dotnetdev - 1 year ago 204
Python Question

# Listing all permutations of a string/integer

A common task in programming interviews (not from my experience of interviews though) is to take a string or an integer and list every possible permutation.

Is there an example of how this is done and the logic behind solving such a problem?

I've seen a few code snippets but they weren't well commented/explained and thus hard to follow.

First of all: it smells like recursion of course!

Since you also wanted to know the principle, I did my best to explain it human language. I think recursion is very easy most of the times. You only have to grasp two steps:

1. The first step
2. All the other steps (all with the same logic)

In human language:

In short:
1. The permutation of 1 element is one element.
2. The permutation of a set of elements is a list each of the elements, concatenated with every permutation of the other elements.

Example:

If the set just has one element -->
return it.
perm(a) -> a

If the set has two characters: for each element in it: return the element, with the permutation of the rest of the elements added, like so:

perm(ab) ->

a + perm(b) -> ab

b + perm(a) -> ba

Further: for each character in the set: return a character, concatenated with a perumation of > the rest of the set

perm(abc) ->

a + perm(bc) --> abc, acb

b + perm(ac) --> bac, bca

c + perm(ab) --> cab, cba

perm(abc...z) -->

a + perm(...), b + perm(....)
....

I found the pseudocode on http://www.programmersheaven.com/mb/Algorithms/369713/369713/permutation-algorithm-help/:

``````makePermutations(permutation) {
if (length permutation < required length) {
for (i = min digit to max digit) {
if (i not in permutation) {
makePermutations(permutation+i)
}
}
}
else {
}
}
``````

C#

OK, and something more elaborate (and since it is tagged c #), from http://radio.weblogs.com/0111551/stories/2002/10/14/permutations.html : Rather lengthy, but I decided to copy it anyway, so the post is not dependent on the original.

The function takes a string of characters, and writes down every possible permutation of that exact string, so for example, if "ABC" has been supplied, should spill out:

ABC, ACB, BAC, BCA, CAB, CBA.

Code:

``````class Program
{
private static void Swap(ref char a, ref char b)
{
if (a == b) return;

a ^= b;
b ^= a;
a ^= b;
}

public static void GetPer(char[] list)
{
int x = list.Length - 1;
GetPer(list, 0, x);
}

private static void GetPer(char[] list, int k, int m)
{
if (k == m)
{
Console.Write(list);
}
else
for (int i = k; i <= m; i++)
{
Swap(ref list[k], ref list[i]);
GetPer(list, k + 1, m);
Swap(ref list[k], ref list[i]);
}
}

static void Main()
{
string str = "sagiv";
char[] arr = str.ToCharArray();
GetPer(arr);
}
}
``````
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