Is Find the Smallest Balanced Index easy or hard?

The problem is typically classified as Medium because the key insight is recognizing that right sums can be derived from the total sum and running prefix. Once that observation is made, the implementation becomes a straightforward linear scan.

Find the Smallest Balanced Index Python/Java solution

Most implementations follow the same pattern: compute the total array sum, iterate once, maintain a running left sum, and compare it with the derived right sum. This logic translates directly to Python, Java, C++, Go, and TypeScript with identical O(n) time complexity.

How to solve Find the Smallest Balanced Index in O(n)?

First compute the total sum of the array. Iterate through the array while tracking a running left sum. For each index i, compute rightSum = totalSum - leftSum - nums[i]. If leftSum equals rightSum, return i immediately because the traversal ensures it is the smallest valid index.

What is the best approach for Find the Smallest Balanced Index?

The optimal solution uses a prefix-sum style linear scan. Compute the total sum of the array, then iterate while maintaining a running left sum. The right sum at index i can be derived as totalSum - leftSum - nums[i]. This approach finds the smallest balanced index in O(n) time and O(1) space.

Is Find the Smallest Balanced Index asked at Google/Amazon/Meta?

Balanced index or pivot index style problems frequently appear in interviews at large tech companies. Variants that compare left and right cumulative sums are common at companies like Amazon and Google because they test array traversal and prefix-sum reasoning.

What data structure is used in Find the Smallest Balanced Index?

The problem mainly uses arrays with a prefix sum technique. Instead of storing a full prefix array, most optimal solutions maintain a running cumulative sum while iterating through the array.

What is the time complexity of Find the Smallest Balanced Index?

The optimal prefix-sum enumeration runs in O(n) time because the array is scanned once. Space complexity is O(1) since only a few variables store running totals. A naive brute-force approach would take O(n^2) time by recalculating sums for every index.

Description Hints 4 Solution Video 13:48

3862. Find the Smallest Balanced Index

Medium19.2% acceptance2 companies

You are given an integer array nums.

An index i is balanced if the sum of elements strictly to the left of i equals the product of elements strictly to the right of i.

If there are no elements to the left, the sum is considered as 0. Similarly, if there are no elements to the right, the product is considered as 1.

Return an integer denoting the smallest balanced index. If no balanced index exists, return -1.

Example 1:

Input: nums = [2,1,2]

Output: 1

Explanation:

For index i = 1:

Left sum = nums[0] = 2
Right product = nums[2] = 2
Since the left sum equals the right product, index 1 is balanced.

No smaller index satisfies the condition, so the answer is 1.

Example 2:

Input: nums = [2,8,2,2,5]

Output: 2

Explanation:

For index i = 2:

Left sum = 2 + 8 = 10
Right product = 2 * 5 = 10
Since the left sum equals the right product, index 2 is balanced.

No smaller index satisfies the condition, so the answer is 2.

Example 3:

Input: nums = [1]

Output: -1

For index i = 0:

The left side is empty, so the left sum is 0.
The right side is empty, so the right product is 1.
Since the left sum does not equal the right product, index 0 is not balanced.

Therefore, no balanced index exists and the answer is -1.

Constraints:

1 <= nums.length <= 10⁵
1 <= nums[i] <= 10⁹

Asked at 2 companies

Topics

Array Prefix Sum

Hints open one at a time

Hint 1

Compute prefix sums for elements to the left of each index.

Hint 2

Compute suffix products for elements to the right with overflow checks.

Hint 3

Check each index i where left sum == right product.

Hint 4

Return the smallest such index, or -1 if none exists.

13:48

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1class Solution:
2    def smallestBalancedIndex(self, nums: list[int]) -> int:
3        

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Examples

Case 1Case 2Case 3

Input

[2,1,2]

Input

[2,8,2,2,5]

Input

[1]

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