Big integer multiplication (divide and conquer) and integer multiplication divide and conquer

Big integer multiplication (divide and conquer) and integer multiplication divide and conquer

Question: enter two big integers, use an array to save each digit, and use the divide and conquer method for calculation;

Train of Thought: input x y, X high to save with array A, low to save with array B, Y high to save with array C, low to save with array D, then: X = A * 10 ^ (n/2) + B Y = C * 10 ^ (n/2) + D

Partitioning Method: X * Y = A * C * 10 ^ n + (A-B) * (D-C) + A * C + B * D) * 10 ^ (n/2) + B * D;

 

The Code is as follows:

#include <iostream>#include <algorithm>#include <cstring>#include <cstdio>#include <cmath>#include <map>#include <vector>using namespace std;void add(int a[],int b[],int c[]){    int tot=0;    int maxn=max(a[0],b[0]);    for(int i=2; i<=maxn+2; i++)    {        c[i]=(a[i]+b[i]+tot)%10;        tot=(a[i]+b[i]+tot)/10;    }    c[0]=maxn+(c[maxn+2]>0);    c[1]=a[1];}void sub(int a[],int b[],int c[]){    int tot=0;    int maxn=max(a[0],b[0]);    c[1]=1;    for(int i=maxn+1; i>=2; i--)    {        if(a[i]>b[i])  break;        if(a[i]<b[i])        {            swap(a,b);            c[1]=-1;            break;        }    }    for(int i=2; i<=maxn+1; i++)    {        c[i]=a[i]+tot-b[i];        if(c[i]<0)        {            c[i]=c[i]+10;            tot=-1;        }        else tot=0;    }    c[0]=a[0];}void process(int a[],int b[],int c[],int g){    if(a[1]>0)    {        if(b[1]*g>0)  add(a,b,c);        else      sub(a,b,c);    }    else    {        if(b[1]*g>0)  sub(b,a,c);        else      add(a,b,c);    }}void Move(int a[],int n){    for(int i=a[0]+1; i>=2; i--)        a[i+n]=a[i];    for(int i=2; i<=n+1; i++)        a[i]=0;    a[0]+=n;}void print(int c[]){    int i;    if(c[1]<0) cout<<"-";    for(i=c[0]+1; i>=2; i--)        if(c[i]) break;    for(; i>=2; i--)        cout<<c[i];    cout<<endl;}void duiqi(int a[],int b[]){    int maxn=max(a[0],b[0]);    int tmp=1;    for(int i=0;i<=10;i++)    {        if(tmp>=maxn) break;        tmp<<=1;    }    a[0]=tmp;    b[0]=tmp;}void calc(int a[],int b[],int c[]){    if(a[0]==1)    {        int tmp=a[2]*b[2];        c[0]=1;        c[2]=tmp%10;        if(tmp>=10)        {            c[3]=tmp/10;            c[0]++;        }        c[1]=a[1]*b[1];        return;    }    int A[1000],B[1000],C[1000],D[1000],E[1000],F[1000];    int m1[1000],m2[1000],m3[1000];    memset(A,0,sizeof(A));    memset(B,0,sizeof(B));    memset(C,0,sizeof(C));    memset(D,0,sizeof(D));    memset(E,0,sizeof(E));    memset(F,0,sizeof(F));    memset(m1,0,sizeof(m1));    memset(m2,0,sizeof(m2));    memset(m3,0,sizeof(m3));    for(int i=1; i<=a[0]/2+1; i++)        B[i]=a[i];    B[0]=a[0]/2;    for(int i=a[0]/2+2; i<=a[0]+1; i++)        A[i-a[0]/2]=a[i];    A[0]=a[0]/2;    A[1]=a[1];    for(int i=1; i<=b[0]/2+1; i++)        D[i]=b[i];    D[0]=b[0]/2;    for(int i=b[0]/2+2; i<=b[0]+1; i++)        C[i-b[0]/2]=b[i];    C[0]=b[0]/2;    C[1]=b[1];    process(A,B,E,-1);    process(D,C,F,-1);    calc(A,C,m1);    calc(E,F,m2);    calc(B,D,m3);    process(m2,m1,E,1);    process(E,m3,F,1);    Move(m1,a[0]);    Move(F,a[0]/2);    process(m1,F,E,1);    process(E,m3,c,1);}int main(){    int a[1000],b[1000],c[2000];    char s1[1000],s2[1000];    cin>>s1>>s2;    a[0]=strlen(s1)-1;    if(s1[0]=='-') a[1]=0;    else       a[1]=1;    a[0]+=a[1];    for(int i=2; i<=a[0]+1; i++)        a[i]=s1[a[0]-a[1]-i+2]-'0';    b[0]=strlen(s2)-1;    if(s2[0]=='-') b[1]=0;    else       b[1]=1;    b[0]+=b[1];    for(int i=2; i<=b[0]+1; i++)        b[i]=s2[b[0]-b[1]-i+2]-'0';    a[1]+=a[1]-1;    b[1]+=b[1]-1;    duiqi(a,b);    calc(a,b,c);    print(c);    return 0;}