum to 0.
3. Iterate over each index in the array.
1. Update the total sum by subtracting the current element.
2. Check if left_sum is equal to the right sum (total sum - left_sum - current element). If true, return the index.
3. Update the left_sum by adding the current element.
4. If no pivot index is found, return -1.

## Solution

def pivotIndex(nums):
total_sum = sum(nums)
left_sum = 0

for i, num in enumerate(nums):
total_sum -= num
if left_sum == total_sum:
return i
left_sum += num

return -1