sort the jumbled numbers leetcode 2191 python

certainly! the leetcode problem "sort the jumbled numbers" (problem 2191) involves sorting a list of numbers based on a specific transformation of their digits. the transformation is defined by a mapping of the digits from 0 to 9.

problem statement

you are given two integer arrays:
1. `mapping`: a list of 10 integers that represents a mapping of the digits from 0 to 9.
2. `nums`: a list of integers that you need to sort based on the transformed values.

the transformation is defined such that for each number in `nums`, you replace each digit `d` with `mapping[d]`. after transforming all the numbers, you sort them based on their transformed values. if two numbers have the same transformed value, they should maintain their original order (i.e., stable sorting).

steps to solve the problem

1. **transform the numbers**: create a function to transform each number using the provided mapping.
2. **sort the numbers**: use a stable sort to sort the numbers based on their transformed values.
3. **return the sorted list**: finally, return the sorted list of numbers.

implementation

here is a python implementation of the solution:

explanation of the code

1. **transform function**:
- the `transform` function takes a number, converts it to a string, and replaces each digit according to the `mapping`. the transformed digits are then concatenated and converted back to an integer.

2. **transformed list**:
- we create a list of tuples where each tuple contains the transformed value and the original number. this helps us keep track of the original numbers while sorting.

3. **sorting**:
- we sort the list of tuples based on the transformed values using a lambda function as the key. python's built-in sort is stable, so it retains the original order of numbers that have the same transformed value.

4. **extracting the sorted numbers**:
- finally, we extract the sorted numbers from the tuples and return them.

conclusion

this approach efficiently transform ...

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