Permutation

## Permutation without recursion

To iterate is human, to recurse is divine.
…but Iteration is "always" (proof that I am wrong;) faster than Recursion.

How to generate a permutation set without recursion:
http://www.geocities.com/permute_it/

# Number of permutations for a given input string

With Excel you can use =PERMUTE(A1;A2) to calculate the
total number of unique combinations of a given input string.

A1: 9
A2: 9

result: 362880

```...
8    1 2 3 4 5 6 7 8    8 7 6 5 4 3 2 1    5040 * 8 = 40320
9    1 2 3 4 5 6 7 8 9    9 8 7 6 5 4 3 2 1    40320 * 9 = 362880
N    1 2 3 . . . (N - 1) N    N (N - 1) . . . 3 2 1    (N - 1)! * N = N!
```

http://www.geocities.com/permute_it/03example.html

# Permutation Call Stack Visualization

``````--- Call Trace of Permute ---

-: Permute({1,2,3}, [-,-,-], 1, 3)
.     .
.           .
.                 .
.                       .
1: Permute({2,3}, [1,-,-], 2, 3)
.   .                            .
.       .                            .
.           .                          2: Permute({1,3}, [2,-,-], 2, 3)
.               .                          etc.
.                   .                      3: Permute({1,2}, [3,-,-], 2, 3)
.                       .                       etc.
1.1: Permute({3}, [1,2,-], 3, 3)
. .                              .
.    .                            1.2: Permute({2}, [1,3,-], 3, 3)
.       .
1.1.1: Permute({}, [1,2,3], 4, 3)
.
.
1.2.1: Permute({}, [1,3,2], 4, 3)```
```
page revision: 4, last edited: 10 Nov 2007 12:21