Finding equilibrium index
Detailed guide and Python implementation for the 'Finding equilibrium index' problem.
1. Concept Overview
The 'Finding equilibrium index' problem is a key challenge in the Arrays section.
This implementation focuses on easy-level logic in Python.
We prioritize technical accuracy and code readability in our provided solutions.
2. Real-World Applications
3. Visual Intuition
Visualizing the logic flow for Finding equilibrium index.
4. Prerequisites
5. Step-by-Step Thinking
1. Understand the problem
Read the problem statement for Finding equilibrium index carefully.
2. Formulate brute force
Draft a simple iterative solution.
3. Identify inefficiency
Look for redundant calculations.
4. Optimize search path
Use hashing or sorting to speed up the process.
5. Final Implementation
Clean up the code for production standards.
Problem Statement
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.
- •1 <= len(arr) <= 10^5
- •-10^9 <= arr[i] <= 10^9
Examples
arr = [-7, 1, 5, 2, -4, 3, 0]
3
At index 3: left sum = -7+1+5 = -1, right sum = -4+3+0 = -1. Both sums are equal.
arr = [1, 2, 3]
-1
No index satisfies the equilibrium condition.
arr = [1, 3, 5, 2, 2]
2
At index 2: left sum = 1+3 = 4, right sum = 2+2 = 4. Equal.
Need a Hint?
Edge Cases to Watch
- Empty input structures
- Single element inputs
- Large numerical bounds
Ready to Solve?
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Interview Insights & Variations
Complexity Analysis Breakdown
Why Time: Directly evaluates all possibilities.
Why Space: Uses standard local memory.
Why Time: Optimized paths reduce total operations.
Why Space: May trade memory for speed.
Optimized Solution Python Code
Optimized Solution Python Code
def find_equilibrium(arr):
# Optimized: Track running left sum and calculate right sum using total
total_sum = sum(arr)
left_sum = 0
for i, val in enumerate(arr):
# total_sum - left_sum - val is the right sum
if left_sum == (total_sum - left_sum - val):
return i
left_sum += val
return -1Brute Force Code (Spoiler Guarded)
Brute Force Code (Spoiler Guarded)
def find_equilibrium(arr):
# Brute force: Check every index by calculating left and right sums
n = len(arr)
for i in range(n):
left_sum = sum(arr[:i])
right_sum = sum(arr[i+1:])
if left_sum == right_sum:
return i
return -1Algorithm Pattern Checklist
When dealing with Arrays data patterns.
Core Prerequisites
Revision Key Notes
Common Mistakes & Pitfalls
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