What is the optimal time complexity of solving Finding equilibrium index?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Finding equilibrium index?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Finding equilibrium index?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Finding equilibrium index?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Python BasicsEasy

Finding equilibrium index

Learn how to solve the 'Finding equilibrium index' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function equilibrium_index(arr) that finds the equilibrium index of the array. An equilibrium index is an index i where the sum of elements at indices less than i equals the sum of elements at indices greater than i. Return the first equilibrium index found, or -1 if none exists. The element at index i is not included in either sum.

Constraints

•1 <= len(arr) <= 10^5
•-10^9 <= arr[i] <= 10^9

Examples

Example 1

Input

arr = [-7, 1, 5, 2, -4, 3, 0]

Output

Explanation

At index 3: left sum = -7+1+5 = -1, right sum = -4+3+0 = -1. Both sums are equal.

Example 2

Input

arr = [1, 2, 3]

Output

-1

Explanation

No index satisfies the equilibrium condition.

Example 3

Input

arr = [1, 3, 5, 2, 2]

Output

Explanation

At index 2: left sum = 1+3 = 4, right sum = 2+2 = 4. Equal.

Need a Hint?

Use simple arithmetic operators (like modulo `%`, division `//`), conditional checks, or loops to inspect number properties.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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