Problem I
Permutations
Let us say two numbers are permutations of each other if it is possible to rearrange the digits of one to get the other.
For example, $3511$ and $3151$ are permutations of each other, but $3151$ and $6329$ are not. Note that $3511$ and $313$ are not permutations even though the contain the same set of digits. Same goes for $3511$ and $135$.
Write a program that, given two numbers $a$ and $b$, answers whether they are permutations of each other.
The program should be split into functions, with a function which takes two parameters $m$ and $n$ and returns True or False based on whether $m$ and $n$ are permutations of each other.
Although the implementation of the function can be short, and can easily be incorporated directly back into the calling code, it can be useful to isolate a part of the problem like this while developing the solution, so that it does not muddle the overall thought process. Then you can focus on how to solve this isolated problem, without getting distracted by the overall context.
Hints
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You can convert an integer to a string to get a string of digits (or just not convert the input to integers to begin with), and then you can convert the string of digits to a list to be able to rearrange the order of the digits.
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To check if it is possible to rearrange the digits of one number to get another, there might be a lot of possible rearrangements, and not obvious how to check them all.
Perhaps you can find a simpler way, by using some kind of canonical representative for the entire set of numbers that are permutations of a particular number. Then, to check if two numbers are permutations of each other, you can find the canonical representative of each number, and compare those instead. If both numbers have the same canonical representative, then they must both be permutations of that representative, and hence of each other. What rearrangement of the digits, independent of the original arrangement of the digits, can you use as such a canonical representative?
Input
The input consists of two lines.
The first line contains an integer $a$, with $0 \leq a \leq 10^8$.
The first line contains an integer $b$, with $0 \leq b \leq 10^8$.
Output
The output consists of one line. The numbers {a} and {b} are permutations of each other. or The numbers {a} and {b} are not permutations of each other. depending on whether $a$ and $b$ are permutations of each other.
| Sample Input 1 | Sample Output 1 |
|---|---|
3511 3151 |
The numbers 3511 and 3151 are permutations of each other. |
| Sample Input 2 | Sample Output 2 |
|---|---|
3511 6329 |
The numbers 3511 and 6329 are not permutations of each other. |
| Sample Input 3 | Sample Output 3 |
|---|---|
3511 135 |
The numbers 3511 and 135 are not permutations of each other. |
