Partitioning Into Minimum Number Of Deci-Binary Numbers

class Solution {
public:
    int countMinPartitions(string num) {
        return *max_element(begin(num), end(num)) - '0';
    }
};

The problem involves finding the minimum number of deci-binary numbers required to partition a given string representing a non-negative integer. A deci-binary number is one where each digit can be either 0 or 1. The solution requires calculating the largest digit in the string, as this represents the minimum number of deci-binary numbers needed.

The solution, implemented in C++, creates a function countMinPartitions which accepts the number as a string. Using the STL function max_element, which is called with the string's beginning and end iterators, the maximal character (digit) in the string is identified. By subtracting the ASCII value of '0' from this character, the function efficiently calculates and returns the integer value of the maximum digit.

This method takes advantage of simple character arithmetic and standard library functions for a concise and efficient solution to the problem.

class Solution {
    public int minNumberNeeded(String digits) {
        int finalMax = 0;
        for (int j = 0; j < digits.length(); j++) {
            finalMax = Math.max(finalMax, digits.charAt(j) - '0');
        }
        return finalMax;
    }
}

The given Java program defines a method within a Solution class for determining the minimum number of deci-binary numbers needed to represent any non-negative integer n described in a string digits. Deci-binary numbers are composed of the digits 0 to 9, but each digit in the number can only be 0 or 1.

Review the steps that the method minNumberNeeded performs:

1. Initialize finalMax to 0, which will store the largest single digit from the input string digits.

2. Iterate through each character in the string digits. For each character:

   • Convert the character to its numerical equivalent.
   • Update finalMax to be the maximum value between finalMax and the numeric value of the current character.

3. After completing the loop, return finalMax. This returned value represents the minimum number of deci-binary numbers needed, as each deci-binary addition contributes to building the maximum single digit present in the string.

This method effectively finds the highest digit in the input string and uses that as the minimum number of deci-binary numbers required, since a deci-binary number contributes a maximum of 1 at any decimal place.

class Minimizer:
    def minimalDecompose(self, digits: str) -> int:
        return int(max(digits))

The provided Python solution effectively resolves the problem of determining the minimum number of deci-binary numbers needed to sum up to each digit of the given number string. Deci-binary numbers use only the digits 0 and 1. The approach taken in this code involves the following steps:

1. Define a class named Minimizer.
2. Implement the minimalDecompose method that:
   • Accepts a string digits as its argument.
   • Returns the maximum digit when this string is converted to its integer form.

Here’s a quick breakdown of how the solution works:

• Once the minimalDecompose method is called, it receives a string of digits.
• It converts each character of this string into an integer and identifies the highest number among them.
• This highest digit is the minimum count of deci-binary numbers required to compose the original number through component addition.

This approach directly determines the minimal number necessary by utilizing Python’s built-in max() function that effortlessly identifies the maximum within the iterable supplied in this case, a string of digits. By focusing on the example of a given input "82735", the max() function isolates '8' as the largest digit. Therefore, at least eight deci-binary additions are required to replicate the number "82735" in a deci-binary sum. Hence, the function returns 8.