长整数运算

Posted 2021-02-15 cuteythyme

这是一道用链表实现大整数相加的题目，就是模拟加法和减法的过程，思路是很简单的，但是过程还是有些麻烦的。

写的过程也有很多小错误，通过运用测试集不断调试，最后终于写好了，自己完完整整写下来还是花了好几个小时的。

#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<math.h>
#define Max_size 100

/*测试样例
输入: 0; 0; 输出: 0
输入: -2345,6789; -7654,3211; 输出:-1,0000,0000
输入: -9999,9999; 1,0000,0000,0000; 输出: 9999,0000,0001
输入: 1,0001,0001; -1,0001,0001;  输出:0
输入： 1,0001,0001; -1,0000,0000;  输出:1
*/

//利用双向循环链表实现长整数的存储
typedef struct Node
{
    int data;
    struct Node *prior;
    struct Node *next;
}DoubleNode,*DoubleList;

DoubleList InitList();
void Insert(DoubleList *L,int number);
void Readnumber(DoubleList *L);
int Length(DoubleList L);
void Add(DoubleList L1,DoubleList L2,DoubleList *L3);
void Minus(DoubleList L1,DoubleList L2,DoubleList *L3);
int Operation(DoubleList L1,DoubleList L2,DoubleList *L3);
int Size(DoubleList L1,DoubleList L2);
void Print(DoubleList L);

int main(void)
{
    DoubleList L1=InitList();
    DoubleList L2=InitList();
    printf("Enter the first integer(each four bits a group,separated by a comma): ");
    Readnumber(&L1);
    int len1=Length(L1);
    printf("Enter the first integer(each four bits a group,separated by a comma): ");
    Readnumber(&L2);
    int len2=Length(L2);
    /*printf("%d %d",len1,len2);
    printf("
");
    int size=Size(L1,L2);
    printf("%d",size);
    printf("
");*/
    DoubleList L3=InitList();
    printf("Add results: ");
    int sign=Operation(L1,L2,&L3);
    if(sign==-1)
       printf("%c",‘-‘);
    Print(L3);
    return 0;

}

//建立一个带有头结点的空循环双链表
DoubleList InitList()
{
    DoubleList L=(DoubleList)malloc(sizeof(DoubleNode));
    L->prior=L;
    L->next=L;
    return L;
}

//插入结点时，让链表的高位在链表的尾部，低位在链表的头部
void Insert(DoubleList *L,int number)
{
    DoubleNode *p=(DoubleNode*)malloc(sizeof(DoubleNode));
    p->data=number;
    p->next=(*L)->next;
    (*L)->next->prior=p;
    (*L)->next=p;
    p->prior=*L;
}

//读取输入的整数，每四个数字存放在一个节点中
void Readnumber(DoubleList *L)
{
    int number,i=0;
    char c;
    scanf("%d%c",&number,&c);
    while(1)
    {
        if(number<0&&i==0)
        {
            (*L)->data=-1;
            number=abs(number);
            Insert(L,number);
        }
        else if(number>=0&&i==0)
        {
            (*L)->data=1;
            Insert(L,number);
        }
        else if(number>=0&&i!=0)
            Insert(L,number);
        if(c==‘;‘)
        {
            i++;
            break;
        }
        scanf("%d%c",&number,&c);
        i++;
    }
}

//求表长
int Length(DoubleList L)
{
    if(L==NULL||(L->next==L&&L->prior==L))
        return 0;
    DoubleNode *p=L->next;
    int count=0;
    while(p!=L)
    {
        count++;
        p=p->next;
    }
    return count;
}

//将链表中对应结点的绝对值相加
void Add(DoubleList L1,DoubleList L2,DoubleList *L3)
{
    DoubleNode *p=L1->next,*q=L2->next;
    int res,carry=0;
    while(p!=L1&&q!=L2)
    {
        res=p->data+q->data+carry;
        if(res>=10000)
        {
            res=res%10000;
            carry=1;
        }
        else
            carry=0;
        Insert(L3,res);
        p=p->next;
        q=q->next;
    }
    if(p==L1&&q!=L2)
    {
        while(q!=L2)
        {
            res=q->data+carry;
            if(res>=10000)
            {
                res=res%10000;
                carry=1;
            }
            else
                carry=0;
            Insert(L3,res);
            q=q->next;
        }
    }
    if(p!=L1&&q==L2)
    {
        while(p!=L1)
        {
            res=p->data+carry;
            if(res>=10000)
            {
                res=res%10000;
                carry=1;
            }
            else
                carry=0;
            Insert(L3,res);
            p=p->next;
        }
    }
    if(carry==1)  //最后最高位的进位有1则在头结点之后插入一个新结点
        Insert(L3,1);
}

//比较两个链表中存储数据的绝对值的大小
//返回值为1: L1>L2  返回值为0: L1=L2  返回值为-1: L1<L2
int Size(DoubleList L1,DoubleList L2)
{
    DoubleNode *p=L1->next;
    DoubleNode *q=L2->next;
    int len1=Length(L1);
    int len2=Length(L2);
    if(len1>len2)
        return 1;
    if(len1<len2)
        return -1;
    //len1==len2
    while(p!=L1&&q!=L2)
    {
        if(p->data>q->data)
            return 1;
        if(p->data<q->data)
            return -1;
        p=p->next;
        q=q->next;
    }
     return 0;
}

//相减时，保证L1>=L2
void Minus(DoubleList L1,DoubleList L2,DoubleList *L3)
{
    DoubleNode *p=L1->next,*q=L2->next;
    int res,borrow=0;
    while(p!=L1&&q!=L2)
    {
        p->data=p->data+borrow;
        if(p->data>=q->data)
        {
            res=p->data-q->data;
            borrow=0;
        }
        else
        {
            res=p->data+10000-q->data;
            borrow=-1;
        }
        Insert(L3,res);
        p=p->next;
        q=q->next;
    }
    if(p!=L1&&q==L2)
    {

        while(p!=L1)
        {
            p->data=p->data+borrow;
            if(p->data<0)
            {
                res=p->data+10000;
                borrow=-1;
                Insert(L3,res);
                p=p->next;
            }
            if(p->data==0)
                return;
        }
    }
}

//加法共有四种情况：正数加正数，正数加负数，负数加负数，负数加正数
int  Operation(DoubleList L1,DoubleList L2,DoubleList *L3)
{
    if(L1->data==1&&L2->data==1)
    {
        Add(L1,L2,L3);
        (*L3)->data=1;
        return 1;
    }
    else if(L1->data==-1&&L2->data==-1)
    {
        Add(L1,L2,L3);
        (*L3)->data=-1;
        return -1;
    }
    else if(L1->data==1&&L2->data==-1)
    {
        if(Size(L1,L2)==1)
        {
            Minus(L1,L2,L3);
            (*L3)->data=1;
            return 1;
        }
        else if(Size(L1,L2)==-1)
        {
            Minus(L2,L1,L3);
            (*L3)->data=-1;
            return -1;
        }
        Insert(L3,0);
        return 1;
    }
    else if(L1->data==-1&&L2->data==1)
    {
        if(Size(L1,L2)==1)
        {
            Minus(L1,L2,L3);
            (*L3)->data=-1;
            return -1;
        }
        else if(Size(L1,L2)==-1)
        {
            Minus(L2,L1,L3);
            (*L3)->data=1;
            return 1;
        }
        Insert(L3,0);
        return 1;
    }
}

//从表头开始输出
void Print(DoubleList L)
{
    DoubleNode *p=L->next;
    while(p->data==0&&p->next!=L)
       p=p->next;
    if(p->next==L)
    {
        printf("%d",p->data);
        return;
    }
    printf("%d",p->data);
    while(p->next!=L)
    {
       p=p->next;
       if(p->data<10)
           printf(",000%d",p->data);
       else if(p->data<100)
           printf(",00%d",p->data);
       else if(p->data<1000)
           printf(",0d",p->data);
       else
       printf(",%d",p->data);
    }
}