Non-negative Integers without Consecutive Ones
A hard-tier problem at 40% community acceptance, tagged with Dynamic Programming. Reported in interviews at Pocket Gems and 0 others.
Non-negative Integers without Consecutive Ones is the kind of problem that looks deceptively simple until you hit it live and realize the brute-force approach times out. You're counting integers up to n where the binary representation never has two 1s in a row. It's a Pocket Gems ask, and the acceptance rate sits at 40%, meaning most candidates either nail the pattern or walk away confused. The trick isn't in the problem statement, it's in recognizing this is a digit DP problem disguised as a number theory question. If you blank on the approach during your assessment, StealthCoder surfaces the working solution invisible to the proctor.
Companies that ask "Non-negative Integers without Consecutive Ones"
Non-negative Integers without Consecutive Ones 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 for the engineer who has done the work but might still blank with a webcam pointed at him.
Get StealthCoderThe naive approach, iterating through all numbers up to n and checking each binary representation, gets killed by time limits on large n. The real solution uses dynamic programming to count valid numbers by building them digit by digit in binary. You track whether the previous bit was 1 (to prevent consecutive ones) and whether you're still bounded by n's digits. The state is simple but the construction logic is where candidates slip: you need to handle the constraint that the number can't exceed n while counting valid patterns. This is digit DP applied to a binary constraint. Most people either try brute force or fumble the state transitions. If the pattern doesn't click during your OA, StealthCoder has the memoization setup and transitions ready.
Pattern tags
You know the problem.
Make sure you actually pass it.
Non-negative Integers without Consecutive Ones recycles across companies for a reason. It's hard-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 for the engineer who has done the work but might still blank with a webcam pointed at him. Works on HackerRank, CodeSignal, CoderPad, and Karat.
Non-negative Integers without Consecutive Ones interview FAQ
Is this really a hard problem or is it misclassified?+
The 40% acceptance rate suggests it's genuinely hard, not misclassified. The difficulty comes from recognizing it's digit DP, not from the logic once you see it. Most candidates don't pattern-match to DP until they've done 20+ similar problems. Pocket Gems asks it, so they expect the optimization.
Can you brute-force this or does it always time out?+
Brute force times out on large n values. Checking every integer up to n and validating its binary representation is O(n log n), which fails when n is 10^9 or higher. The DP solution runs in O(log n) space and O(log^2 n) time because you iterate through at most 32-40 bits.
What's the trick to the state transitions?+
Track two things: whether the previous bit was 1 (so you can't place another 1), and whether you're still bounded by n's bits. When the previous bit was 1, you can only place a 0 next. When it was 0, you can place either. The tricky part is managing the bound constraint without losing valid counts.
How does this relate to standard DP patterns?+
It's digit DP, the same pattern used for problems like count-digit-one and numbers-at-most-n-given-digit-set. You build the number digit by digit, maintain a tight bound, and memoize states. If you've drilled digit DP, the structure is familiar. If not, it feels like a new pattern entirely.
Why do companies ask this instead of easier DP problems?+
It tests whether you can recognize a pattern (digit DP) and implement stateful constraints under pressure. Easy DP problems just ask you to fill a table. This requires you to see the constraint model first, then code it. That's the difference between a 40-50% problem and a 70% problem.
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