大数加减乘法

大数的相关计算问题一直是编程比赛常考的题目，在蓝桥杯比赛之前又把大数的加减乘法做了一遍。大数除法比较难，还没有去尝试实现，以后有机会了再继续补全好了。

算法分析：三种方法相似，都是按位操作，动态存储。处理好输入数据后，对每一位的逐个操作，很容易得到答案。

大数加法

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>

#define MAX 1010
using namespace std;

string A,B;
int a[MAX],b[MAX];
int sum[MAX];
int T,l1,l2;
int main()
{
    memset(a,0,sizeof(a));
    memset(b,0,sizeof(b));
    memset(sum,0,sizeof(sum));
    cin>>A;cin>>B;
    bool flag=true;
    l1=A.length();
    l2=B.length();
    for( int i = l1-1; i >= 0; i-- )
        a[l1-1-i]=A[i]-‘0‘;
    for( int i = l2-1; i >= 0; i-- )
        b[l2-1-i]=B[i]-‘0‘;
    for( int i = 0; i < max(l1,l2)+2; i++ )
    {
        sum[i]+=a[i]+b[i];
        if( sum[i] >= 10 )
        {
            sum[i+1]+=sum[i]/10;
            sum[i]%=10;
        }
    }
    for( int i = MAX-1; i >= 0; i-- )
    {
        if( sum[i] == 0 && flag )
            continue;
        flag=false;
        printf("%d",sum[i]);
    }
    printf("\n");
}

大数减法

#include <iostream>
#include <cstdio>
#include <cstring>
#define MAX 210

using namespace std;

char a[MAX];
char b[MAX];
char c[MAX];
int l1,l2;
bool flag=false;
int num1[MAX],num2[MAX];
bool if_exchange();
void exchange();
void Minus(int x);
void Print();

int main()
{
    while( gets(a)&&gets(b) )
    {
        l1=l2=0;
        memset(num1,0,sizeof(num1));
        memset(num2,0,sizeof(num2));
        memset(c,0,sizeof(c));
        flag=if_exchange();
        for( int i = strlen(a)-1; i >= 0 ; i-- )
        {
            num1[l1]=a[i]-‘0‘;
            l1++;
        }
        for( int i = strlen(b)-1; i >= 0 ; i-- )
        {
            num2[l2]=b[i]-‘0‘;
            l2++;
        }
        for( int i = 0; i < l1; i++ )
            Minus(i);
        Print();
    }
    return 0;
}

bool if_exchange()
{
    if( strlen(a) < strlen(b) )
    {
        exchange();
        return true;
    }
    else if( strlen(a) == strlen(b) )
    {
        for( int i = 0; i < (int)strlen(a); i++ )
        {
            if( a[i] > b[i] )
                break;
            else if( a[i] < b[i] )
            {
                exchange();
                return true;
            }
            else
                continue;
        }
    }
    return false;
}

void exchange()
{
    strcpy(c,a);
    strcpy(a,b);
    strcpy(b,c);
    return ;
}

void Minus(int x)
{
    if( num1[x] >= num2[x] )
        num1[x]-=num2[x];
    else
    {
        num1[x+1]--;
        num1[x]=num1[x]+10-num2[x];
    }
    return ;
}

void Print()
{
    int i;
    bool sflag=true;
    if( flag )
        cout<<‘-‘;
    for( i = l1-1; i >= 0;i-- )
    {
        if( sflag && num1[i]==0 )
            continue;
        else
        {
            sflag=false;
            printf("%d",num1[i]);
        }
    }
    if( sflag )
        cout<<0;
    cout<<endl;
    return ;
}

大数乘法

#include <iostream>
#include <cstdio>
#include <cstring>
#define MAX 210

using namespace std;

char a[MAX];
int l1,l2;
int length;
int num1[MAX],num2[MAX];
int save[2*MAX];
void Time(int x);
void Print();
int main()
{
    l1=l2=0;
    length=0;
    memset(num1,0,sizeof(num1));
    memset(num2,0,sizeof(num2));
    memset(save,0,sizeof(save));
    gets(a);
    for( int i = strlen(a)-1; i >= 0 ; i-- )
    {
        num1[l1]=a[i]-‘0‘;
        l1++;
    }
    gets(a);
    for( int i = strlen(a)-1; i >= 0 ; i-- )
    {
        num2[l2]=a[i]-‘0‘;
        l2++;
    }
    for( int i = 0; i < l1; i++ )
        Time(i);
    Print();
    cout<<endl;
    return 0;
}

void Time(int x)
{
    int ass=num1[x];
    int tem[MAX];
    int lmax=0;
    memset(tem,0,sizeof(tem));
    for( int i = 0; i < l2; i++ )
    {
        int mid=ass*num2[i];
        tem[i]+=mid;
        tem[i+1]+=tem[i]/10;
        tem[i]%=10;
        lmax=i+1;
        if(tem[i+1]!=0)
            lmax++;
    }
    for( int i = x; i < x+lmax; i++ )
    {
        save[i]+=tem[i-x];
        save[i+1]+=save[i]/10;
        save[i]%=10;
        length=i;
        if( save[i+1]!=0 )
            length++;
    }
    return ;
}

void Print()
{
    bool flag=true;
    int i;
    for( i = length; i >= 0; i-- )
    {
        if( flag && save[i]==0 )
            continue;
        else
        {
            flag=false;
            printf("%d",save[i]);
        }
    }
    if( i < 0 && flag == true )
        cout<<0;
    return ;
}