Partitioning Into Minimum Number Of Deci-Binary Numbers - Video Solutions

Problem Overview: You are given a numeric string n. The task is to split it into the minimum number of deci-binary numbers (numbers containing only digits 0 or 1) such that their sum equals n. The result depends on how many 1s are required in each digit position across all constructed numbers.

Approach 1: Maximum Digit Evaluation (Greedy, O(n) time, O(1) space)

The key observation: every deci-binary number contributes at most 1 to each digit position. If a digit in n is d, you need at least d deci-binary numbers to sum to that position. Therefore, the minimum number of required deci-binary numbers equals the maximum digit present in the string. The algorithm simply iterates through the characters of the string, converts each digit, and tracks the maximum value seen. This greedy observation removes the need to explicitly construct the deci-binary numbers. The scan takes O(n) time and only a few variables, giving O(1) space.

This works because each resulting deci-binary number can contribute a 1 in positions where the original digit still needs value. Once you know the largest digit, you know how many parallel deci-binary layers are required to build the number.

Approach 2: Direct Conversion and Maximum (O(n) time, O(n) space)

This version first converts the numeric string into a list or array of integers, then scans the collection to find the maximum digit. Conceptually it follows the same greedy insight as the previous approach, but separates the parsing and evaluation steps. First iterate through the string and store each digit in an integer array. Then perform a second pass to compute the maximum element.

The algorithmic idea is identical: the maximum digit determines the minimum number of deci-binary numbers needed. However, this approach uses additional memory for the converted array, resulting in O(n) extra space. It can be useful in situations where the digits are reused for additional processing.

Both approaches rely on a simple greedy insight about digit contribution rather than constructing the numbers explicitly. Problems like this commonly appear in greedy and string processing categories, where scanning input once reveals the optimal answer.

Recommended for interviews: The Maximum Digit Evaluation approach. Interviewers expect you to recognize the greedy property quickly: the largest digit determines the number of required deci-binary layers. A brute-force construction approach would be unnecessarily complex, while identifying the max digit shows strong problem reduction and reasoning skills.