Find the Equilibrium Index of a List in Python

Find every index in a list where the sum of elements to its left equals the sum to its right, using a single pass.

Easy Python 3.9+ Aug 9, 2026 Algorithms & data structures 13 views 0 copies

equilibrium-index prefix-sums arrays two-pointers

Python code

16 lines

Python 3.9+

def find_equilibrium_indexes(arr):
    total = sum(arr)
    left_sum = 0
    indexes = []
    for i, num in enumerate(arr):
        total -= num
        if left_sum == total:
            indexes.append(i)
        left_sum += num
    return indexes

if __name__ == "__main__":
    test = [1, 2, 3, -1, 2, 3]
    result = find_equilibrium_indexes(test)
    print("Array:", test)
    print("Equilibrium indexes:", result)

Output

stdout

Array: [1, 2, 3, -1, 2, 3]
Equilibrium indexes: [3]

How it works

The algorithm starts with total being the sum of the whole list and left_sum as 0. On each iteration it subtracts the current number from total so total now represents the right-side sum, compares it to left_sum, and appends the index when they match. Then it adds the current number to left_sum before moving on. This keeps the time complexity at O(n) with O(1) extra space aside from the result list.

Common mistakes

Forgetting that an empty list has no equilibrium indexes
Treating the comparison before updating `left_sum`, which would produce incorrect results
Assuming only one equilibrium index can exist when multiple are possible

Variations

Use prefix sums to precompute left and right totals, then compare them at each index
Use recursion to split the list and check the middle index recursively

Real-world use cases

Analyzing CPU load balancing by finding the moment where accumulated task load equals the remaining load.
Segmenting a revenue stream so that the total profit before a date equals the total after it, for tax or accounting reports.
Splitting a dataset for training and prediction when you need an index that splits a cumulative metric in half.

Find the Equilibrium Index of a List in Python

Python code

Output

How it works

Common mistakes

Variations

Real-world use cases

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Python code

Output

How it works

Common mistakes

Variations

Real-world use cases

More from Algorithms & data structures

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