算法-大数的四则运算

题目描述以加法为例
给出两个正整数A和B，计算A+B的值。保证A和B的位数不超过500位。

输入描述 Input Description
读入两个用空格隔开的正整数

输出描述 Output Description
输出A+B的值

样例输入 Sample Input
3 12

样例输出 Sample Output
15

大数加法

#include"stdio.h"
#include"string.h"
#include"stdlib.h"
int main()
{
	char s1[500],s2[500];
	int i,j,k=0,*a,n;
	scanf("%s%s",s1,s2);
	i=strlen(s1)-1;
	j=strlen(s2)-1;
	n=i>j? i:j;
	a=(int*)malloc((n+2)*sizeof(int));
	while(k<=n+1)
	     a[k++]=0;
	k=0;
	while(i>=0||j>=0)
	{
	     if(i>=0&&j>=0)
		  a[k]+=(s1[i]-'0')+(s2[j]-'0');
	     else if(j<0)
		  a[k]+=s1[i]-'0';
	     else
		  a[k]+=s2[j]-'0';
	     if(a[k]>=10)
	     {
		  a[k]=a[k]-10;
		  a[k+1]=1;
	     }
	     k++;i--;j--;
	}
	if(a[k]==0)
	     k=k-1;
	while(k>=0)
	     printf("%d",a[k--]);	
  	free(a);	
	return 0;
}

大数减法

#include"stdio.h"
#include"string.h"
#include"stdlib.h"
int main()
{
	char s1[500],s2[500],t[500];
	int flg=1,i,j,k=0,*a,n;
	scanf("%s%s",s1,s2);
	i=strlen(s1)-1;
	j=strlen(s2)-1;
	n=i>j? i:j;
	a=(int*)malloc(n*sizeof(int));	
	if(i==j)
	{
	     flg=strcmp(s1,s2);
	     if(flg==0)
		 printf("0");
	}	
	else
	{
	     if(i<j)
	     {
		 flg=-1;
		 strcpy(t,s1);
		 memset(s1,0,sizeof(s1));
		 strcpy(s1,s2);
		 memset(s2,0,sizeof(s2));
		 strcpy(s2,t);
		 k=i;
		 i=j;
		 j=k;k=0;
	     }
	     while(i>=0||j>=0)
	     {
		 if(i>=0&&j>=0)
		 {
		      a[k]=s1[i]-s2[j];
		      if(a[k]<0)
		      {
			   a[k]=10+a[k];
			   s1[i-1]=s1[i-1]-1;
		      }
		      j--;
	         }
	         else if(j<0)
		      a[k]=s1[i]-'0';
	         k++;i--;
	     }
	     k=k-1;
	     i=k;
	     while(i>0)
	        if(a[i]>0)
	        {
		    k=i;i--;break;
	        }			
	     if(flg<0)
	        printf("-");
	     while(k>=0)
	     {
	        printf("%d",a[k]);
	        k--;
	     }	 	
	}
    free(a);
    return 0;
}

大数乘法

#include"stdio.h"
#include"string.h"
void mult(char a[],char b[],char s[])
{
    int i,j,k=0,alen,blen,sum=0,res[65][65]={0},flag=0;
    char result[65];
    alen=strlen(a);blen=strlen(b); 
    for(i=0;i<alen;i++)
    	for(j=0;j<blen;j++)
	    res[i][j]=(a[i]-'0')*(b[j]-'0');
    for(i=alen-1;i>=0;i--)
    {
        for(j=blen-1;j>=0;j--)
	     sum=sum+res[i+blen-j-1][j];
        result[k]=sum%10;
        k=k+1;
        sum=sum/10;
    }
    for(i=blen-2;i>=0;i--)
    {
        for(j=0;j<=i;j++) 
	    sum=sum+res[i-j][j];
        result[k]=sum%10;
        k=k+1;
        sum=sum/10;
    }
    if(sum!=0)
    {
	 result[k]=sum; 
	 k=k+1;
     }
    for(i=0;i<k;i++)
	result[i]+='0';
    for(i=k-1;i>=0;i--)
	s[i]=result[k-1-i];
    s[k]='\0';
    while(1)
    {
        if(strlen(s)!=strlen(a)&&s[0]=='0') 
            strcpy(s,s+1);
        else
            break;
    }
}
int main(){
	char a[500],b[500],c[1100];
	gets(a);
	gets(b);
	mult(a,b,c);
	puts(c);
	return 0;
}

大数除法

#include"stdio.h"
#include"string.h"
#define MAXSIZE 200
void div(char *str1, char *str2, char *str3)
{
	int i1,i2,i,j,jj,tag,carry,cf,c[MAXSIZE];
	int len1 = strlen(str1), len2 = strlen(str2), lend;
	char d[MAXSIZE];
	memset(c, 0, sizeof(c));
	memcpy(d, str1, len2);
	lend = len2; j = 0;
	for( i1=len2-1; i1 < len1; ++i1 ){
	     if( lend < len2 ){
		  d[lend] = str1[i1+1]; c[j] = 0;
		  ++j; ++lend;
	     }
	     else if( lend == len2 )
	     {
		  jj = 1;
		  for( i=0; i < lend; ++i )
		  {
		       if( d[i] > str2[i] ) break;
		       else if( d[i] < str2[i] )
		       {
			    jj = 0; break;
		       }
		  }
		  if( jj == 0 )
		  {
		       d[lend] = str1[i1+1]; c[j] = 0;
		       ++j; ++lend;
		       continue;
		  }
	     }
	     if( jj==1 || lend > len2 )
	     {
		  cf = jj=0;
		  while( d[jj] <= '0' && jj < lend )
		       ++jj;
		  if( lend-jj > len2 )
		       cf = 1;
		  else if( lend-jj < len2 ) 
		       cf = 0;
		  else
		  {
		       i2 = 0; cf = 1;
		       for( i=jj; i < lend; ++i )
		       {
			    if( d[i] < str2[i2] )
			    {
				cf = 0; break;
			    }
			    else if( d[i] > str2[i2] )
				break;				
			    ++i2;
		       }
		  }//else
		  while( cf )
		  {
		       i2 = len2-1; cf = 0;
		       for( i=lend-1; i >= lend-len2; --i )
		       {
			    d[i] = d[i]-str2[i2]+'0';
			    if( d[i] < '0' )
			    {
				d[i] = d[i]+10;  carry = 1;
				--d[i-1];
			    }
			    else 
			        carry = 0;
			    --i2;
		       }
		       ++c[j]; jj=0;
		       while( d[jj] <= '0' && jj < lend )
			    ++jj;
		       if( lend-jj > len2 ) 
			    cf = 1;
		       else if( lend-jj < len2 ) 
			    cf = 0;
		       else
		       {
			    i2 = 0; cf = 1;
			    for( i=jj; i < lend; ++i )
			    {
				 if( d[i] < str2[i2] )
				 {
				      cf = 0; break;
				 }
				 else if( d[i] > str2[i2] )
				      break;
				 ++i2;
			    }
		       }
		  }
		  jj = 0;
		  while( d[jj] <= '0' && jj < lend )
		       ++jj;
		  for( i=0;i < lend-jj; ++i )
		       d[i] = d[i+jj];
		  d[i] = str1[i1+1];  
		  lend = i+1;
		  ++j;
	     }
	}
	i = tag = 0;
	while(c[i] == 0 )
	    ++i;
	for( ; i < j; ++i, ++tag ) 
	    str3[tag] = c[i]+'0';
	str3[tag] = '\0';
}
int main(){
	char a[MAXSIZE],b[MAXSIZE],c[MAXSIZE];
	scanf("%s%s",a,b);
	div(a,b,c);
	puts(c);
	return 0;
}