724. Find Pivot Index

Problem

Given an array of integers nums, write a method that returns the "pivot" index of this array.

We define the pivot index as the index where the sum of all the numbers to the left of the index is equal to the sum of all the numbers to the right of the index.

If no such index exists, we should return -1. If there are multiple pivot indexes, you should return the left-most pivot index.

Example 1:

Input: nums = [1,7,3,6,5,6]
Output: 3
Explanation:
The sum of the numbers to the left of index 3 (nums[3] = 6) is equal to the sum of numbers to the right of index 3.
Also, 3 is the first index where this occurs.

Example 2:

Input: nums = [1,2,3]
Output: -1
Explanation:
There is no index that satisfies the conditions in the problem statement.

Constraints:

• The length of nums will be in the range [0, 10000].
• Each element nums[i] will be an integer in the range [-1000, 1000].

Problem Summary

Given an integer array nums, write a method that returns the array's "pivot index". We define the pivot index of an array as follows: the sum of all elements to the left of the pivot index is equal to the sum of all elements to the right. If the array has no pivot index, we should return -1. If the array has multiple pivot indexes, we should return the one closest to the left.

Solution Approach

• In the array, find a number such that the sum of the numbers to its left is equal to the sum of the numbers to its right. If it exists, return the index of this number; otherwise, return -1.
• There is an equation here; we only need to satisfy this equation to meet the condition: leftSum + num[i] = sum - leftSum => 2 * leftSum + num[i] = sum.
• The problem states that if multiple indexes exist, return the leftmost one, so compute the sum from the left rather than from the right.

Code

package leetcode

// 2 * leftSum + num[i] = sum
// Time: O(n)
// Space: O(1)
func pivotIndex(nums []int) int {
	if len(nums) <= 0 {
		return -1
	}
	var sum, leftSum int
	for _, num := range nums {
		sum += num
	}
	for index, num := range nums {
		if leftSum*2+num == sum {
			return index
		}
		leftSum += num
	}
	return -1
}