724.Find_Pivot_Index(Easy).md

724. Find Pivot Index (Easy)

Date and Time: Oct 14, 2024, 21:03 (EST)

Link: https://leetcode.com/problems/find-pivot-index/

Question:

Given an array of integers nums, calculate the pivot index of this array.

The pivot index is 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 the index is on the left edge of the array, then the left sum is 0 because there are no elements to the left. This also applies to the right edge of the array.

Return the leftmost pivot index. If no such index exists, return -1.

Example 1:

Input: nums = [1,7,3,6,5,6]

Output: 3

Explanation:
The pivot index is 3.
Left sum = nums[0] + nums[1] + nums[2] = 1 + 7 + 3 = 11
Right sum = nums[4] + nums[5] = 5 + 6 = 11

Example 2:

Input: nums = [1,2,3]

Output: -1

Explanation:
There is no index that satisfies the conditions in the problem statement.

Example 3:

Input: nums = [2,1,-1]

Output: 0

Explanation:
The pivot index is 0.
Left sum = 0 (no elements to the left of index 0)
Right sum = nums[1] + nums[2] = 1 + -1 = 0

Constraints:

• 1 <= nums.length <= 10^4

• -1000 <= nums[i] <= 1000

Walk-through:

Maintain sumLeft, sumRight, we first initialize sumLeft = 0, sumRight = sum(nums). Then, we loop over i in nums, we subtract nums[i] for sumRight then compare with sumLeft, we return index i when sumLeft == sumRight, otherwise, we increment sumLeft += nums[i]. In the end, we should return -1.

Python Solution:

class Solution:
    def pivotIndex(self, nums: List[int]) -> int:
        # index i, prefixSum (0 -> i - 1), suffixSum (i+1 -> n)
        # return i, when prefixSum == suffixSum
        # otherwise, return -1

        # TC: O(n), SC: O(1)
        sumLeft, sumRight = 0, sum(nums)
        for i in range(len(nums)):
            sumRight -= nums[i]
            if sumLeft == sumRight:
                return i
            sumLeft += nums[i]
        return -1

Time Complexity: $O(n)$
Space Complexity: $O(1)$