Amazon·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

May 2026

Summary

Amazon coding round, one problem the whole session. It looked like a graph/greedy thing at first but the right approach turned out to be subset DP, which I was not expecting.

Questions Asked (1)

You have n feature branches (n <= 15), each containing a sequence of commits, where each commit touches one or more file paths. You can merge the branches into main in any order. The first branch merged has zero conflicts. For each subsequent branch, a commit is 'conflicting' if it touches any file already modified by a previously merged branch (counted once per commit regardless of how many files overlap). After merging a branch, all files it touched are added to the global modified set. Implement a function that returns the minimum total number of conflicting commits across all branches.

Algorithms & Data Structures

Author's notes

I spent the first few minutes trying to think of a greedy ordering, like merge the branch with the fewest overlapping files first.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

Model the problem as finding a permutation of branches that minimizes the total number of conflicting commits. Since n ≤ 15, use bitmask dynamic programming where the state is the set of already merged branches, and the DP value is the minimum conflicts so far. Precompute for each branch the set of files it touches and the number of commits that conflict with any given set of files.

Pro tip: Emphasize that the conflict count for a branch depends only on the union of files touched by previously merged branches, not on their order. This allows efficient precomputation and makes the DP state sufficient.

1. Understand the problem and constraints

Clarify that conflicts are counted per commit, not per file, and that the first branch merged has zero conflicts. Note that n ≤ 15 suggests an exponential algorithm like bitmask DP.

2. Precompute branch file sets and commit overlaps

For each branch, compute the set of files it touches. Also, for each branch, determine for every possible subset of files (or efficiently during DP) how many of its commits conflict with that subset.

3. Define DP state and transition

Let dp[mask] = minimum conflicts after merging the branches in mask. For each branch not in mask, the additional conflicts are the number of commits in that branch that touch any file in the union of files from branches in mask. Transition to dp[mask | (1<<i)].

4. Optimize conflict counting

Precompute for each branch i and each mask the number of conflicting commits when merging i after the set mask. This can be done by iterating over commits and checking if any file is in the union of files of mask, or by using bitmask of files and precomputed commit masks.

5. Return the minimum over all full masks

After filling the DP table, the answer is dp[(1<<n)-1]. Discuss time complexity: O(2^n * n * C) where C is total commits, or O(2^n * n) with precomputation.

Key Points to Mention

Bitmask dynamic programming to handle permutations of up to 15 branches.
Precomputing the set of files touched by each branch and the union of files for any subset of branches.
Counting conflicts per commit: a commit conflicts if it touches any file already modified by previously merged branches.
The order of branches affects the total conflicts, so we must consider all permutations.
Time complexity: O(2^n * n * total_commits) or optimized to O(2^n * n) with precomputed conflict counts.
Space complexity: O(2^n) for the DP table.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.