高精度乘法（Trachtenberg速算法）

一.介绍：

Trachtenberg速算法：（转载）

二.代码实现：

#include <set>
#include <map>
#include <ctime>
#include <queue>
#include <cmath>
#include <stack>
#include <vector>
#include <cstdio>
#include <sstream>
#include <cstring>
#include <cstdlib>
#include <iostream>
#include <algorithm>
#define eps 1e-4
#define PI acos(-1.0)
#define ll long long int
using namespace std;

struct node
{
    int pos;
    char num;
};

const int M = 1010;
struct node a[M], b[M];
int len = 0;
int len1 = 0;
int len2 = 0;
int ans[M * M];

void Print()
{
    int i = len;
    while(!ans[i])
        i--;
    for(; i >= 0; --i)
        printf("%d", ans[i]);
    printf("\n");
}

void Trachtenberg()
{
    while(b[0].pos != len1 + 1)
    {
        for(int i = 0; i < len2; ++i)
        {
            if(b[i].pos == 0)
                ans[len] += ((b[i].num - '0') * (a[len1 - 1].num - '0')) % 10;
            else if(b[i].pos == len1)
                ans[len] += ((b[i].num - '0') * (a[0].num - '0')) / 10;
            else if(b[i].pos > 0 && b[i].pos < len1)
                ans[len] += ((b[i].num - '0') * (a[len1 - b[i].pos - 1].num - '0')) % 10 + ((b[i].num - '0') * (a[len1 - b[i].pos].num - '0')) / 10;
            b[i].pos++;
        }
        ans[len + 1] += ans[len] / 10;
        ans[len] %= 10;
        len++;
    }
    Print();
}

void Scan(string s1, string s2)
{
    len1 = s1.size();
    len2 = s2.size();
    for(int i = 0; i < len1; ++i)
        a[i].num = s1[i];
    for(int i = 0; i < len2; ++i)
        b[i].num = s2[i];
    for(int i = len2 - 1; i >= 0; --i)
    {
        if(i == len2 - 1)
            b[i].pos = 0;
        else
            b[i].pos = b[i + 1].pos - 1;
    }
}

int main()
{
    string s1, s2;
    cin >> s1 >> s2;
    Scan(s1, s2);
    if(a[0].num == '0' && len1 == 1 || b[0].num == '0' && len2 == 1)
        printf("0\n");
    else
        Trachtenberg();
    return 0;
}