一、字典序法
1) 从序列P的右端开始向左扫描,直至找到第一个比其右边数字小的数字,即。
2) 从右边找出所有比大的数中最小的数字,即。
3) 交换与。
4) 将右边的序列翻转,即可得到字典序的下一个排列。
5) 重复上面的步骤,直至得到字典序最大的排列,即左边数字比右边的大的降序排列。
//字典序法 void dictionary(int length){ int * data = (int *)malloc(sizeof(int) * length); int index; for (index = 0; index < length; ++index) data[index] = index + 1; FILE * fp = fopen("dictionary.txt", "w"); print(fp, data, length); while (nextPermutation(data, 0, length)){ print(fp, data, length); } fclose(fp); free(data); } void swap(int data[], int i, int j){//交换两个元素 char temp; temp = data[i]; data[i] = data[j]; data[j] = temp; } void reverse(int data[], int first, int last){//翻转序列 last--; while (first < last){ swap(data, first++, last--); } } int nextPermutation(int data[], int first, int last){ int i, j; i = last - 2; while (i >= 0 && data[i] >= data[i+1]) --i; if (i == -1){ reverse(data, first, last); return 0; } j = last - 1; while (data[j] <= data[i]){ --j; } swap(data, i, j); reverse(data, i + 1, last); return 1; } void print(FILE * fp, int data[], int length){ int index; for (index = 0; index < length; ++index){ fprintf(fp, "%d ", data[index]); } fprintf(fp, " "); }
二、SJT Algorithm
初始状态为。
1) 找到最大的可移动数m(当一个数指向一个比它小的数是,该数就是可移动数)
2) 交换m和m所指向的数
3) 改变所有比m大的数的方向
4) 重复上面的步骤,直至找不到可移动数
//邻位对换法 void exchange(int length){ Item * data = (Item *)malloc(sizeof(Item) * length); int index, indexOfMax; for (index = 0; index < length; ++index){ data[index].digit = index + 1; data[index].direction = -1; data[index].mobile = (index != 0) ? 1 : 0; } indexOfMax = length - 1; FILE * fp = fopen("exchange.txt", "w"); exPrint(data, length, fp); while (1== data[indexOfMax].mobile || existMobile(data, length)){ if (1== data[indexOfMax].mobile){ int direction = data[indexOfMax].direction; exSwap(data, indexOfMax, indexOfMax+direction); indexOfMax += direction; if ((indexOfMax == 0 && direction == -1) || (indexOfMax == length-1 && direction == 1)){ toMobileorNot(data, length); } } else{ index = findMax(data, length); if (index == -1) break; int direction = data[index].direction; exSwap(data, index, index + direction); index += direction; changeDirection(data, length, index); toMobileorNot(data, length); } exPrint(data, length, fp); } fclose(fp); free(data); } int existMobile(Item data[], int length){//判断是否存在可移动数 int index; for (index = 0; index < length; ++index){ if (data[index].mobile == 1) return 1; } return 0; } int findMax(Item data[], int length){//找到最大的可移动数 int ans = -1; for (int index = 0; index < length; ++index){ if (data[index].mobile == 1){ if (ans == -1) ans = index; else if (data[index].digit > data[ans].digit) ans = index; } } return ans; } void changeDirection(Item data[], int length, int index){//改变大于可移动数的数的方向 for (int i = 0; i < length; ++i){ if (data[i].digit > data[index].digit){ data[i].direction = -data[i].direction; } } } void toMobileorNot(Item data[], int length){ if (data[0].direction == 1 && data[0].digit > data[1].digit) data[0].mobile = 1; else data[0].mobile = 0; for (int i = 1; i < (length - 1); ++i){ int direction = data[i].direction; if (data[i].digit > data[i+direction].digit) data[i].mobile = 1; else data[i].mobile = 0; } if (data[length-1].direction == -1 && data[length-1].digit > data[length-2].digit) data[length-1].mobile = 1; else data[length-1].mobile = 0; } void exPrint(Item data[], int length, FILE * fp){ for (int index = 0; index < length; ++index){ fprintf(fp, "%d ", data[index].digit); } fprintf(fp, " "); } void exSwap(Item data[], int i, int j){ Item tmp = data[i]; data[i] = data[j]; data[j] = tmp; }
三、Heap's Algorithm
procedure generate(n : integer, A : array of any): if n = 1 then output(A) else for i := 1; i ≤ n; i += 1 do generate(n - 1, A) if n is odd then j ← 1 else j ← i swap(A[j], A[n])
以上算法描述摘自维基百科
//Recursive implementation. #include <stdio.h> #include <stdlib.h> #include <time.h> FILE * fp = NULL; int len; int str2int(char str[]){ int i = 0; int result = 0; while (str[i] != ' '){ result = result * 10 + str[i] - '0'; ++i; } return result; } void print(int data[]){ int i; for (i = 0; i < len; ++i) fprintf(fp, "%d ", data[i]); fprintf(fp, " "); } void swap(int *x, int *y){ int tmp = *x; *x = *y; *y = tmp; } void generate(int data[], int n){ int i; if (1 == n) print(data); //return; else{ for (i = 0; i < n; ++i){ generate(data, n-1); if (n % 2 == 1){ swap(&data[1], &data[n-1]); } else{ swap(&data[i], &data[n-1]); } } } } void heapAlgorithm(int n){ int * data = (int *)malloc(sizeof(int) * n); int i; for(i = 0; i < n; ++i) data[i] = i + 1; generate(data, n); free(data); } int main(int argc, char **argv){ fp = fopen("heap.txt", "w"); len = (argc > 1) ? str2int(argv[1]) : 10; clock_t time = clock(); heapAlgorithm(len); time = clock() - time; printf("Heap's Algorithm takes %d clocks(%f seconds). ", time, ((float)time)/CLOCKS_PER_SEC); return 0; }