Sort the Jumbled Numbers

class Solution {
public:
    vector<int> reorderNumbers(vector<int>& map, vector<int>& numList) {
        vector<pair<int, int>> mappedNumbers;
    
        for (int i = 0; i < numList.size(); ++i) {
            int newNumber = 0;
            int currentNum = numList[i];
            int multiplier = 1;
    
            if (currentNum == 0) {
                mappedNumbers.push_back({map[0], i});
                continue;
            }
    
            while (currentNum != 0) {
                newNumber += multiplier * map[currentNum % 10];
                multiplier *= 10;
                currentNum /= 10;
            }
    
            mappedNumbers.push_back({newNumber, i});
        }
    
        sort(mappedNumbers.begin(), mappedNumbers.end());
        vector<int> sortedNumbers;
        for (auto &numPair : mappedNumbers) {
            sortedNumbers.push_back(numList[numPair.second]);
        }
        return sortedNumbers;
    }
};

This summary explains the C++ solution for sorting a list of jumbled numbers based on a given mapping. The reorderNumbers function accepts two vectors: map (maps each digit to a new digit) and numList (contains the numbers to be sorted). The function implements the following steps:

1. Start by creating a vector of pairs, mappedNumbers, to store the mapped numbers and their original indices.
2. Traverse each number in numList:
   • For each number, compute its new representation using the mapping provided by map.
   • If the number is zero, directly append {map[0], index} to mappedNumbers.
   • If not zero, decompose the number into its digits and reconstruct a new number using the mapped digits.
   • Append this mapped number along with the original index to mappedNumbers.
3. Sort mappedNumbers based on the mapped numbers.
4. Create a vector, sortedNumbers, and populate it with numbers from numList using the sorted order of indices from mappedNumbers.
5. Finally, return sortedNumbers.

This solution uses straightforward number manipulation and sorting mechanism to rearrange the original numbers as per the mapping sequence, ensuring they are sorted correctly as per the transformed values.

public class Solution {
    
    public int[] rearrangeDigits(int[] map, int[] originalArray) {
        List<int[]> pairedList = new ArrayList<int[]>();
    
        for (int idx = 0; idx < originalArray.length; idx++) {
            int transformed = 0;
            int number = originalArray[idx];
            int weight = 1;
    
            if (number == 0) {
                pairedList.add(new int[] { map[0], idx });
                continue;
            }
            while (number != 0) {
                transformed = weight * map[number % 10] + transformed;
                weight *= 10;
                number /= 10;
            }
            pairedList.add(new int[] { transformed, idx });
        }
    
        Collections.sort(pairedList, (x, y) -> x[0] - y[0]);
    
        int[] sortedArray = new int[originalArray.length];
        for (int j = 0; j < pairedList.size(); j++) {
            sortedArray[j] = originalArray[pairedList.get(j)[1]];
        }
    
        return sortedArray;
    }
}

This Java solution involves sorting an array of integers according to a transformation defined by a given map array. Here, the map array dictates how each digit of the numbers must be transformed during sorting. Follow these steps in the code to understand the method being implemented:

1. Initialize pairedList, a list that holds pairs consisting of the transformed number and its original index.
2. Iterate through each number in the originalArray:
   • Initialize variables for the transformed number (transformed) and its weight (weight).
   • Handle the special case where the number is zero by directly mapping it to its mapped value and continue to the next iteration.
   • For non-zero numbers, decompose the number digit by digit, transform each digit according to the map, and combine them to form transformed.
   • Add the pair of the transformed value and the original index to the pairedList.
3. Sort pairedList based on the transformed values.
4. Extract the numbers from originalArray using the sorted indices into sortedArray.

This approach rearranges the original numbers so that they follow an order dictated by the map's transformation of their digits, effectively customizing the sorting criteria.

class Solution:
    def reorder(self, mapList: List[int], elements: List[int]) -> List[int]:
        mapped_pairs = []
    
        for idx in range(len(elements)):
            new_value = 0
            current_element = elements[idx]
    
            decimal_place = 1
            if current_element == 0:
                mapped_pairs.append((mapList[0], idx))
                continue
    
            while current_element != 0:
                new_value = decimal_place * mapList[current_element % 10] + new_value
                decimal_place *= 10
                current_element //= 10
            mapped_pairs.append((new_value, idx))
    
        mapped_pairs.sort()
        result = [elements[p[1]] for p in mapped_pairs]
    
        return result

In the provided Python code, the task is to sort a list of numbers based on a customized mapping of digits. Below is a concise breakdown of the approach used:

• Define a class Solution with a method reorder, which accepts two lists: mapList that contains the mapping for each digit, and elements which is the list of numbers to be sorted.
• Initiate an empty list mapped_pairs to store tuples of new mapped values and original indices of elements.
• Iterate through each number in the elements list:
  • Calculate a new value for each number by mapping its individual digits according to mapList. Digits are processed from least significant to most significant due to the way integers are handled.
  • Utilize the modulo operator to isolate each digit of the number and the integer division to reduce the number by a factor of ten after each iteration.
  • Collect the newly computed value and the original index of the number in a tuple, and append it to mapped_pairs.
• Sort mapped_pairs primarily by the new mapped value.
• Extract the elements in their new order, creating a sorted list based on the custom digit mapping.
• Return the sorted list, concluding the method.

This technique effectively reorders the initial list of numbers by translating each number into a new form via the provided mapping, then sorting and reversing this process to achieve the desired order. This method can be specifically useful when the sort order needs to be determined by unconventional numerical representations.