数据结构线性表的链式存储结构

1.实验目的掌握线性表的链式存储结构设计与基本操作的实现。

2.实验内容与要求⑴定义线性表的链式存储表示；⑵基于所设计的存储结构实现线性表的基本操作；⑶编写一个主程序对所实现的线性表进行测试；⑷线性表的应用：①设线性表L1和L2分别代表集合A和B，试设计算法求A和B的并集C，并用线性表L3代表集合C；②设线性表L1和L2中的数据元素为整数，且均已按值非递减有序排列，试设计算法对L1和L2进行合并，用线性表L3保存合并结果，要求L3中的数据元素也按值非递减有序排列。

⑸设计一个一元多项式计算器，要求能够：①输入并建立多项式；②输出多项式；③执行两个多项式相加；④执行两个多项式相减；3.数据结构设计逻辑结构：线性结构存储结构：链式存储结构4.算法设计#include <stdio.h>#include <malloc.h>#include <windows.h>typedef struct LNode{int data;struct LNode *next;}LNode;typedef struct Pnode{ float coef;int exp;struct Pnode *next;}Polynode;void menu(){printf("******************************* **************\n");printf("* 作者：Dick *\n");printf("* 信计1001 xxxxxxxxxx *\n");printf("*********************MENU**** ***************\n");printf("1 求A和B的并集C\n");printf("2 对A和B进行合并,用线性表C保存合并结果(有序)\n");printf("3 建立一元多项式(两个)\n");printf("4 两个一元多项式相加\n");printf("5 两个一元多项式相减\n");printf("6 退出程序\n");}void UnionList(){//先输入两个链表，然后判断是否为空，头结点还是要的。

int i;LNode *List1,*List2,*List3,*p,*q,*r;List1 = (LNode *)malloc( sizeof(LNode) );List2 = (LNode *)malloc( sizeof(LNode) );List3 = (LNode *)malloc( sizeof(LNode) );List1->next = List2->next = List3->next = NULL;printf("请输入第一个链表的数据(1~100),以0结束\n");p = q = r = (LNode *)malloc( sizeof(LNode) );while(1){p = (LNode *)malloc( sizeof(LNode) );do{printf("请输入数据\n");scanf("%d",&i);if(i < 0 || i > 100)printf("输入错误，请重新输入\n");}while(i < 0 || i > 100);p->data = i;if(p->data == 0){q->next = NULL;free(p);break;}q->next = p;q = p;}//这个时候链表基本搞定,连接上就行了List1 = r;p = List1->next;printf("\n您输入的链表为\n");while(p != NULL){i++;printf("%d\t",p->data);if(i == 5){i = 0;printf("\n");}p = p->next;}//第二个。

printf("请输入第二个链表的数据(1~100),以0结束\n");p = q = r = (LNode *)malloc( sizeof(LNode) );while(1){p = (LNode *)malloc( sizeof(LNode) );do{printf("请输入数据\n");scanf("%d",&i);if(i < 0 || i > 100)printf("输入错误，请重新输入\n");}while(i < 0 || i > 100);p->data = i;if(p->data == 0){q->next = NULL;free(p);break;}q->next = p;q = p;}List2 = r;p = List2->next;printf("\n您输入的链表为\n");while(p != NULL){i++;printf("%d\t",p->data);if(i == 5){i = 0;printf("\n");}p = p->next;}//List3已经初始化了，现在先检测List1中是否有重复项p = List1->next;q = p->next;while(p->next != NULL){while(q != NULL){if(p->data == q->data){r = List1->next;while(r->next != q)r = r->next;r->next = q->next;free(q);q = r->next;}elseq = q->next;}if(p->next != NULL){p = p->next;q = p->next;}elsebreak;}//检测两个链表的重复项p = List1->next;q = List2->next;while(p != NULL ){while(q != NULL){if(p->data == q->data){r = List2;while( r ->next != q)r = r->next;r->next = q->next;free(q);q = r->next;}elseq = q->next;}q = List2->next;p = p->next;}List3->next = List1->next;r = List1;while(r->next != NULL)r = r->next;r->next = List2->next;//这里输出printf("\n并集C为:\n");p = List3->next;i = 0;while(p != NULL){i++;printf("%d\t",p->data);if(i == 5){i = 0;printf("\n");}p = p->next;}printf("\n请输入回车键继续\n");getchar();getchar();system("CLS");}void UnionSort(){//前面是一样的,抽空考虑优化代码//写的有问题。

破坏了链表结构所以这里就不能优化了。

int i;LNode *List1,*List2,*List3,*p,*q,*r;List1 = (LNode *)malloc( sizeof(LNode) );List2 = (LNode *)malloc( sizeof(LNode) );List3 = (LNode *)malloc( sizeof(LNode) );List1->next = List2->next = List3->next = NULL;printf("请输入第一个链表的数据(1~100),以0结束\n");p = q = r = (LNode *)malloc( sizeof(LNode) );while(1){p = (LNode *)malloc( sizeof(LNode) );do{printf("请输入数据\n");scanf("%d",&i);if(i < 0 || i > 100)printf("输入错误，请重新输入\n");}while(i < 0 || i > 100);p->data = i;if(p->data == 0){q->next = NULL;free(p);break;}q->next = p;q = p;}//这个时候链表基本搞定,连接上就行了List1 = r;//输出下好了p = List1->next;printf("\n您输入的链表为\n");while(p != NULL){i++;printf("%d\t",p->data);if(i == 5){i = 0;printf("\n");}p = p->next;}//第二个。

printf("请输入第二个链表的数据(1~100),以0结束\n");p = q = r = (LNode *)malloc( sizeof(LNode) );while(1){p = (LNode *)malloc( sizeof(LNode) );do{printf("请输入数据\n");scanf("%d",&i);if(i < 0 || i > 100)printf("输入错误，请重新输入\n");}while(i < 0 || i > 100);p->data = i;if(p->data == 0){q->next = NULL;free(p);break;}q->next = p;q = p;}List2 = r;p = List2->next;printf("\n您输入的链表为\n");while(p != NULL){i++;printf("%d\t",p->data);if(i == 5){i = 0;printf("\n");}p = p->next;}//这里默认已经有序了,直接连接到第三个上面p = List1->next;q = List2->next;List3 = r = List1;while(p != NULL && q != NULL){if(p->data <= q->data){r->next = p;r = p;p = p->next;}else{r->next = q;r = q;q = q->next;}}r->next = p?p:q;free(List2);//这里输出printf("\n合并后的表格是:\n");p = List3->next;i = 0;while(p != NULL){i++;printf("%d\t",p->data);if(i == 5){i = 0;printf("\n");}p = p->next;}printf("\n请输入回车键继续\n");getchar();getchar();system("CLS");}void InitPolynomial(Polynode *&Poly1,Polynode *&Poly2){float j;int i;Polynode *p,*q,*r;Poly1->next = Poly2->next = NULL;extern void DisplayList(Polynode *&Poly3);printf("请输入第一个多项式的数据(1~100),以0结束\n");p = q = r = (Polynode *)malloc( sizeof(Polynode) );while(1){p = (Polynode *)malloc( sizeof(Polynode) );do{printf("请输入多项式系数\n");scanf("%f",&j);if(j < 0 || j > 100)printf("输入错误，请重新输入\n");}while(j < 0 || j > 100);p->coef = j;do{printf("请输入多项式次数\n");scanf("%d",&i);if(i < 0 || i > 100)printf("输入错误，请重新输入\n");}while(i < 0 || i > 100);p->exp = i;if( (int) (p->coef - 0) <0.01 ){q->next = NULL;free(p);break;}q->next = p;q = p;}//这个时候链表基本搞定,连接上就行了Poly1 = r;printf("请输入第二个多项式的数据(1~100),以0结束\n");p = q = r = (Polynode *)malloc( sizeof(Polynode) );while(1){p = (Polynode *)malloc( sizeof(Polynode) );do{printf("请输入多项式系数\n");scanf("%f",&j);if(j < 0 || j > 100)printf("输入错误，请重新输入\n");}while(j < 0 || j > 100);p->coef = j;do{printf("请输入多项式次数\n");scanf("%d",&i);if(i < 0 || i > 100)printf("输入错误，请重新输入\n");}while(i < 0 || i > 100);p->exp = i;if( (int) (p->coef - 0) <0.01 ){q->next = NULL;free(p);break;}q->next = p;q = p;}Poly2 = r;//输出多项式DisplayList(*&Poly1);DisplayList(*&Poly2);}void PolyPlus(Polynode *&Poly1,Polynode *&Poly2){Polynode *Poly3,*p,*q,*r,*s;extern void DisplayList(Polynode *&Poly3);Poly3 = (Polynode *)malloc( sizeof(Polynode) );s = Poly3;p = Poly1->next;q = Poly2->next;//两个链表相加,都是判断语句，比较两个表中每个元素的次数while(p != NULL && q != NULL){r = (Polynode *)malloc( sizeof(Polynode) );if(p->exp > q->exp){r->coef = q ->coef;r->exp = q->exp;s->next = r;s = r;q = q->next;}else if(p->exp < q->exp){r->coef = p ->coef;r->exp = p->exp;s->next = r;s = r;p = p->next;}else if( p->exp == q->exp){r->coef = p->coef + q->coef;if(r->coef == 0){free(r);}else if(r->coef != 0){r->exp = p->exp;s->next = r;s = r;}p = p->next;q = q->next;}}if(p != NULL)while(p != NULL){r = (Polynode *)malloc( sizeof(Polynode) );r->coef = p->coef;r->exp = p->exp;s->next = r;s = r;p = p->next;}elsewhile(q != NULL){r = (Polynode *)malloc( sizeof(Polynode) );r->coef = q->coef;r->exp = q->exp;s->next = r;s = r;q = q->next;}r->next = NULL;DisplayList(*&Poly3);}void PolySub(Polynode *&Poly1,Polynode *&Poly2){Polynode *Poly3,*p,*q,*r,*s;extern void DisplayList(Polynode *&Poly3);Poly3 = (Polynode *)malloc( sizeof(Polynode) );s = Poly3;p = Poly1->next;q = Poly2->next;//和上面的基本一样,只不过变了个符号而已,感觉还能和上面的函数//加起来还能优化while(p != NULL && q != NULL){r = (Polynode *)malloc( sizeof(Polynode) );if(p->exp > q->exp){r->coef = -(q->coef);r->exp = q->exp;s->next = r;s = r;q = q->next;}else if(p->exp < q->exp){r->coef = p ->coef;r->exp = p->exp;s->next = r;s = r;p = p->next;}else if( p->exp == q->exp){r->coef = (p->coef) - (q->coef);if(r->coef == 0){free(r);}else if(r->coef != 0){r->exp = p->exp;s->next = r;s = r;}p = p->next;q = q->next;}}if(p != NULL)while(p != NULL){r = (Polynode *)malloc( sizeof(Polynode) );r->coef = p->coef;r->exp = p->exp;s->next = r;s = r;p = p->next;}elsewhile(q != NULL){r = (Polynode *)malloc( sizeof(Polynode) );r->coef = -(q->coef);r->exp = q->exp;s->next = r;s = r;q = q->next;}r->next = NULL;DisplayList(*&Poly3);}void DisplayList(Polynode *&Poly3){int i=0;Polynode *p;p = Poly3->next;printf("\n结果为\n");printf("F(x)= ");while(p->next != NULL){i++;//首先判断的是系数是否为1,为1的话就不输出系数了if( p->coef != 1 ){//这里判断次数，次数为0不输出"x"if( p->exp == 0){if( (p->coef - (int)p->coef) < 0.01 )if(p->coef < 0)printf("\b%d+",(int)p->coef);elseprintf("%d+",(int)p->coef);elseif(p->coef < 0)printf("\b%6.3f+",p->coef);elseprintf("%6.3f+",p->coef);if(i == 10){i = 0;printf("\n");}}//这里判断次数是否为1,次数为1只输出一个"x"else if( p->exp == 1 ){if( (p->coef - (int)p->coef) < 0.01 )if(p->coef < 0)printf("\b%dx+",(int)p->coef);elseprintf("%dx+",(int)p->coef);elseif(p->coef < 0)printf("\b%6.3fx+",p->coef);elseprintf("%6.3fx+",p->coef);if(i == 10){i = 0;printf("\n");}}else{if( (p->coef - (int)p->coef) < 0.01 )if(p->coef < 0)printf("\b%dx^%d+",(int)p->coef,p->exp );elseprintf("%dx^%d+",(int)p->coef,p->exp);elseif(p->coef < 0)printf("\b%6.3fx^%d+",p->coef,p->exp);elseprintf("%6.3fx^%d+",p->coef,p->exp);if(i == 10){i = 0;printf("\n");}}}else{if( p->exp == 0){if(p->coef < 0)printf("\b%d+",(int)p->coef);elseprintf("%d+",(int)p->coef);if(i == 10){i = 0;printf("\n");}}else if( p->exp ==1){if(p->coef < 0)printf("\bx+",(int)p->coef);elseprintf("x+",(int)p->coef);if(i == 10){i = 0;printf("\n");}}else{if(p->coef < 0)printf("\bx^%d+",p->exp);elseprintf("x^%d+",p->exp);if(i == 10){i = 0;printf("\n");}}}p = p->next;}//这里是最后一个位置，因为最后少输出一个运算符//所以再进行一次输出,不然上面再增加判断语句的话//就更乱了i++;if( p->coef != 1 ){if( p->exp == 0){if( (p->coef - (int)p->coef) < 0.01 )if(p->coef < 0)printf("\b%d",(int)p->coef);elseprintf("%d",(int)p->coef);elseif(p->coef < 0)printf("\b%6.3f",p->coef);elseprintf("%6.3f",p->coef);if(i == 10){i = 0;printf("\n");}}else if( p->exp ==1){if( (p->coef - (int)p->coef) < 0.01 )if(p->coef < 0)printf("\b%dx",(int)p->coef);elseprintf("%dx",(int)p->coef);elseif(p->coef < 0)printf("\b%6.3fx",p->coef);elseprintf("%6.3fx",p->coef);if(i == 10){i = 0;printf("\n");}}else{if( (p->coef - (int)p->coef) < 0.01 )if(p->coef < 0)printf("\b%dx^%d",(int)p->coef,p->exp);elseprintf("%dx^%d",(int)p->coef,p->exp);elseif(p->coef < 0)printf("\b%6.3fx^%d",p->coef,p->exp);else printf("%6.3fx^%d",p->coef,p->exp);if(i == 10){i = 0;printf("\n");}}}else{if( p->exp == 0){if(p->coef < 0)printf("\b%d+",(int)p->coef);elseprintf("%d+",(int)p->coef);if(i == 10){i = 0;printf("\n");}}else if( p->exp ==1){if(p->coef < 0)printf("\bx+",(int)p->coef);elseprintf("x+",(int)p->coef);if(i == 10){i = 0;printf("\n");}}else{if(p->coef < 0)printf("\bx^%d+",p->exp);elseprintf("x^%d+",p->exp);if(i == 10){i = 0;printf("\n");}}}printf("\n");printf("\n请输入回车键继续\n");getchar();getchar();}void main(){int i;Polynode *Poly1,*Poly2;Poly1 = (Polynode *)malloc( sizeof(Polynode) );Poly2 = (Polynode *)malloc( sizeof(Polynode) );while(1){menu();do //这里循环直到你输入正确的数字为止{printf ( "请输入要进行的操作\n" );scanf ("%d",&i);if (i<1||i>6)printf("错误数字，请重新输入\n");}while (i<1||i>6);switch (i){case 1: UnionList(); break;case 2: UnionSort(); break;//清屏函数放到break前面可以有效的在执行完一系列函数之后才清屏case 3: InitPolynomial(*&Poly1,*&Poly2);system("CLS");break;case 4: PolyPlus(*&Poly1,*&Poly2);system("CLS");break;case 5: PolySub(*&Poly1,*&Poly2);system("CLS");break;case 6: exit(0); break;}}}5.测试结果图一：非递减有序排列图二：求并集图四：两个多项式相加图五：两个多项式相减图三：输入两个多项式。