生成排列的算法实现
1 #include <stdio.h>
2
3 #define LEFT -1
4 #define RIGHT 1
5
6 int get_max_moveable_index(int array_direction[], int array_permutation[], int num_of_ints);
7 void johnson_trotter(int n);
8 void swap_array(int array[], int i, int j);
9 void print_permutation(int value_table[], int direction_table[], int number_of_ints);
10 int main(){
11 int n;
12 printf("Enter an integer n:");
13 scanf("%d",&n);
14 johnson_trotter(n);
15 printf("All permutations are generated!\r\n");
16 return 0;
17 }
18
19
20
21 void johnson_trotter(int n){
22 //The johnson_trotter algorithm to generate all permutations of an integer set {1,2,...,n}
23 //Input: A positive integer n
24 //Output: a list of all permutations of {1,2,...,n}
25 int direction_array[n+1];
26 int permutation_array[n+1];
27 for(int k = 1;k <= n;k++){
28 direction_array[k] = LEFT;
29 permutation_array[k] = k;
30 }
31
32 //Initial
33 printf("Initial:\r\n");
34 print_permutation(permutation_array,direction_array,n);
35 int max_moveable_index;
36 int num_counter = 1;
37 while((max_moveable_index = get_max_moveable_index(direction_array,permutation_array,n)) > 0){
38 int num_max_moveable = permutation_array[max_moveable_index];
39 //Print
40 printf("Max Moveable:%d(%s)\r\n",num_max_moveable,direction_array[max_moveable_index] == 1?"-->":"<--");
41 int pointed_index = max_moveable_index + direction_array[max_moveable_index];
42 swap_array(permutation_array,max_moveable_index,pointed_index);
43 swap_array(direction_array,max_moveable_index,pointed_index);
44 for( int k = 1; k <= n; k++){
45 if(permutation_array[k] > num_max_moveable)
46 direction_array[k] *= -1;
47 }
48 print_permutation(permutation_array,direction_array,n);
49 num_counter++;
50 }
51 printf("Total permutations:%d\r\n",num_counter);
52 }
53 /**
54 * @param array_direction: the direction array thats saves the directions of the numbers in permutation array_permutation
55 * @param array_permutation: the observed permutation
56 * @param num_of_ints: number of observed numbers
57 * @return the index of the largest moveable number in permutation array array_permutation
58 * */
59 int get_max_moveable_index(int array_direction[], int array_permutation[], int num_of_ints){
60 int num_of_max_moveable = 0;// the largest moveable number
61 int max_moveable_index = 0; // the index of the largest moveable number
62 //scan for all the moveable numbers and get the largest one of them
63 for(int k = num_of_ints; k > 0; k--){
64 int index_pointed = k + array_direction[k];//the index of the number that the observed number points to
65 int current_num = array_permutation[k];
66 //make sure that the current number is pointed to a valid position
67 if(index_pointed > 0 && index_pointed <= num_of_ints && array_permutation[index_pointed] < current_num){
68 // the current number is moveable
69 if(current_num > num_of_max_moveable){
70 //the current number is the largest moveable number
71 num_of_max_moveable = current_num;
72 max_moveable_index = k;
73 }
74 }
75 }
76 return max_moveable_index;
77 }
78 /**
79 * @param array: the array in which two elements are swapped.
80 * @param i: the index of the first to-be-swapped element
81 * @param j: the index of the second to-be-swapped element
82 * */
83 void swap_array(int array[], int i, int j){
84 int tmp = array[i];
85 array[i] = array[j];
86 array[j] = tmp;
87 }
88
89 /**
90 * prints a permutation and its relevant directions
91 * @param permutation_array:
92 * @param direction_array:
93 * @param number_of_ints: length of array. position zero is not used.
94 * */
95 void print_permutation(int permutation_array[], int direction_array[], int number_of_ints){
96 for(int k = 1; k <= number_of_ints; k++){
97 printf("%4d(%s)\t",permutation_array[k],direction_array[k] == 1?"-->":"<--");
98 }
99 printf("\r\n");
100 }
2
3 #define LEFT -1
4 #define RIGHT 1
5
6 int get_max_moveable_index(int array_direction[], int array_permutation[], int num_of_ints);
7 void johnson_trotter(int n);
8 void swap_array(int array[], int i, int j);
9 void print_permutation(int value_table[], int direction_table[], int number_of_ints);
10 int main(){
11 int n;
12 printf("Enter an integer n:");
13 scanf("%d",&n);
14 johnson_trotter(n);
15 printf("All permutations are generated!\r\n");
16 return 0;
17 }
18
19
20
21 void johnson_trotter(int n){
22 //The johnson_trotter algorithm to generate all permutations of an integer set {1,2,...,n}
23 //Input: A positive integer n
24 //Output: a list of all permutations of {1,2,...,n}
25 int direction_array[n+1];
26 int permutation_array[n+1];
27 for(int k = 1;k <= n;k++){
28 direction_array[k] = LEFT;
29 permutation_array[k] = k;
30 }
31
32 //Initial
33 printf("Initial:\r\n");
34 print_permutation(permutation_array,direction_array,n);
35 int max_moveable_index;
36 int num_counter = 1;
37 while((max_moveable_index = get_max_moveable_index(direction_array,permutation_array,n)) > 0){
38 int num_max_moveable = permutation_array[max_moveable_index];
39 //Print
40 printf("Max Moveable:%d(%s)\r\n",num_max_moveable,direction_array[max_moveable_index] == 1?"-->":"<--");
41 int pointed_index = max_moveable_index + direction_array[max_moveable_index];
42 swap_array(permutation_array,max_moveable_index,pointed_index);
43 swap_array(direction_array,max_moveable_index,pointed_index);
44 for( int k = 1; k <= n; k++){
45 if(permutation_array[k] > num_max_moveable)
46 direction_array[k] *= -1;
47 }
48 print_permutation(permutation_array,direction_array,n);
49 num_counter++;
50 }
51 printf("Total permutations:%d\r\n",num_counter);
52 }
53 /**
54 * @param array_direction: the direction array thats saves the directions of the numbers in permutation array_permutation
55 * @param array_permutation: the observed permutation
56 * @param num_of_ints: number of observed numbers
57 * @return the index of the largest moveable number in permutation array array_permutation
58 * */
59 int get_max_moveable_index(int array_direction[], int array_permutation[], int num_of_ints){
60 int num_of_max_moveable = 0;// the largest moveable number
61 int max_moveable_index = 0; // the index of the largest moveable number
62 //scan for all the moveable numbers and get the largest one of them
63 for(int k = num_of_ints; k > 0; k--){
64 int index_pointed = k + array_direction[k];//the index of the number that the observed number points to
65 int current_num = array_permutation[k];
66 //make sure that the current number is pointed to a valid position
67 if(index_pointed > 0 && index_pointed <= num_of_ints && array_permutation[index_pointed] < current_num){
68 // the current number is moveable
69 if(current_num > num_of_max_moveable){
70 //the current number is the largest moveable number
71 num_of_max_moveable = current_num;
72 max_moveable_index = k;
73 }
74 }
75 }
76 return max_moveable_index;
77 }
78 /**
79 * @param array: the array in which two elements are swapped.
80 * @param i: the index of the first to-be-swapped element
81 * @param j: the index of the second to-be-swapped element
82 * */
83 void swap_array(int array[], int i, int j){
84 int tmp = array[i];
85 array[i] = array[j];
86 array[j] = tmp;
87 }
88
89 /**
90 * prints a permutation and its relevant directions
91 * @param permutation_array:
92 * @param direction_array:
93 * @param number_of_ints: length of array. position zero is not used.
94 * */
95 void print_permutation(int permutation_array[], int direction_array[], int number_of_ints){
96 for(int k = 1; k <= number_of_ints; k++){
97 printf("%4d(%s)\t",permutation_array[k],direction_array[k] == 1?"-->":"<--");
98 }
99 printf("\r\n");
100 }
采用的是Johnson_Trotter算法。很少在Linux下编程，编码有点乱。
源码下载：Johnson_trotter.cpp
posted on 2011-04-26 11:31 Joshua Leung 阅读(290) 评论(0) 收藏 举报
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