大数相乘，大数相加

大数相乘，大数相加的具体运用！

以杭电的BigNums的7题（1002，1042,1047,1063,1316,1715,1753）为例作为练习！如下：

1002

算法分析：

源码实现：

#include <iostream>#include <string.h>#include <stdio.h>using namespace std;#define max 1010char* cal(char *s1,int l1,char *s2,int l2);int main(){    int m,l1,l2,count=1;    char a[max],b[max];    char *result;    cin>>m;        while(count<=m)       {        memset(a,0,sizeof(a));        memset(b,0,sizeof(b));        cin>>a>>b;        l1=strlen(a);        l2=strlen(b);        printf("Case %d:\n",count);        printf("%s + %s = ",a,b);        result=cal(a,l1,b,l2);        printf("%s\n",result);        if(count<m)        printf("\n");        count++;       }    return 0;}char* cal(char *s1,int l1,char *s2,int l2){    int array[max];    char *result = new char[max];    memset(result,'\0',sizeof(result));    memset(array,-1,sizeof(array));    int i,j,t,temp;    for(i=0;i<l1/2;i++)    {       temp=s1[i];       s1[i]=s1[l1-1-i];       s1[l1-1-i]=temp;    }    for(i=0;i<l2/2;i++)    {       temp=s2[i];       s2[i]=s2[l2-1-i];       s2[l2-1-i]=temp;    }    for(i=0;i<l1&&i<l2;i++)        array[i]=s1[i]-48+s2[i]-48;    while(i<l2)    {        array[i]=s2[i]-48;        i++;    }    while(i<l1)    {        array[i]=s1[i]-48;        i++;    }    j=0;    do{            if(array[j]/10 > 0)            {                temp=array[j]/10;                array[j]=array[j]%10;                j++;                if(array[j]==-1)                {                    array[j]++;                    array[j]+=temp;                }                else                array[j]+=temp;            }            else            {                j++;            }    }while(array[j] != -1);    t=--j;    for(i=t,j=0;i>=0;i--,j++)    {        result[j]=array[i]+48;    }    result[j]='\0';       return result;}

1042

算法分析：

源码实现：

         

#include <iostream>#include <string.h>#include <stdlib.h>#include <stdio.h>#define MAX 30000using namespace std;int array[MAX];char result[MAX];char number[MAX];char *p;char * multyplus(char *s1,char *s2,int l1,int l2){               int k;               int i,j;               memset(result,'\0',sizeof(result));               memset(array,-1,sizeof(array));               for(i=0;i<l1;i++)               {                         k=i;                         for(j=0;j<l2;j++)                         {                                 if(array[k]==-1)                                    array[k++]=(s1[i]-48)*(s2[j]-48);                                 else                                 array[k++]+=(s1[i]-48)*(s2[j]-48);                         }               }               for(k=0;;k++)               {                       if((array[k+1]==-1)&&(array[k]/10!=0))                       {                            array[k+1]++;                       }                       array[k+1]+=array[k]/10;                       array[k]=array[k]%10;                       if(array[k+1]==-1)                        break;               }               for(i=k,j=0;i>=0;i--,j++)               {                       result[j]=array[i]+48;               }               result[j]='\0';               strcpy(number,result);               return number;}char *itos(int m){    int i;    char *res = new char[10];    memset(res,'\0',10);    for(i=0;;i++)    {        res[i]=m%10+48;        m=m/10;        if(0==m)            break;    }    res[++i]='\0';    return res;}void transverse(char *temp,int len){    int i,t;    for(i=0;i<len/2;i++)    {        t=temp[i];        temp[i]=temp[len-1-i];        temp[len-1-i]=t;    }}char *multi(int m){    int i;    int len1,len2;    char *count = new char[10];    char *temp;    memset(count,'\0',sizeof(count));    count[0]='1';    for(i=1;i<=m;i++)    {        temp = itos(i);        len1 = strlen(count);        len2 = strlen(temp);        transverse(count,len1);        if(len1>len2)            count = multyplus(count,temp,len1,len2);        else            count = multyplus(temp,count,len2,len1);    }    return count;}int main(){    int m;    char *num;    while(scanf("%d",&m)!=-1)    {        num = multi(m);        cout<<num<<endl;    }    return 0;}

1047

算法分析：

     和1002差不多，只是这里是多位连续相加，1002只是两个数相加

源码实现：

    

#include <iostream>#include <string.h>#include <stdio.h>using namespace std;#define MAX 1000char *result = new char[MAX];char *input = new char[MAX];char *res = new char[MAX];int array[MAX];char* cal(char *s1,int l1,char *s2,int l2){    memset(array,-1,sizeof(array));    int i,j,t,temp;    for(i=0;i<l1/2;i++)    {       temp=s1[i];       s1[i]=s1[l1-1-i];       s1[l1-1-i]=temp;    }    for(i=0;i<l2/2;i++)    {       temp=s2[i];       s2[i]=s2[l2-1-i];       s2[l2-1-i]=temp;    }    for(i=0;i<l1&&i<l2;i++)        array[i]=s1[i]-48+s2[i]-48;    while(i<l2)    {        array[i]=s2[i]-48;        i++;    }    while(i<l1)    {        array[i]=s1[i]-48;        i++;    }    j=0;    do{            if(array[j]/10 > 0)            {                temp=array[j]/10;                array[j]=array[j]%10;                j++;                if(array[j]==-1)                {                    array[j]++;                    array[j]+=temp;                }                else                array[j]+=temp;            }            else            {                j++;            }    }while(array[j] != -1);    t=--j;    for(i=t,j=0;i>=0;i--,j++)    {        result[j]=array[i]+48;    }    result[j]='\0';       return result;}int main(){    int m;    int i;    int len1,len2;    cin>>m;        for(i=1;i<=m;i++)        {                memset(result,'\0',sizeof(result));                result[0]='0';                memset(input,'\0',sizeof(input));                while(scanf("%s",input)!=-1)                {                       if(input[0]=='0')                         break;                       strcpy(res,input);                       len1 = strlen(result);                       len2 = strlen(res);                       result = cal(result,len1,res,len2);                }                cout<<result<<endl;                if(i<m)                    cout<<endl;        }    return 0;}

1063

算法分析：

   

源码实现：

    

#include <iostream>#include <string.h>#include <stdio.h>using namespace std;#define MAX 1000char result[MAX];int array[MAX];char number[MAX];void multyplus(char *s1,char *s2,int l1,int l2){               int k;               int i,j;               memset(result,'\0',sizeof(result));               memset(array,-1,sizeof(array));               for(i=0;i<l1;i++)               {                         k=i;                         for(j=0;j<l2;j++)                         {                                 if(array[k]==-1)                                    array[k++]=(s1[i]-48)*(s2[j]-48);                                 else                                 array[k++]+=(s1[i]-48)*(s2[j]-48);                         }               }               for(k=0;;k++)               {                       if((array[k+1]==-1)&&(array[k]/10!=0))                       {                            array[k+1]++;                       }                       array[k+1]+=array[k]/10;                       array[k]=array[k]%10;                       if(array[k+1]==-1)                        break;               }               for(i=k,j=0;i>=0;i--,j++)               {                       result[j]=array[i]+48;               }               result[j]='\0';               strcpy(number,result);               return;}int FindPointPosition(char *s){    int i,j,len=strlen(s);    for(i=0;i<len;i++)    {        if(s[i]=='.')        {            for(j=i;j<len-1;j++)                s[j]=s[j+1];                s[len-1]='\0';            return 5-i;        }    }    if(i>=len)        return 0;}void transverse(char *s){    int len=strlen(s);    int i,t;    for(i=0;i<len/2;i++)    {        t=s[i];        s[i]=s[len-1-i];        s[len-1-i]=t;    }}void killzero(char *s){    int len=strlen(s);    int i,j;    for(i=0;i<len;i++)    {        if(s[i]!='0')        {            j=i;            break;        }    }    for(i=0;j<=len-1;)    {        s[i++]=s[j++];    }    for(;i<=len-1;)    {        s[i++]='\0';    }}int main(){    char a[7];    int m,i,j,k,l,flag,label,f;    int point;    int len;    while(scanf("%s%d",&a,&m)!=-1)    {        flag=1;        point=m*FindPointPosition(a);        killzero(a);//kill the pre zero        if(a[0]=='\0')        {            cout<<"0"<<endl;            flag=0;        }        else if(m==0)        {            cout<<"1"<<endl;            flag=0;        }        if(flag!=0)        {            memset(number,'\0',sizeof(number));            strcpy(number,a);            if(m!=1)            {                transverse(a);                for(i=1;i<=m-1;i++)                {                    transverse(number);                    multyplus(number,a,strlen(number),strlen(a));                }            }        memset(result,'\0',sizeof(result));        len=strlen(number);        j=len-point;//确定小数点的位置，        for(i=len-1;i>=0;i--)            if(number[i]!='0'||i==(j-1))            break;        len=i;        if(j>0)        {            for(i=len,k=0;i>j-1;)            {                result[k++]=number[i--];            }            label=k;            result[k++]='.';            for(;i>=0;)                result[k++]=number[i--];            k--;        }        else        {            for(i=len,k=0;i>=0;)            {                result[k++]=number[i--];            }            for(;i>=j;i--)                result[k++]='0';            label=k;            result[k]='.';        }        for(f=0;f<=label;f++)        {            if(f==0&&result[f]=='.')            {                l=1;                break;            }            if(result[f]!='0'&&result[f]!='.')            {                l=f;                break;            }        }        if(f>label)            l=f;        for(;k>=l;k--)        {            cout<<result[k];        }        cout<<endl;        }    }    return 0;}

1316

算法分析：

     主要就是计算斐波那契数列，和大数加法类型的类似！

源码实现：

#include <iostream>#include <string.h>#include <stdio.h>using namespace std;#define MAX 150int array[MAX];char s1[MAX],s2[MAX];char f1[MAX],f2[MAX];char temp1[MAX],temp2[MAX];char *f3 = new char[MAX];char* Fibonacci(char *s1,int l1,char *s2,int l2){    memset(array,-1,sizeof(array));    int i,j,t,temp;    for(i=0;i<l1/2;i++)    {       temp=s1[i];       s1[i]=s1[l1-1-i];       s1[l1-1-i]=temp;    }    for(i=0;i<l2/2;i++)    {       temp=s2[i];       s2[i]=s2[l2-1-i];       s2[l2-1-i]=temp;    }    for(i=0;i<l1&&i<l2;i++)        array[i]=s1[i]-48+s2[i]-48;    while(i<l2)    {        array[i]=s2[i]-48;        i++;    }    while(i<l1)    {        array[i]=s1[i]-48;        i++;    }    j=0;    do{            if(array[j]/10 > 0)            {                temp=array[j]/10;                array[j]=array[j]%10;                j++;                if(array[j]==-1)                {                    array[j]++;                    array[j]+=temp;                }                else                array[j]+=temp;            }            else            {                j++;            }    }while(array[j] != -1);    t=--j;    for(i=t,j=0;i>=0;i--,j++)    {        f3[j]=array[i]+48;    }    f3[j]='\0';       return f3;}int Strcmp(char *s1,char *s2){    int len1=strlen(s1);    int len2=strlen(s2);    if(len1>len2)        return 1;    else if(len1<len2)         return -1;         else         return strcmp(s1,s2);}int main(){    int count,l1,l2;    while(scanf("%s%s",s1,s2),s1[0]!='0'||s2[0]!='0')    {        memset(f1,'\0',sizeof(f1));        memset(f2,'\0',sizeof(f2));        memset(temp1,'\0',sizeof(temp1));        memset(temp2,'\0',sizeof(temp2));        f1[0]='1';        f2[0]='2';        count = 0;        l1=Strcmp(f1,s1);        l2=Strcmp(f1,s2);        if(l1>=0 && l2<=0)            count++;        l1=Strcmp(f2,s1);        l2=Strcmp(f2,s2);        if(l1>=0 && l2<=0)            count++;        f3=Fibonacci(f1,strlen(f1),f2,strlen(f2));        l1=Strcmp(f3,s2);        while(l1<=0)        {             l2=Strcmp(f3,s1);             if(l2>=0)             count++;             memset(f1,'\0',sizeof(f1));             memset(temp1,'\0',sizeof(temp1));             strcpy(f1,f2);             strcpy(temp1,f1);             memset(temp2,'\0',sizeof(temp2));             memset(f2,'\0',sizeof(f2));             strcpy(f2,f3);             strcpy(temp2,f2);             memset(f3,'\0',sizeof(f3));             f3=Fibonacci(temp1,strlen(temp1),temp2,strlen(temp2));             l1=Strcmp(f3,s2);        }       cout<<count<<endl;    }    return 0;}

1715

算法分析：

     同上题；

源码实现：

#include <iostream>#include <string.h>using namespace std;#define MAX1 1002#define MAX2 300char s[MAX1][MAX2];char temp1[MAX2],temp2[MAX2];int array[MAX2];void Fibonacci(char *s1,int l1,char *s2,int l2,int m){    memset(array,-1,sizeof(array));    int i,j,t,temp;    for(i=0;i<l1/2;i++)    {       temp=s1[i];       s1[i]=s1[l1-1-i];       s1[l1-1-i]=temp;    }    for(i=0;i<l2/2;i++)    {       temp=s2[i];       s2[i]=s2[l2-1-i];       s2[l2-1-i]=temp;    }    for(i=0;i<l1&&i<l2;i++)        array[i]=s1[i]-48+s2[i]-48;    while(i<l2)    {        array[i]=s2[i]-48;        i++;    }    while(i<l1)    {        array[i]=s1[i]-48;        i++;    }    j=0;    do{            if(array[j]/10 > 0)            {                temp=array[j]/10;                array[j]=array[j]%10;                j++;                if(array[j]==-1)                {                    array[j]++;                    array[j]+=temp;                }                else                array[j]+=temp;            }            else            {                j++;            }    }while(array[j] != -1);    t=--j;    for(i=t,j=0;i>=0;i--,j++)    {        s[m][j]=array[i]+48;    }    s[m][j]='\0';    return;}void init(char s[][MAX2]){    memset(s,'\0',sizeof(s));    memset(temp1,'\0',sizeof(temp1));    memset(temp1,'\0',sizeof(temp2));    s[1][0]='1';    s[2][0]='1';    for(int i=3;i<=1000;i++)    {        memset(temp1,'\0',sizeof(temp1));        memset(temp1,'\0',sizeof(temp2));        strcpy(temp1,s[i-1]);        strcpy(temp2,s[i-2]);        Fibonacci(temp1,strlen(temp1),temp2,strlen(temp2),i);    }}int main(){    int m,n;    init(s);    cin>>m;    while(m--)    {          cin>>n;          cout<<s[n]<<endl;    }    return 0;}

1753

算法流程：

    

源码实现：

      

#include <iostream>#include <string.h>#include <stdio.h>using namespace std;#define MAX 440char s1[MAX],s2[MAX];char result[MAX];void multiflus(char *s1,int len1,char *s2,int len2,int point1,int point2){    int i,j,k=0,l=0;    int len,temp;    memset(result,'\0',sizeof(result));    for(i=point1,j=point2;i<len1 && j<len2;i++,j++)    {        result[k++]+=s1[i]-'0'+s2[j]-'0';        result[k-1]+=48;    }    while(i<len1)    {        result[k++]+=s1[i++]-'0';        result[k-1]+=48;    }    while(j<len2)    {        result[k++]+=s2[j++]-'0';        result[k-1]+=48;    }    len = strlen(result);    for(i=0;i<len/2;i++)    {        temp=result[i];        result[i]=result[len-1-i];        result[len-1-i]=temp;    }    for(i=0;;i++)    {        if((result[i]-48)/10 > 0)        {            result[i+1]+=1;            result[i]-=48;            result[i]%=10;            result[i]+=48;        }        if(result[i+1]=='\0')                break;    }    if(k==i&&k!=0)//有小数位进位    {        result[k++]='.';        result[k]+=1;    }    else//没有小数进位    {        result[k++]='.';    }    //除掉末尾的0,和全为0的小数点,以及末尾为0的小数点    i=0;    while(i<k-1)    {        if(result[i]!='0')            break;        i++;    }    if(i<k-1)        l=i;    else        l=k;    //    for(i=point1-2,j=point2-2;i>=0 && j>=0;i--,j--)    {        result[k++]+=s1[i]-'0'+s2[j]-'0';        if(result[k-1]/10 > 0)        {            result[k]+=result[k-1]/10;            result[k-1]=result[k-1]%10;        }        result[k-1]+=48;    }    while(i>=0)    {        result[k++]+=s1[i--]-'0';        if(result[k-1]/10 > 0)        {            result[k]+=result[k-1]/10;            result[k-1]=result[k-1]%10;        }        result[k-1]+=48;    }    while(j>=0)    {        result[k++]+=s2[j--]-'0';        if(result[k-1]/10 > 0)        {            result[k]+=result[k-1]/10;            result[k-1]=result[k-1]%10;        }        result[k-1]+=48;    }    if(result[k]!='\0')        result[k++]+=48;    result[k]='\0';    for(i=k-1;i>=l;i--)        cout<<result[i];    cout<<endl;}int FindPointPosition(char *s){    int i,len=strlen(s);    for(i=0;i<len;i++)    {        if(s[i]=='.')            return i+1;    }    if(i>=len)        return i+1;}int main(){    int point1,point2;    int len1,len2;    while(scanf("%s%s",s1,s2)!=-1)    {        len1=strlen(s1);        len2=strlen(s2);        point1=FindPointPosition(s1);        point2=FindPointPosition(s2);        multiflus(s1,len1,s2,len2,point1,point2);        memset(s1,'\0',sizeof(s1));        memset(s2,'\0',sizeof(s2));    }    return 0;}