设有多项式a=1+3x+2^4，试用线性链表示

设有多项式a=1+3x+2^4，试用线性链表示

#include
#include
#include

typedef struct _POLYNODE{
int coef;//系数
int exp;//指数
struct _POLYNODE *next;
}polynode,*polyptr;

void createPoly(polynode **P, char ch[]);//建立项式链表
void polyAdd(polynode *A,polynode *B);//项式加
void polyMinus(polynode *A,polynode *B);//减
void polyMulti(polynode *A,polynode *B);//乘
void polyDiv(polynode *A,polynode *B);//除
void order(polynode **P);//排序
void display(polynode *P);//展示项式
void destroy(polynode **P);//销毁项式
void menu();//命令菜单
int isPut(char ch[]);
//菜单
void menu(){
printf("1.输入项式.\n"
"2.项式相加.\n"
"3.项式相减.\n"
"4.项式相乘.\n"
"5.项式相除.\n"
"6.显示项式.\n"
"7.销毁项式.\n"
"8.退.\n");
}
//判断菜单选择
int IsChoice(int choice){
if(0 choice && 9 > choice)
return 1;
else
return 0;
}

int isPut(char ch[]){
int i,j = 1;
for(i = 0; ch[i] != '\0'; i++){
{if(0 == j && '^' == ch[i])
return 0;
if('^' == ch[i] && 1 == j)
j = 0;
if(('+' ==ch[i] || '-' == ch[i] || '*' == ch[i] || '/' == ch[i]) && 0 == j)
j = 1;

}
if('.' != ch[i] && 'x' != ch[i] && 'X' != ch[i] && '^' != ch[i] && '+' != ch[i] && '-' != ch[i] && '*' != ch[i] && '/' != ch[i] && !isdigit(ch[i]))
return 0;
else{
if('+' ==ch[0] || '*' == ch[0] || '/' == ch[0] || '^' == ch[0] || '.' == ch[0])
return 0;
if('\0' == ch[i+1] && '+' ==ch[0] || '*' == ch[0] || '/' == ch[0] || '^' == ch[0])
return 0;
// 面判断字符串首尾否合格 面间部
if(0 != i && ch[i+1] != '\0' ){
if(('X' == ch[i] || 'x' == ch[i]) && !isdigit(ch[i-1]) && '+' != ch[i-1] && '-' != ch[i-1] && '*' != ch[i-1] && '/' != ch[i-1] && '.' != ch[i-1])
return 0;
if(('X' == ch[i] || 'x' == ch[i]) && '^' != ch[i+1] && '+' != ch[i+1] && '-' != ch[i+1] && '*' != ch[i+1] && '/' != ch[i+1])
return 0;
if(('+' == ch[i] || '-' == ch[i] || '*' == ch[i] || '/' == ch[i]) && !isdigit(ch[i-1]) && 'X' != ch[i-1] && 'x' != ch[i-1] && !isdigit(ch[i+1]) && 'X' != ch[i+1] && 'x' != ch[i+1])
return 0;
if('^' == ch[i] && 'X' != ch[i-1] && 'x' != ch[i-1])
return 0;
if('^' == ch[i] && !isdigit(ch[i+1]))
return 0;
if('.' == ch[i] && !isdigit(ch[i+1]) && !isdigit(ch[i-1]))
return 0;
}
}
}
return 1;
}

void createPoly(polynode **P, char ch[]){
char *t = ch;
int i = 0, j = 1;
int iscoef = 1,isminus = 1;
polyptr Q,L;

if('-' == ch[0]){
isminus = -1;
*t++;
}
while('\0' != *t){
Q = (polyptr)malloc(sizeof(polynode));
Q->coef = 1;
Q->exp = 0;
Q->next = NULL;//申请节点初始化参数1.

if(-1 == isminus){
Q->coef *= isminus;
isminus = 1;
}

while('+' != *t && '-' != *t && '*' != *t && '/' != *t && '\0' != *t){
if('x' != *t && 'X' != *t){
while(isdigit(*t)){
i =((int)*t - 48) + i*10;
t++;
j *= i;
}//抽取数字
if(1 == iscoef && 0 != i){
Q->coef *= i;
}
if(0 == iscoef){
Q->exp += i;
iscoef = 1;
}
//i=0,则

}
else{
iscoef = 0;
t++;
if('^' == *t)
t++;
else
Q->exp = 1;
}
i = 0;
}//while 遍历加减乘除,则退循环,新节点
iscoef = 1;
if('\0' != *t){
if('-' == *t)
isminus = -1;
t++;
}
if(0 == j){
Q->coef = 0;
j = 1;
}
printf("系数:%d,指数:%d\n",Q->coef,Q->exp);

if(NULL == *P){
*P = Q;
}
else{
L->next = Q;
}
L = Q;

}//while遍历整字符串

}
void polyAdd(polynode *A,polynode *B){
polyptr P = A, Q,L;
polyptr COPYA = NULL,COPYB = NULL;
if(NULL == A || NULL == B){
printf("项式未建立,请先输入项表达式.\n");
return ;
}

while(NULL != P){//复制A
Q = (polyptr)malloc(sizeof(polynode));
Q->coef = P->coef;
Q->exp = P->exp;
Q->next = NULL;
if(NULL == COPYA)
COPYA = Q;
else
L->next = Q;
L = Q;
P = P->next;
}
P = B;
while(NULL != P){//复制B
Q = (polyptr)malloc(sizeof(polynode));
Q->coef = P->coef;
Q->exp = P->exp;
Q->next = NULL;
if(NULL == COPYB)
COPYB = Q;
else
L->next = Q;
L = Q;
P = P->next;
}

L->next = COPYA;//COPYA,COPYB两项式连接起,整理OK.
order(?B);
order(?B);
printf("相加结:");
display(COPYB);
destroy(?B);
}
void polyMinus(polynode *A,polynode *B){//相减相加差
polyptr P = A, Q,L;
polyptr COPYA = NULL,COPYB = NULL;
if(NULL == A || NULL == B){
printf("项式未建立,请先输入项表达式.\n");
return ;
}

while(NULL != P){//复制A
Q = (polyptr)malloc(sizeof(polynode));
Q->coef = P->coef;
Q->exp = P->exp;
Q->next = NULL;
if(NULL == COPYA)
COPYA = Q;
else
L->next = Q;
L = Q;
P = P->next;
}
P = B;
while(NULL != P){//复制B
Q = (polyptr)malloc(sizeof(polynode));
Q->coef = -(P->coef);
Q->exp = P->exp;
Q->next = NULL;
if(NULL == COPYB)
COPYB = Q;
else
L->next = Q;
L = Q;
P = P->next;
}

L->next = COPYA;//COPYA,COPYB两项式连接起,整理OK.
order(?B);
order(?B);
printf("相减结:");
display(COPYB);
destroy(?B);

}
void polyMulti(polynode *A,polynode *B){
polyptr R = A, P = B, Q, L = NULL, T;

if(NULL == A || NULL == B){
printf("项式未建立,请先输入项表达式.\n");
return ;
}
if(0 == A->coef || 0 == B->coef){
printf("项式乘积:0\n");
return ;
}

while(NULL != R){
while(NULL != P){
Q = (polyptr)malloc(sizeof(polynode));
Q->coef = P->coef * R->coef;
Q->exp = P->exp + R->exp;
Q->next = NULL;

if(NULL == L)
L = Q;
else
T->next = Q;
T = Q;
P = P->next;
}
P = B;
R = R->next;
}
order(&L);
order(&L);
printf("项式乘积:\n");
display(L);
destroy(&L);
}
void polyDiv(polynode *A,polynode *B){//项式除
polyptr P = A, Q,L,R,T,C,D;
polyptr COPYA = NULL,COPYB = NULL;
if(NULL == A || NULL == B){
printf("项式未建立,请先输入项表达式.\n");
return ;
}
if(A->coef == 0){
printf("0.\n");
return ;
}
if(B->coef == 0){
printf("除数0,错误!\n");
return ;
}
if(A->coef B->coef){
printf("商:0,余数:");
display(A);
return ;
}
while(NULL != P){//复制A
Q = (polyptr)malloc(sizeof(polynode));
Q->coef = P->coef;
Q->exp = P->exp;
Q->next = NULL;
if(NULL == COPYA)
COPYA = Q;
else
L->next = Q;
L = Q;
P = P->next;
}
P = B;
while(NULL != P){//复制B
Q = (polyptr)malloc(sizeof(polynode));
Q->coef = -(P->coef);
Q->exp = P->exp;
Q->next = NULL;
if(NULL == COPYB)
COPYB = Q;
else
L->next = Q;
L = Q;
P = P->next;
}
C = P = Q = L = R = T = NULL;

//------------------始计算
while(COPYA->exp >= COPYB->exp){
D = COPYA;
while(NULL != D->next)
D = D->next;
R = COPYB;
Q = (polyptr)malloc(sizeof(polynode));
Q->coef = (-COPYA->coef) / R->coef;
Q->exp = COPYA->exp - R->exp;
Q->next = NULL;
if(NULL == L)
L = Q;
else
P->next = Q;
P = Q;

while(NULL != R){
Q = (polyptr)malloc(sizeof(polynode));
Q->coef = P->coef * R->coef;
Q->exp = P->exp + R->exp;
Q->next = NULL;

if(NULL == T)
T = Q;
else
C->next = Q;
C = Q;

R = R->next;
}
D->next = T;
order(?A);
order(?A);
T = NULL;
C = NULL;
}
order(&L);
order(?A);
printf("A除B,商:");
display(L);
printf("余数:");
display(COPYA);

destroy(&L);
destroy(?A);
destroy(?B);
}

void display(polynode *P){
//考虑情况系数1,指数1,0,般数;系数系数1,指数1,0,般数;
//系数负数,指数1,0,般数,主要考虑间符号问题.
if(NULL == P){
printf("项式空.\n");
return ;
}
if(1 == P->coef){
if(0 == P->exp)
printf("1");
else if(1 == P->exp) printf("x");
else printf("x^%d",P->exp);
}
else{
if(-1 == P->coef){
if(0 == P->exp)
printf("-1");
else if(1 == P->exp) printf("-x");
else printf("-x^%d",P->exp);
}
else if(0 == P->exp)
printf("%d",P->coef);
else if(1 == P->exp) printf("%dx",P->coef);
else
printf("%dx^%d",P->coef,P->exp);
}
P = P->next;
while(NULL != P){
if(0 P->coef){
if(1 == P->coef){
if(0 == P->exp)
printf("+1");
else if(1 == P->exp) printf("+x");
else printf("+x^%d",P->exp);
}
else{
if(0 == P->exp)
printf("+%d",P->coef);
else if(1 == P->exp) printf("+%dx",P->coef);
else
printf("+%dx^%d",P->coef,P->exp);
}
}
else{
if(-1 == P->coef){
if(0 == P->exp)
printf("-1");
else if(1 == P->exp) printf("-x");
else printf("-x^%d",P->exp);
}
else{
if(0 == P->exp)
printf("%d",P->coef);
else if(1 == P->exp) printf("%dx",P->coef);
else
printf("%dx^%d",P->coef,P->exp);
}
}
P = P->next;
}
printf("\n");
}

void destroy(polynode **P){
polyptr Q = *P;
if(NULL == *P)
return ;
while(*P != NULL){
Q = *P;
*P = (*P)->next;
delete Q;
}

}

void order(polynode **P){
//首先 系数零要清掉,其指数高低排序,再者系数相同要合并.
polyptr prev,curr,OUT,INcurr;//前节点前节点
int temp;

//第节点系数0项
while(NULL != *P){
if(0 != (*P)->coef)
break;
else{
if(NULL == (*P)->next)
return;
curr = *P;
(*P) = (*P)->next;
delete curr;
}
}
if(NULL == *P || NULL == (*P)->next)//剩1项或空,则需要整理,退函数
return;
//冒泡排序
OUT = INcurr = *P;
while(NULL != OUT->next){//外循环
while(NULL != INcurr->next){//内循环
prev = INcurr;
INcurr = INcurr->next;
if(prev->exp INcurr->exp){
temp = prev->coef;
prev->coef = INcurr->coef;
INcurr->coef = temp;//交换系数

temp = prev->exp;
prev->exp = INcurr->exp;
INcurr->exp = temp;//交换指数
}
}
OUT = OUT->next;
INcurr = *P;
}

//除0项
prev = curr = *P;
curr = curr->next;
while(NULL != curr){
if(0 == curr->coef){
prev->next = curr->next;
delete curr;
curr = prev->next;
}
else{
prev = curr;
curr = curr->next;
}
}
//合并同类项
OUT = INcurr = *P;
while(NULL != OUT->next){
while(NULL != INcurr->next){
prev = INcurr;
INcurr = INcurr->next;
if(INcurr->exp == OUT->exp){
OUT->coef += INcurr->coef;
prev->next = INcurr->next;
delete INcurr;
INcurr = prev;
}
}
INcurr = OUT = OUT->next;
if(NULL == OUT)
return;
}

}

void main(){
int choice;
// int i;
char ch[100];
polynode *polyA,*polyB;

polyA = polyB = NULL;

menu();
scanf("%d",&choice);
while(!IsChoice(choice)){
menu();
printf("输入错误,重新输入.\n");
scanf("%d",&choice);
}
while(8 != choice){
switch(choice){
case 1:
if(NULL != polyA || NULL != polyB){
destroy(&polyA);
destroy(&polyB);
printf("原项式销毁.\n");
}
printf("项式输入格式:4x^3+7x^2+x+6--x写.\n输入项式A:\n");
scanf("%s",&ch);

while(!isPut(ch)){
printf("输入错误!重新输.\n");
scanf("%s",&ch);
}
createPoly(&polyA,ch);//建立项式A链表

printf("输入项式B:\n");
scanf("%s",&ch);
while(!isPut(ch)){
printf("输入错误!重新输.\n");
scanf("%s",&ch);
}
createPoly(&polyB,ch);//建立项式B链表
order(&polyB);
order(&polyA);//整理排序项式,默认降幂

printf("建立项式功!项式:\nA:");
display(polyA);
printf("B:");
display(polyB);
break;
case 2:
polyAdd(polyA,polyB);
break;
case 3:
polyMinus(polyA,polyB);
break;
case 4:
polyMulti(polyA,polyB);
break;
case 5:
printf("PS:系数支持整数,计算除存误差;\n除数所项系数1,能确答案,或者某些情况系数刚整除.");
polyDiv(polyA,polyB);
break;
case 6:
printf("------显示项式------\nA :");
display(polyA);
printf("B :");
display(polyB);
break;
case 7:
destroy(&polyA);
destroy(&polyB);
printf("项式已清空.\n");
break;
default:
return ;
}
choice = 0;
menu();
scanf("%d",&choice);
while(!IsChoice(choice) || 0 == choice){
menu();
printf("输入错误,重新输入.\n");
scanf("%d",&choice);
}
}
}