How do you solve Find the Middle Index in Array on LeetCode?

Find the Middle Index in Array (LeetCode #1991) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(1) space complexity. Key insight: Using prefix sums can significantly reduce the number of calculations needed.

What is the brute force solution for Find the Middle Index in Array?

The brute force approach for Find the Middle Index in Array is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach checks each index to see if it satisfies the middle index condition by calculating the sums of elements on both sides. This is straightforward but inefficient as it recalculates sums repeatedly. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Find the Middle Index in Array?

Find the Middle Index in Array uses the following concepts: Array, Prefix Sum. The recommended patterns to study are: Prefix Sum, Array.

What are the interview tips for Find the Middle Index in Array?

Always think about how to reduce repeated calculations. Consider edge cases and test your solution with them. Explain your thought process clearly as you code.

What are common mistakes when solving Find the Middle Index in Array?

Not considering edge cases like arrays with only two elements. Failing to update the left sum correctly in the optimal solution.

#1991

Find the Middle Index in Array

Easy

ArrayPrefix SumPrefix SumArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(1)

💡

Intuition

Time O(n)Space O(1)

The optimal approach uses a single pass to calculate the total sum and then iteratively checks each index while maintaining the left sum. This avoids redundant calculations and reduces time complexity.

⚙️

Algorithm

5 steps

1Step 1: Calculate the total sum of the array.
2Step 2: Initialize a variable for left sum as 0.
3Step 3: Loop through each index and update the right sum by subtracting the current element from total sum.
4Step 4: If left sum equals right sum, return the current index.
5Step 5: Update left sum by adding the current element before moving to the next index.

solution.py11 lines

1# Full working Python code
2
3def findMiddleIndex(nums):
4    total_sum = sum(nums)
5    left_sum = 0
6    for i in range(len(nums)):
7        right_sum = total_sum - left_sum - nums[i]
8        if left_sum == right_sum:
9            return i
10        left_sum += nums[i]
11    return -1

ℹ

Complexity note: This complexity is achieved because we only traverse the array a constant number of times (once for total sum and once for checking middle index).

1Using prefix sums can significantly reduce the number of calculations needed.
2Iterating through the array while maintaining a running total allows for efficient checks.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.