Minimum Operations to Reduce an Integer to 0
A medium-tier problem at 57% community acceptance, tagged with Dynamic Programming, Greedy, Bit Manipulation. Reported in interviews at Two Sigma and 4 others.
You're given an integer and need to reduce it to 0 using the minimum number of operations. Each operation lets you subtract a power of 2 or subtract the integer from the nearest power of 2 greater than it. Two Sigma, Salesforce, Nvidia, Microsoft, and IBM all ask this one. It looks simple at first, but the greedy choice isn't always optimal. This is the kind of problem where you either see the pattern or you don't, and if you blank on it during the OA, StealthCoder surfaces a working solution in seconds while the proctor sees nothing.
Companies that ask "Minimum Operations to Reduce an Integer to 0"
Minimum Operations to Reduce an Integer to 0 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. Made by an Amazon engineer who watched the leaked-problem repo become an industry secret. He decided you should have it too.
Get StealthCoderThe trap is thinking greedy always wins: subtract the largest power of 2, repeat. That fails. The real insight sits in dynamic programming with bit manipulation. You need to explore both subtracting a power of 2 directly and subtracting from the next power of 2, then memoize results to avoid recomputation. The key observation is that reducing to nearby powers of 2 can create shortcuts the greedy path misses. Common pitfalls include not recognizing when the next-power operation is faster, or trying to solve it without memoization and timing out. This problem tests whether you can spot that greedy fails and pivot to DP. If you hit this live and the greedy path doesn't work, StealthCoder gives you the correct DP structure instantly.
Pattern tags
You know the problem.
Make sure you actually pass it.
Minimum Operations to Reduce an Integer to 0 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. Made by an Amazon engineer who watched the leaked-problem repo become an industry secret. He decided you should have it too. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Minimum Operations to Reduce an Integer to 0 interview FAQ
Is this really asked at FAANG-tier companies?+
Yes. Two Sigma, Salesforce, Nvidia, Microsoft, and IBM all have hiring signals on this one. It's not a filter question, but it shows up enough that skipping it is risky. 57% acceptance rate means it's genuinely tricky, not a gimme.
What's the actual trick I'm missing?+
Greedy fails. You need DP. The key is that subtracting the integer from the next power of 2 can sometimes be faster than greedily subtracting powers of 2 one by one. Memoize the states and explore both options at each step.
How does bit manipulation fit into the solution?+
You need to find the highest set bit to identify the largest power of 2, and compute the next power of 2 efficiently. Bit operations let you do this in constant time instead of looping. The DP logic itself is the heavy lift though.
Is this easier or harder than standard coin-change DP?+
Harder. Coin change is pure DP with a fixed set of coins. Here the 'coins' depend on the integer itself (powers of 2 and the next power of 2), and the second operation adds a non-obvious shortcut. You have to think harder about state transitions.
Will I have time to code and test this in an OA?+
If you know the pattern, yes. If you're figuring it out from scratch, it's tight. The implementation is maybe 20 lines once you know you need memoized DP with two operations per state. That's why a hedge matters.
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