Minimum Time to Break Locks I
A medium-tier problem at 30% community acceptance, tagged with Array, Dynamic Programming, Backtracking. Reported in interviews at IVP and 0 others.
Minimum Time to Break Locks is a medium-difficulty problem that combines backtracking with bitmask DP to track which locks you've already broken. You're given an array of times, and you need to find the minimum total time to break all locks, where each lock takes longer to break if you've already broken others first. It's the kind of problem that looks deceptively simple until you realize the greedy approach fails. IVP has asked it. If you hit this during your OA and freeze on the state representation, StealthCoder solves it invisible to the proctor.
Companies that ask "Minimum Time to Break Locks I"
Minimum Time to Break Locks I is the kind of problem that decides whether you pass. StealthCoder reads the problem on screen and surfaces a working solution in under 2 seconds. Invisible to screen share. The proctor sees nothing. Built by an Amazon engineer who realized the OA tests how well you memorized 200 problems, not how well you code.
Get StealthCoderThe trap here is assuming you should always break locks in a fixed order. You can't. The problem requires trying all possible orderings and computing the time cost for each permutation, which is where bitmask comes in. You use a bitmask to represent which locks are already broken, then recursively try breaking each remaining lock. Dynamic programming caches results by (mask, position) to avoid recomputing the same subproblems. The backtracking explores the decision tree, pruning with memoization. Common mistake: forgetting that the time to break a lock depends on how many locks you've broken before it. If you implement a clean bitmask-DP solution with DFS, you'll pass. StealthCoder is your safety net if the pattern doesn't click during the live assessment.
Pattern tags
You know the problem.
Make sure you actually pass it.
Minimum Time to Break Locks I recycles across companies for a reason. It's medium-tier, and most candidates blank under the timer. StealthCoder is the hedge: an AI overlay invisible during screen share. It reads the problem and surfaces a working solution in under 2 seconds. Built by an Amazon engineer who realized the OA tests how well you memorized 200 problems, not how well you code. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Minimum Time to Break Locks I interview FAQ
Why can't I just sort and break locks in order?+
Because the time to break each lock depends on the number of locks already broken, not which ones. Different orderings produce different total times. You must try all permutations and find the minimum. That's why backtracking with bitmask state matters.
What's the bitmask for if I'm just iterating through locks?+
The bitmask represents which locks you've broken so far. It lets you uniquely identify a state (which subset is done, how many are broken). Combined with memoization, it avoids recomputing the same subproblems multiple times across different orderings.
Is this still asked at companies besides IVP?+
IVP is the only company in the data set that's reported asking it. That doesn't mean it won't show up elsewhere. Bitmask DP and backtracking are evergreen OA topics. If you're prepping for roles that ask optimization and state-space search problems, this pattern is worth knowing.
How do I debug if my backtracking isn't pruning?+
Check your memoization key. It should include both the bitmask (which locks are broken) and the current position or count. If you're only caching by mask, you might reuse a result from a different starting point. Print the cache hit rate during local testing to verify pruning is working.
What's the acceptance rate telling me about difficulty?+
30 percent acceptance is lower than typical medium problems. It suggests most people either miss the backtracking insight or implement memoization incorrectly. If you understand bitmask DP and recursion well, you're ahead of the median candidate.
Want the actual problem statement? View "Minimum Time to Break Locks I" on LeetCode →