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Find The Middle Index In Array

Problem​

Given a 0-indexed integer array nums, find the leftmost middleIndex (i.e., the smallest amongst all the possible ones).

A middleIndex is an index where nums[0] + nums[1] + ... + nums[middleIndex-1] == nums[middleIndex+1] + nums[middleIndex+2] + ... + nums[nums.length-1].

If middleIndex == 0, the left side sum is considered to be 0. Similarly, if middleIndex == nums.length - 1, the right side sum is considered to be 0.

Return the leftmost middleIndex that satisfies the condition, or -1 if there is no such index.

Examples​

Example 1:

Input: nums = [2,3,-1,8,4]

Output: 3

Explanation: The sum of the numbers before index 3 is: 2 + 3 + -1 = 4 The sum of the numbers after index 3 is: 4 = 4

Example 2:

Input: nums = [1,-1,4]

Output: 2

Explanation: The sum of the numbers before index 2 is: 1 + -1 = 0 The sum of the numbers after index 2 is: 0

Example 3:

Input: nums = [2,5]

Output: -1

Explanation: There is no valid middleIndex.

Constraints​

  • 1 <= nums.length <= 100
  • -1000 <= nums[i] <= 1000

Approach​

  1. Initialize prefix to 0 and suffix to the sum of all elements in nums.

  2. Iterate through the elements of nums:

  • For each element, subtract it from suffix.
  • Check if prefix is equal to suffix. If true, return the current index i.
  • Add the current element to prefix.
  1. If no such index is found, return -1.

Solution for Remove Linked List Elements​

Java Solution​

class Solution {
  public int findMiddleIndex(int[] nums) {
    int prefix = 0;
    int suffix = Arrays.stream(nums).sum();

    for (int i = 0; i < nums.length; ++i) {
      suffix -= nums[i];
      if (prefix == suffix)
        return i;
      prefix += nums[i];
    }

    return -1;
  }
}

C++ solution​

class Solution {
 public:
  int findMiddleIndex(vector<int>& nums) {
    int prefix = 0;
    int suffix = accumulate(nums.begin(), nums.end(), 0);

    for (int i = 0; i < nums.size(); ++i) {
      suffix -= nums[i];
      if (prefix == suffix)
        return i;
      prefix += nums[i];
    }

    return -1;
  }
};

Python Solution​

class Solution:
  def findMiddleIndex(self, nums: List[int]) -> int:
    prefix = 0
    suffix = sum(nums)

    for i, num in enumerate(nums):
      suffix -= num
      if prefix == suffix:
        return i
      prefix += num

    return -1

Complexity Analysis​

Time Complexity: O(n)

Space Complexity: O(1)

References​

LeetCode Problem: find-the-middle-index-in-array