长整数加法运算

问题描述 :

假设2个任意长度的整数x、y分别由双向链表A和B存储，现要求设计一个算法，实现x+y。计算结果存储在链表C中。

说明：

由于A和B输出时需要从头至尾遍历，而做加法时需要从尾至头遍历，因此使用双向链表存储。

可以从长整数的低位开始拆分（4位为一组，即不超过9999的非负整数），依次存放在链表的每个结点的数据域中；头结点的数据域存放正负数标志（正数或0：1，负数：-1）。

输入说明 :

第一行：长整数x

第二行：长整数y 

输出说明 :

第一行：格式化后的长整数x（从低位到高位每4位用","分开）

第二行：格式化后的长整数y（从低位到高位每4位用","分开）

第三行：空行

第四行：单链表C的遍历结果

第五行：格式化后的计算结果（从低位到高位每4位用","分开）

输入范例 :

-53456467576846547658679870988098
435643754856985679

输出范例 :

-5345,6467,5768,4654,7658,6798,7098,8098
43,5643,7548,5698,5679

5345->6467->5768->4611->2014->9250->1400->2419
-5345,6467,5768,4611,2014,9250,1400,2419

#define _CRT_SECURE_NO_WARNINGS
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <iostream>
#include <algorithm>
#include<iomanip>
#include <vector>
#define MY_MAX_LEN 100000
using namespace std;
typedef struct node
{
    int  val;//做头结点时 -1为负数 0为正数
    struct node* next;
    struct node* pre;
    node() {}
    node(int v) :val(v), next(0), pre(0) {}
}Node;
void display(Node* head)
{
    Node* p = head->next;
    while (p && p->val == 0)p = p->next;
    if (!p) { cout << 0 << endl; return; }
    if (p)
    {
        cout << p->val;
        p = p->next;
    }
    while (p)
    {
        cout << "->";
        cout << setw(4) << setfill('0') << p->val;
        p = p->next;
    }
    cout << endl;
}
void my_print(Node* head)
{
    Node* p = head->next;
    while (p && p->val == 0)p = p->next;
    if (!p) { cout << 0 << endl; return; }
    if (head->val == -1)cout << "-";
    if (p)
    {
        cout << p->val;
        p = p->next;
    }
    while (p)
    {
        cout << ",";
        cout << setw(4) << setfill('0') << p->val;
        p = p->next;
    }
    cout << endl;
}
Node* creatByVector(vector<Node*>& node_vec)
{
    int i;
    if (node_vec.size() >= 2)
    {
        node_vec[0]->next = node_vec[1];
        node_vec[node_vec.size() - 1]->pre = node_vec[node_vec.size() - 2];
        node_vec[node_vec.size() - 1]->next = NULL;
    }
    for (i = 1; i < node_vec.size() - 1; i++)
    {
        node_vec[i]->next = node_vec[i + 1];
        node_vec[i]->pre = node_vec[i - 1];
    }
    return node_vec[0];
}
//使用atoi时一定要记得将字符串末尾设为
Node* creatByStr(char* str)
{
    Node* head = new Node();
    if (str[0] == '-')
    {
        head->val = -1;
        strcpy(str, &str[1]);
    }
    else
        head->val = 0;
    vector<Node*> node_vec;
    node_vec.push_back(head);
    char temp[5];
    int len = strlen(str);
    int x = len % 4;
    if (x)
    {
        strncpy(temp, str, x);
        temp[x] = '';
        node_vec.push_back(new Node(atoi(temp)));
        len -= x;
        strcpy(str, &str[x]);
    }
    while (len)
    {
        strncpy(temp, str, 4);
        temp[4] = '';
        node_vec.push_back(new Node(atoi(temp)));
        strcpy(str, &str[4]);
        len -= 4;
    }
    return creatByVector(node_vec);
}
//符号相同时 直接算加法
Node* add_fun(Node* head_a, Node* head_b)
{
    //* ta = NULL, * tb = NULL,
    Node* pa = head_a->next, * pb = head_b->next;
    while (pa->next)pa = pa->next; //ta = pa;
    while (pb->next)pb = pb->next; //tb = pb;
    vector<Node*> node_vec;
    int carry = 0, cur;
    while (pa != head_a && pb != head_b)
    {
        cur = pa->val + pb->val + carry;
        //cout << pa->val << " " << pb->val << " " << carry << " " << cur % 10000 << " " << endl;
        carry = cur / 10000;
        node_vec.push_back(new Node(cur % 10000));
        pa = pa->pre;
        pb = pb->pre;
    }
    while (pa != head_a)
    {
        cur = pa->val + carry;
        carry = cur / 10000;
        node_vec.push_back(new Node(cur % 10000));
        pa = pa->pre;
    }
    while (pb != head_b)
    {
        cur = pb->val + carry;
        carry = cur / 10000;
        node_vec.push_back(new Node(cur % 10000));
        pb = pb->pre;
    }
    if (carry)
        node_vec.push_back(new Node(carry));
    node_vec.push_back(new Node(head_a->val));
    //for (auto i : node_vec)cout << i->val << ' ';
    //cout << endl;
    reverse(node_vec.begin(), node_vec.end());
    //for (auto i : node_vec)cout << i->val<<' ';
    //cout << endl;
    return creatByVector(node_vec);
}
//符号相反时 比较绝对值的大小 最后的符号与绝对值大的相同 head_a为绝对值大的数
Node* sub_fun(Node* head_a, Node* head_b)
{
    //* ta = NULL, * tb = NULL,
    Node* pa = head_a->next, * pb = head_b->next;
    while (pa->next)pa = pa->next; //ta = pa;
    while (pb->next)pb = pb->next; //tb = pb;
    vector<Node*> node_vec;
    int carry = 0, cur;
    while (pa != head_a && pb != head_b)
    {
        //cout << pa->val << " " << pb->val << " " << carry << " " << pa->val - carry - pb->val 
        //    << " " << pa->val + 10000 - carry - pb->val<< endl;
        if (pa->val - carry >= pb->val)//若可以减
        {
            node_vec.push_back(new Node(pa->val - carry - pb->val));
            //cout << "1 "<<pa->val - carry - pb->val << endl;
            carry = 0;
        }
        else//若不够减
        {
            node_vec.push_back(new Node(pa->val + 10000 - carry - pb->val));
            //cout << "2 " << pa->val + 10000 - carry - pb->val << endl;
            carry = 1;
        }
        pa = pa->pre;
        pb = pb->pre;
    }
    while (pa != head_a)//被减数还有剩余
    {
        cur = pa->val - carry;
        if (cur > 0)
        {
            node_vec.push_back(new Node(cur));
            //cout << "3 " << cur << endl;
            carry = 0;
        }
        else if (cur < 0)
        {
            node_vec.push_back(new Node(cur + 1000));
            //cout << "4 " << cur+10000 << endl;
            carry = 1;
        }
        pa = pa->pre;
    }
    node_vec.push_back(new Node(head_a->val));
    //for (auto i : node_vec)cout << i->val << ' ';
    //cout << endl;
    reverse(node_vec.begin(), node_vec.end());
    //for (auto i : node_vec)cout << i->val<<' ';
    //cout << endl;
    return creatByVector(node_vec);
}
Node* my_fun(Node* ha, Node* hb, int flag)
{
    if (ha->val == hb->val) return add_fun(ha, hb);
    else if (flag == -1) return sub_fun(hb, ha);
    else if (flag == 1)return sub_fun(ha, hb);
    else return new Node(0);
}
//比较a与b的绝对值 谁大
int judge(char* a, char* b)
{
    char ta[1000], tb[1000];
    if (a[0] == '-')strcpy(ta, &a[1]);
    else strcpy(ta, a);
    if (b[0] == '-')strcpy(tb, &b[1]);
    else strcpy(tb, b);
    int lena = strlen(ta), lenb = strlen(tb);
    if (lena > lenb) return 1;
    else if (lenb > lena) return -1;
    else
    {
        if (!strcmp(ta, tb))return 0;
        int i = 0;
        while (i != lena)
        {
            if (ta[i] > tb[i])return 1;
            else if (ta[i] < tb[i])return -1;
            i++;
        }
    }
}
int main()
{
    char str_a[MY_MAX_LEN];
    char str_b[MY_MAX_LEN];
    scanf("%s", str_a); getchar();
    scanf("%s", str_b);
    int flag = judge(&str_a[0], &str_b[0]);
    Node* head_a = creatByStr(str_a);
    Node* head_b = creatByStr(str_b);
    my_print(head_a);
    my_print(head_b);
    cout << endl;
    Node* res = my_fun(head_a, head_b, flag);
    display(res);
    my_print(res);
    return 0;
}