SoFi·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

May 2026

Summary

SoFi software engineer round with a pretty gnarly bit manipulation problem. Not a vibe check, they wanted actual algorithmic thinking and combinatorics knowledge, not just brute force that happens to pass.

Questions Asked (1)

Given a positive integer n, define f(n) as the smallest integer >= n whose binary form is all 1s (like 2^k - 1). Return the count of integers other than n that are <= f(n) and share the same number of set bits as n. You need to solve this more efficiently than brute force, using bit manipulation and combinatorics.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

This one took me a minute to even parse.

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AI HintsAI Generated

Suggested Approach

First, identify f(n) as the smallest all-ones number >= n, which is 2^k - 1 where k is the bit length of n. Then, count the numbers <= f(n) with the same popcount as n, excluding n itself, by using combinatorial counting of numbers with a given popcount up to a limit. Finally, subtract 1 to exclude n and return the count.

Pro tip: Clarify that f(n) is always of the form 2^k - 1 and that the count can be computed by counting all numbers with the same popcount up to f(n) and subtracting 1. This avoids brute force and shows you understand the structure of the problem.

1. Understand f(n)

Determine f(n) as the smallest all-ones number >= n. Since n is positive, f(n) = 2^k - 1 where k is the number of bits in n (i.e., k = floor(log2(n)) + 1).

2. Count numbers with same popcount up to f(n)

Use combinatorics to count how many numbers from 1 to f(n) have exactly the same number of set bits as n. This can be done by iterating over bit positions and using binomial coefficients.

3. Exclude n itself

Subtract 1 from the count to exclude n, since the problem asks for integers other than n.

4. Handle edge cases

Consider cases where n is already all ones (then f(n)=n) and ensure the count is correct. Also handle small n like 1.

5. Optimize and verify

Ensure the solution runs in O(log n) time by using bit manipulation and precomputed binomial coefficients. Test with examples to verify correctness.

Key Points to Mention

f(n) is always of the form 2^k - 1, where k is the bit length of n.
The count of numbers with a given popcount up to a limit can be computed using combinatorial counting (binomial coefficients).
Subtract 1 to exclude n itself from the count.
Edge cases: n is all ones, n=1, and n=0 (though n is positive).
Time complexity: O(log n) using bit manipulation and precomputed binomial coefficients.
Space complexity: O(log n) for storing binomial coefficients or O(1) if computed on the fly.

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