摘要：用Python语言程序表述的分子式解析与集合操作。Python不同材料元素集合合并为总集合分析复合材料所有组成元素-化学中的应用。等等。
离散量与结构数学-组合数学计算机处理实例
组合数学应用
用Python语言程序表述的分子式解析与集合操作。Python不同材料元素集合合并为总集合分析复合材料所有组成元素-化学中的应用。等等。
C语言由于它的自身严谨-硬件操作与数值计算问题的根性应用，包括各种C编译器也就非常严谨。所以有了下面程序的第一行代码。
#pragma warning(disable:4996)
///////////////////////
#include
#include
#include
#define MAX_ELEMENTS 100
#define MAX_LENGTH 100
void swap(char* a, char* b) {
char temp = *a;
*a = *b;
*b = temp;
}
void permute_without_duplicates(char* elements, int start, int end) {
if (start == end) {
printf("%s\n", elements);
}
else {
for (int i = start; i
int is_duplicate = 0;
for (int j = start; j
if (elements[j] == elements[i]) {
is_duplicate = 1;
break;
}
}
if (is_duplicate) continue;
swap(&elements[start], &elements[i]);
permute_without_duplicates(elements, start + 1, end);
} } }
int compare(const void* a, const void* b) {
return strcmp(*(const char**)a, *(const char**)b);
}
void generate_permutations(char* elements, int start, int end, char*** permutations, int* count, int* capacity) {
if (start == end) {
if (*count >= *capacity) {
*capacity *= 2;
*permutations = realloc(*permutations, (*capacity) * sizeof(char*));
if (!*permutations) {
printf("内存分配失败\n");
exit(1);
} }
(*permutations)[*count] = malloc((end - start + 2) * sizeof(char));
if (!(*permutations)[*count]) {
printf("内存分配失败\n");
exit(1);
}
strcpy((*permutations)[*count], elements);
(*count)++;
}
else {
for (int i = start; i
swap(&elements[start], &elements[i]);
generate_permutations(elements, start + 1, end, permutations, count, capacity);
} } }
void permute_with_duplicates(char* elements, int start, int end) {
int capacity = 10;
int count = 0;
char** permutations = malloc(capacity * sizeof(char*));
if (!permutations) {
printf("内存分配失败\n");
exit(1);
}
generate_permutations(elements, start, end, &permutations, &count, &capacity);
qsort(permutations, count, sizeof(char*), compare);
for (int i = 0; i
if (i == 0 || strcmp(permutations[i], permutations[i - 1]) != 0) {
printf("%s\n", permutations[i]);
}
free(permutations[i]);
}
free(permutations);
}
void permute_with_length(char* elements, int len, int current_length,
char* current_permutation, int used) {
if (current_length == len) {
current_permutation[current_length] = '\0';
printf("%s\n", current_permutation);
return;
}
for (int i = 0; elements[i] != '\0'; i++) {
if (!used[i]) {
if (current_length >= MAX_LENGTH - 1) {
printf("超出最大长度限制(%d)", MAX_LENGTH);
return;
}
used[i] = 1;
current_permutation[current_length] = elements[i];
permute_with_length(elements, len, current_length + 1, current_permutation, used);
used[i] = 0;
} } }
int main {
int choice;
char elements[MAX_ELEMENTS] = { 0 };
int length;
printf("请选择限制条件：\n");
printf("1. 无重复元素的全排列\n");
printf("2. 有重复元素的全排列\n");
printf("3. 指定长度的排列\n");
printf("请输入选择的序号 (1/2/3): ");
if (scanf_s("%d", &choice) != 1 || choice 3) {
printf("输入无效，请输入有效的数字(1/2/3)。\n");
return 1;
}
getchar;
printf("请输入元素，用逗号分隔: ");
if (fgets(elements, MAX_ELEMENTS, stdin) == NULL) {
printf("输入无效\n");
return 1;
}
int j = 0;
for (int i = 0; elements[i] != '\0' && j
if (elements[i] == ',' || elements[i] == '\n' || elements[i] == ' ') {
continue;
}
elements[j++] = elements[i];
}
elements[j] = '\0';
if (strlen(elements) == 0) {
printf("未输入有效元素\n");
return 1;
}
switch (choice) {
case 1:
permute_without_duplicates(elements, 0, strlen(elements) - 1);
break;
case 2:
permute_with_duplicates(elements, 0, strlen(elements) - 1);
break;
case 3: {
printf("请输入排列长度: ");
if (scanf_s("%d", &length) != 1 || length strlen(elements)) {
printf("输入无效，请输入1-%d之间的数字。\n", strlen(elements));
return 1;
}
getchar;
char current_permutation[MAX_LENGTH] = { 0 };
int used[MAX_ELEMENTS] = { 0 };
permute_with_length(elements, length, 0, current_permutation, used);
break;
}
default:
printf("无效选择\n");
}
return 0;
}
来源：三日雨-等风来
