🍢 Beginner-Friendly Guide 'Partitioning Into Minimum Number Of Deci-Binary Numbers' - Problem 1689 (C++, Python, JavaScript)

At first glance, this problem looks like a complex mathematical challenge involving partitions and sums. However, once you peek under the hood, you will find it is actually a clever logic puzzle that tests your ability to identify the "bottleneck" in a system. Problem Summary You're given: A string $n$ representing a very large positive integer. Your goal: Find the minimum number of "deci-binary" numbers (numbers consisting only of digits 0 and 1) that sum up to $n$. Intuition To solve this, we need to think about how addition works digit by digit. A deci-binary number can only contribute a value of 0 or 1 to any specific decimal place. If you have a digit 7 in the units place, you need at least 7 separate deci-binary numbers to provide enough 1s to sum up to that 7. Even if other digits in the number are smaller, like 2 or 3, they can be satisfied by using 0s in those specific positions for some of the deci-binary numbers. Therefore, the "limiting factor" is simply the largest digit p