离散数学实践:集合的表示与运算

实验目的

熟悉集合的基本概念，并在计算机中用适当的数据结构来表示。

实验内容

简单集合（如数字集合）的数组表示法和链表表示法，并测试正确性。编程实现集合的并、交、差、补和对称差运算。

 实验要求

列出实验目的、实验内容、实验步骤、实验的源程序和实验结果。

实验参考

集合的表示是集合论的基础，我们可以选择数组和链表这两种常用的数据结构来实现。根据集合的五种基本运算的含义，对参与运算的两个集合做遍历，从而求出其计算结果。

源程序参考

/**************************************************************************  * (C) Copyright 2015-2018 by Gavin  Y. Liu  All Rights Reserved.         *  *                                                                        *  * DISCLAIMER: The authors and publisher shall not be liable in any event *   * for incidental or consequential damages in connection with, or arising *  * out of, the furnishing, performance, or use of these programs.         *  **************************************************************************/ #ifndef _SETLOGICHEADER_H_#define _SETLOGICHEADER_H_#define MAX_NUM 200#define MAX_SIZE 100typedef struct{int size;char ele[MAX_NUM][MAX_SIZE];}ArraySet;typedef struct LinkSet{char ele[MAX_SIZE];struct LinkSet* next;}LinkSet;/*Private function prototypes*/static void arrayset_union_oper(ArraySet set1, ArraySet set2, ArraySet* resu);static void arrayset_inter_oper(ArraySet set1, ArraySet set2, ArraySet* resu);static void arrayset_differ_oper(ArraySet set1, ArraySet set2, ArraySet* resu);static void arrayset_symdiffer_oper(ArraySet set1, ArraySet set2, ArraySet* resu);static void arrayset_comple_oper(ArraySet e, ArraySet set1, ArraySet* resu);static void linkset_union_oper(LinkSet* set1, LinkSet* set2, LinkSet* resu);static void linkset_inter_oper(LinkSet* set1, LinkSet* set2, LinkSet* resu);static void linkset_differ_oper(LinkSet* set1, LinkSet* set2, LinkSet* resu);static void linkset_symdiffer_oper(LinkSet* set1, LinkSet* set2, LinkSet* resu);static void linkset_comple_oper(LinkSet* e, LinkSet* set, LinkSet* resu);static int str_cmp(const char* s1, const char* s2);static int fun(const void* a, const void* b);static void arrayset_init(ArraySet* set);static int arrayset_push(ArraySet* set, const char* data);static int arrayset_pop(ArraySet* set, const char* data);static void arrayset_modify(ArraySet* set, char* olddata, char* newdata);static void arrayset_destroy(ArraySet* set);static void arrayset_print(const ArraySet set);static int linkset_init(LinkSet** head);static void linkset_destroy(LinkSet** set);static void linkset_print(const LinkSet* set);static void linkset_print(const LinkSet* set);static int linkset_pop(LinkSet* set, char* data);static int linkset_push(LinkSet* set, const char* data);static int linkset_modify(LinkSet* set, char* olddata, char* newdata);/*Public function prototypes*/void sample_arrayset_test();void sample_linkset_test();#endif // end of _SETLOGICHEADER_H_

/**************************************************************************  * (C) Copyright 2015-2018 by Gavin  Y. Liu  All Rights Reserved.         *  *                                                                        *  * DISCLAIMER: The authors and publisher shall not be liable in any event *   * for incidental or consequential damages in connection with, or arising *  * out of, the furnishing, performance, or use of these programs.         *  **************************************************************************/ #include <stdio.h>#include <stdlib.h>#include <string.h>#include <assert.h>#include "SetLogicHeader.h"//union operatingstatic void arrayset_union_oper(ArraySet set1, ArraySet set2, ArraySet* resu){int i = 0;for(i = 0; i < set1.size; i++){arrayset_push(resu, set1.ele[i]);}for(i = 0; i < set2.size; i++){arrayset_push(resu, set2.ele[i]);}}//inter operatingstatic void arrayset_inter_oper(ArraySet set1, ArraySet set2, ArraySet* resu){int i = 0, j = 0, k = 0;for(i = 0; i < set1.size; i++){for(; j < set2.size;){k = str_cmp(set2.ele[j], set1.ele[i]);if(k < 0)j++;else if(k == 0){arrayset_push(resu, set1.ele[i]);j++;break;}elsebreak;}}}//defference operatingstatic void arrayset_differ_oper(ArraySet set1, ArraySet set2, ArraySet* resu){int i = 0, j = 0, k = 0;for(i = 0; i < set1.size; i++){if(j >= set2.size){arrayset_push(resu, set1.ele[i]);continue;}for(; j < set2.size;){k = str_cmp(set2.ele[j], set1.ele[i]);if(k < 0)j++;else if(k > 0){arrayset_push(resu, set1.ele[i]);break;}else{j++;break;}}}}// symdifferecne operatingstatic void arrayset_symdiffer_oper(ArraySet set1, ArraySet set2, ArraySet* resu){ArraySet tmp1;ArraySet tmp2;arrayset_init(&tmp1);arrayset_init(&tmp2);arrayset_differ_oper(set1, set2, &tmp1);arrayset_differ_oper(set2, set1, &tmp2);arrayset_union_oper(tmp1, tmp2, resu);arrayset_destroy(&tmp1);arrayset_destroy(&tmp2);}// comple operatingstatic void arrayset_comple_oper(ArraySet e, ArraySet set1, ArraySet* resu){arrayset_differ_oper(e, set1, resu);}/*linkset operating*/static void linkset_union_oper(LinkSet* set1, LinkSet* set2, LinkSet* resu){//|while(set1->next != NULL){set1 = set1->next;linkset_push(resu, set1->ele);}while(set2->next != NULL){set2 = set2->next;linkset_push(resu, set2->ele);}}static void linkset_inter_oper(LinkSet* set1, LinkSet* set2, LinkSet* resu){//^while(set1->next != NULL){set1 = set1->next;while(set2 != NULL){int k = str_cmp(set2->ele, set1->ele);if(k < 0){set2 = set2->next;}else if(k == 0){linkset_push(resu, set1->ele);set2 = set2->next;break;}elsebreak;}}}static void linkset_differ_oper(LinkSet* set1, LinkSet* set2, LinkSet* resu){//-while(set1->next != NULL){set1 = set1->next;if(set2 == NULL){linkset_push(resu, set1->ele);continue;}while(set2 != NULL){int k = str_cmp(set2->ele, set1->ele);if(k < 0){set2 = set2->next;}else if(k > 0){linkset_push(resu, set1->ele);break;}else{set2 = set2->next;break;}}}}static void linkset_symdiffer_oper(LinkSet* set1, LinkSet* set2, LinkSet* resu){//+LinkSet *tmp1, *tmp2;linkset_init(&tmp1);linkset_init(&tmp2);linkset_differ_oper(set1, set2, tmp1);linkset_differ_oper(set2, set1, tmp2);linkset_union_oper(tmp1, tmp2, resu);linkset_destroy(&tmp1);linkset_destroy(&tmp2);}static void linkset_comple_oper(LinkSet* e, LinkSet* set, LinkSet* resu){//~linkset_differ_oper(e, set, resu);}static int str_cmp(const char* s1, const char* s2){int l1 = strlen(s1);int l2 = strlen(s2);if(l1 < l2)return -1;else if(l1 > l2)return 1;elsereturn strcmp(s1, s2);}static int fun(const void* a, const void* b){return str_cmp((char*)a, (char*)b);}static void arrayset_init(ArraySet* set){set->size = 0;memset(set->ele, '\0', sizeof(char) * MAX_NUM * MAX_SIZE);}static int arrayset_push(ArraySet* set, const char* data){assert(set->size < MAX_SIZE);int i = 0;for(i = 0; i < MAX_NUM; i++){if(strcmp(set->ele[i], data) == 0){return 0;}}strcpy_s(set->ele[set->size++], data);qsort(set->ele, set->size, sizeof(set->ele[0]), fun);return 1;}static int arrayset_pop(ArraySet* set, const char* data){int i = 0;while(i < set->size && strcmp(set->ele[i], data) != 0){ i++; }if(i >= set->size)return 0;for(; i < set->size - 1; i++){strcpy_s(set->ele[i], set->ele[i + 1]);}strcpy_s(set->ele[set->size--], "\0");return 1;}static void arrayset_modify(ArraySet* set, char* olddata, char* newdata){int i = 0;while(i < set->size && strcmp(set->ele[i], olddata) != 0){ i++;}strcpy_s(set->ele[i], newdata);}static void arrayset_destroy(ArraySet* set){memset(set->ele, 0, sizeof(char) * set->size * MAX_SIZE);set->size = 0;}static void arrayset_print(const ArraySet set){int i = 0;printf("{");for(i = 0; i < set.size; i++){printf("%s   ", set.ele[i]);}printf("}\n");}static int linkset_init(LinkSet** head){if((*head = (LinkSet*)malloc(sizeof(LinkSet))) == NULL){return 0;}(*head)->next = NULL;strcpy_s((*head)->ele, "\0");return 1;}static void linkset_print(const LinkSet* set){printf("{");while(set->next != NULL){printf("%s   ", set->next->ele);set = set->next;}printf("}\n");}static int linkset_push(LinkSet* set, const char* data){assert(set != NULL);while(set != NULL){if(strcmp(set->ele, data) == 0)return 0;else if(set->next == NULL){LinkSet* node = (LinkSet*)malloc(sizeof(LinkSet));set->next = node;node->next = NULL;strcpy_s(node->ele, data);return 1;}else{int l1 = strlen(data), l2 = strlen(set->next->ele);if(l1 < l2 || (l1 == l2 && strncmp(data, set->next->ele, l1) < 0)){LinkSet* node = (LinkSet*)malloc(sizeof(LinkSet));node->next = set->next;set->next = node;strcpy_s(node->ele, data);return 1;}}set = set->next;}return 0;}static int linkset_pop(LinkSet* set, char* data){assert(set != NULL);while(set->next != NULL){if(strcmp(set->next->ele, data) == 0){LinkSet* tmp = set->next;set->next = tmp->next;free(tmp);return 1;}set = set->next;}return 0;}static int linkset_modify(LinkSet* set, char* olddata, char* newdata){while(set != NULL){if(strcmp(set->ele, olddata) == 0){strcpy_s(set->ele, newdata);return 1;}set = set->next;}return 0;}static void linkset_destroy(LinkSet** set){while((*set)->next != NULL){LinkSet* tmp = *set;(*set) = (*set)->next;free(tmp);}}void sample_linkset_test(){printf("\nlink set test:\n");char s[100];LinkSet *e;   //  Universal SetLinkSet *set1; LinkSet *set2;LinkSet *resu_u;LinkSet *resu_i;LinkSet *resu_d;LinkSet *resu_s;LinkSet *resu_c;linkset_init(&e);linkset_init(&set1);linkset_init(&set2);linkset_init(&resu_u);linkset_init(&resu_i);linkset_init(&resu_d);linkset_init(&resu_s);linkset_init(&resu_c);while(scanf("%s", s) && strcmp(s, "#") != 0)// input Universal Set{printf("Please Enter Universal Set:\n");linkset_push(e, s);memset(s, '\0', sizeof(char) * 100);}while(scanf("%s", s) && strcmp(s, "#") != 0){printf("Please Enter Set1:\n");linkset_push(set1, s);memset(s, '\0', sizeof(char) * 100);}while(scanf("%s", s) && strcmp(s, "#") != 0){printf("Please Enter Set2:\n");linkset_push(set2, s);memset(s, '\0', sizeof(char) * 100);}printf("Univrsal Set(E) is:    "); linkset_print(e);printf("Set1 is: "); linkset_print(set1);printf("Set2 is: "); linkset_print(set2);linkset_union_oper(set1, set2, resu_u);linkset_inter_oper(set1, set2, resu_i);linkset_differ_oper(set1, set2, resu_d);linkset_symdiffer_oper(set1, set2, resu_s);linkset_comple_oper(e, set1, resu_c);printf("union set1 and set2: "); linkset_print(resu_u);printf("inter set1 and set2: "); linkset_print(resu_i);printf("differ set1 and set2: "); linkset_print(resu_d);printf("symdiffer set1 and set2: "); linkset_print(resu_s);printf("comple e and set2: "); linkset_print(resu_c);linkset_destroy(&resu_u);linkset_destroy(&resu_i);linkset_destroy(&resu_d);linkset_destroy(&resu_s);linkset_destroy(&resu_c);linkset_destroy(&e);linkset_destroy(&set1);linkset_destroy(&set2);}//集合的数组表示测试void sample_arrayset_test(){printf("\narray set test:\n");char s[100];ArraySet e, set1, set2;//全集，集合，集合ArraySet resu_u, resu_i, resu_d, resu_s, resu_c;//并，交，差，相对差，补运算的结果arrayset_init(&e);//集合数组初始化arrayset_init(&set1);arrayset_init(&set2);arrayset_init(&resu_u);arrayset_init(&resu_i);arrayset_init(&resu_d);arrayset_init(&resu_s);arrayset_init(&resu_c);while(scanf("%s", s) && strcmp(s, "#") != 0)//输入全集{arrayset_push(&e, s);memset(s, '\0', sizeof(char) * 100);}while(scanf("%s", s) && strcmp(s, "#") != 0)//输入集合{arrayset_push(&set1, s);memset(s, '\0', sizeof(char) * 100);}while(scanf("%s", s) && strcmp(s, "#") != 0)//输入集合{arrayset_push(&set2, s);memset(s, '\0', sizeof(char) * 100);}printf("e is:    "); arrayset_print(e);printf("set1 is: "); arrayset_print(set1);printf("set2 is: "); arrayset_print(set2);arrayset_union_oper(set1, set2, &resu_u);//并arrayset_inter_oper(set1, set2, &resu_i);//交arrayset_differ_oper(set1, set2, &resu_d);//差arrayset_symdiffer_oper(set1, set2, &resu_s);//相对差arrayset_comple_oper(e, set1, &resu_c);//补printf("union set1 and set2: "); arrayset_print(resu_u);printf("inter set1 and set2: "); arrayset_print(resu_i);printf("differ set1 and set2: "); arrayset_print(resu_d);printf("symdiffer set1 and set2: "); arrayset_print(resu_s);printf("comple e and set2: "); arrayset_print(resu_c);arrayset_destroy(&resu_u);//销毁数组arrayset_destroy(&resu_i);arrayset_destroy(&resu_d);arrayset_destroy(&resu_s);arrayset_destroy(&resu_c);arrayset_destroy(&e);arrayset_destroy(&set1);arrayset_destroy(&set2);}

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