The Partitioning Into Minimum Number Of Deci-Binary Numbers problem asks for the minimum number of "deci-binary" numbers (numbers where each digit is 0 or 1) that sum to a given number n (as a string). The key insight: the answer is simply the maximum digit in n. This is an elegant greedy observation disguised as a coding problem. The string and greedy interview pattern is demonstrated.
Nutanix and Amazon ask this because it rewards candidates who think mathematically. The insight — each deci-binary number can contribute at most 1 to each digit position, so you need as many deci-binary numbers as the maximum digit in n — turns a potentially complex problem into a one-liner.
Maximum digit observation. Return max(int(c) for c in n). Each digit d in n requires at least d deci-binary numbers to contribute to that position (each contributes 0 or 1). The maximum digit is the bottleneck.
n="32". Max digit=3. Need at least 3 deci-binary numbers:
n="82". Max digit=8. Need 8 deci-binary numbers.
n="927346502". Max digit=9. Answer = 9.
This problem is a prime example of "mathematical insight beats algorithmic complexity." Before coding any solution, ask: "Is there a pattern?" Here, the maximum digit directly gives the answer. Practice recognizing similar mathematical shortcuts in problems. If a problem seems hard but has a "minimum number of X" structure, check if the answer depends on a single extreme value (max, min, or specific element property).
| Title | Difficulty | Topics | LeetCode |
|---|---|---|---|
| Maximum Value after Insertion | Medium | Solve | |
| Minimum Number of Swaps to Make the Binary String Alternating | Medium | Solve | |
| String Without AAA or BBB | Medium | Solve | |
| Lexicographically Smallest String After Substring Operation | Medium | Solve | |
| Minimum Suffix Flips | Medium | Solve |
