(Countdown) QuickPerm Tail Reversals:
(Formally EXAMPLE_04)

EXAMPLE 04 - Permutation Reversals on the Tail of a Linear Array Without Using Recursion

// NOTICE: Copyright 1991-2008, Phillip Paul Fuchs #define N 12 // number of elements to permute. Let N > 2 void example_04(void) { const unsigned int ax = N - 1; // constant index ceiling (a[N] length) unsigned int a[N], p[N]; // target array and index control array  register unsigned int i, j, tmp; // index variables and tmp for swap for(i = 0; i < N; i++) // initialize arrays; a[N] can be any type { a[i] = N - i; // a[i] value is arbitrary and not revealed p[i] = N - i; } //display(a); // remove comment to display array a[] i = ax; // setup first swap point to be ax while (i > 0) { p[i]--; // decrease index "weight" for i by one i--; // i must be less then j (i < j) j = ax; // reset j to ax do // reverse target array from i to j { tmp = a[j]; // swap(a[i], a[j]) a[j] = a[i]; a[i] = tmp; j--; // decrement j by 1 i++; // increment i by 1 } while (j > i); //display(a); // remove comment to display target array a[] i = ax; // reset index i to ax (assumed) while (!p[i]) // while (p[i] == 0) { p[i] = N - i; // reset p[i] zero value i--; // set new index value for i (decrease by one) } // while (!p[i]) } // while (i > 0) } // example_04()

EXAMPLE 04a - Function to Display Permutations (Optional)

// NOTICE: Copyright 1991-2008, Phillip Paul Fuchs                          void display(unsigned int *a) { for(unsigned int x = 0; x < N; x++) printf("%d ",a[x]); printf("\n"); getch(); // press any key to continue... } // display()

Fundamental Analysis of Permutation Example 04 Above

Number of Objects to Permute (N)	a[N] Display of Initial Sequence	a[N] Display of Final Sequence	Total Number of Unique Combinations Produced (N!)
3	3 2 1	1 2 3	2 * 3 = 6
4	4 3 2 1	1 2 3 4	6 * 4 = 24
5	5 4 3 2 1	1 2 3 4 5	24 * 5 = 120
6	6 5 4 3 2 1	1 2 3 4 5 6	120 * 6 = 720
7	7 6 5 4 3 2 1	1 2 3 4 5 6 7	720 * 7 = 5040
8	8 7 6 5 4 3 2 1	1 2 3 4 5 6 7 8	5040 * 8 = 40320
9	9 8 7 6 5 4 3 2 1	1 2 3 4 5 6 7 8 9	40320 * 9 = 362880
N	N (N - 1) . . . 3 2 1	1 2 3 . . . (N - 1) N	(N - 1)! * N = N!

The Meta-Permutation class supplies head and tail indices to EXAMPLE 05, which is next on our tour...