大数运算解读

#include

#include

#define DIGIT 4

#define DEPTH 10000

#define MAX 100

typedef int bignum_t[MAX+1];

int read(bignum_t a,istream& is=cin){

char buf[MAX*DIGIT+1],ch;

int i,j;

memset((void*)a,0,sizeof(bignum_t));

if (!(is>>buf)) return 0;

for (a[0]=strlen(buf),i=a[0]/2-1;i>=0;i--)

ch=buf[i],buf[i]=buf[a[0]-1-i],buf[a[0]-1-i]=ch;

for

(a[0]=(a[0]+DIGIT-1)/DIGIT,j=strlen(buf);j

for (i=1;i<=a[0];i++)

for (a[i]=0,j=0;j

a[i]=a[i]*10+buf[i*DIGIT-1-j]-'0';

for (;!a[a[0]]&&a[0]>1;a[0]--);

return 1;

}

void write(const bignum_t a,ostream& os=cout){

int i,j;

for (os<

for (j=DEPTH/10;j;j/=10)

os<

}

int comp(const bignum_t a,const bignum_t b){

int i;

if (a[0]!=b[0])

return a[0]-b[0];

for (i=a[0];i;i--)

if (a[i]!=b[i])

return a[i]-b[i];

return 0;

}

int comp(const bignum_t a,const int b){

int c[12]={1};

for

(c[1]=b;c[c[0]]>=DEPTH;c[c[0]+1]=c[c[0]]/DEPTH,c[c[0]]%=DEPTH,c[0]+ +);

return comp(a,c);

}

int comp(const bignum_t a,const int c,const int d,const bignum_t b){ int i,t=0,O=-DEPTH*2;

if (b[0]-a[0]

return 1;

for (i=b[0];i>d;i--){

t=t*DEPTH+a[i-d]*c-b[i];

if (t>0) return 1;

if (t

}

for (i=d;i;i--){

t=t*DEPTH-b[i];

if (t>0) return 1;

if (t

}

return t>0;

}

void add(bignum_t a,const bignum_t b){

int i;

for (i=1;i<=b[0];i++)

if ((a[i]+=b[i])>=DEPTH)

a[i]-=DEPTH,a[i+1]++;

if (b[0]>=a[0])

a[0]=b[0];

else

for (;a[i]>=DEPTH&&i

a[0]+=(a[a[0]+1]>0);

}

void add(bignum_t a,const int b){

int i=1;

for

(a[1]+=b;a[i]>=DEPTH&&i

for

(;a[a[0]]>=DEPTH;a[a[0]+1]=a[a[0]]/DEPTH,a[a[0]]%=DEPTH,a[0]++); }

void sub(bignum_t a,const bignum_t b){

int i;

for (i=1;i<=b[0];i++)

if ((a[i]-=b[i])<0)

a[i+1]--,a[i]+=DEPTH;

for (;a[i]<0;a[i]+=DEPTH,i++,a[i]--);

for (;!a[a[0]]&&a[0]>1;a[0]--);

}

void sub(bignum_t a,const int b){

int i=1;

for

(a[1]-=b;a[i]<0;a[i+1]+=(a[i]-DEPTH+1)/DEPTH,a[i]-=(a[i]-DEPTH+1)/DEP TH*DEPTH,i++);

for (;!a[a[0]]&&a[0]>1;a[0]--);

}

void sub(bignum_t a,const bignum_t b,const int c,const int d){ int i,O=b[0]+d;

for (i=1+d;i<=O;i++)

if ((a[i]-=b[i-d]*c)<0)

a[i+1]+=(a[i]-DEPTH+1)/DEPTH,a[i]-=(a[i]-DEPTH+1)/DEPTH*DEPTH;

for

(;a[i]<0;a[i+1]+=(a[i]-DEPTH+1)/DEPTH,a[i]-=(a[i]-DEPTH+1)/DEPTH*DEP TH,i++);

for (;!a[a[0]]&&a[0]>1;a[0]--);

}

void mul(bignum_t c,const bignum_t a,const bignum_t b){

int i,j;

memset((void*)c,0,sizeof(bignum_t));

for (c[0]=a[0]+b[0]-1,i=1;i<=a[0];i++)

for (j=1;j<=b[0];j++)

if ((c[i+j-1]+=a[i]*b[j])>=DEPTH)

c[i+j]+=c[i+j-1]/DEPTH,c[i+j-1]%=DEPTH;

for (c[0]+=(c[c[0]+1]>0);!c[c[0]]&&c[0]>1;c[0]--);

}

void mul(bignum_t a,const int b){

int i;

for (a[1]*=b,i=2;i<=a[0];i++){

a[i]*=b;

if (a[i-1]>=DEPTH)

a[i]+=a[i-1]/DEPTH,a[i-1]%=DEPTH;

}

for

(;a[a[0]]>=DEPTH;a[a[0]+1]=a[a[0]]/DEPTH,a[a[0]]%=DEPTH,a[0]++);

for (;!a[a[0]]&&a[0]>1;a[0]--);

}

void mul(bignum_t b,const bignum_t a,const int c,const int d){ int i;

memset((void*)b,0,sizeof(bignum_t));

for (b[0]=a[0]+d,i=d+1;i<=b[0];i++)

if ((b[i]+=a[i-d]*c)>=DEPTH)

b[i+1]+=b[i]/DEPTH,b[i]%=DEPTH;

for (;b[b[0]+1];b[0]++,b[b[0]+1]=b[b[0]]/DEPTH,b[b[0]]%=DEPTH);

for (;!b[b[0]]&&b[0]>1;b[0]--);

}

void div(bignum_t c,bignum_t a,const bignum_t b){

int h,l,m,i;

memset((void*)c,0,sizeof(bignum_t));

c[0]=(b[0]

for (i=c[0];i;sub(a,b,c[i]=m,i-1),i--)

for (h=DEPTH-1,l=0,m=(h+l+1)>>1;h>l;m=(h+l+1)>>1)

if (comp(b,m,i-1,a)) h=m-1;

else l=m;

for (;!c[c[0]]&&c[0]>1;c[0]--);

c[0]=c[0]>1?c[0]:1;

}

void div(bignum_t a,const int b,int& c){

int i;

for (c=0,i=a[0];i;c=c*DEPTH+a[i],a[i]=c/b,c%=b,i--);

for (;!a[a[0]]&&a[0]>1;a[0]--);

}

void sqrt(bignum_t b,bignum_t a){

int h,l,m,i;

memset((void*)b,0,sizeof(bignum_t));

for (i=b[0]=(a[0]+1)>>1;i;sub(a,b,m,i-1),b[i]+=m,i--)

for (h=DEPTH-1,l=0,b[i]=m=(h+l+1)>>1;h>l;b[i]=m=(h+l+1)>>1) if (comp(b,m,i-1,a)) h=m-1;

else l=m;

for (;!b[b[0]]&&b[0]>1;b[0]--);

for (i=1;i<=b[0];b[i++]>>=1);

}

int length(const bignum_t a){

int t,ret;

for (ret=(a[0]-1)*DIGIT,t=a[a[0]];t;t/=10,ret++);

return ret>0?ret:1;

}

int digit(const bignum_t a,const int b){

int i,ret;

for (ret=a[(b-1)/DIGIT+1],i=(b-1)%DIGIT;i;ret/=10,i--);

return ret%10;

}

int zeronum(const bignum_t a){

int ret,t;

for (ret=0;!a[ret+1];ret++);

for (t=a[ret+1],ret*=DIGIT;!(t%10);t/=10,ret++);

return ret;

}

void comp(int* a,const int l,const int h,const int d){ int i,j,t;

for (i=l;i<=h;i++)

for (t=i,j=2;t>1;j++)

while (!(t%j))

a[j]+=d,t/=j;

}

void convert(int* a,const int h,bignum_t b){

int i,j,t=1;

memset(b,0,sizeof(bignum_t));

for (b[0]=b[1]=1,i=2;i<=h;i++)

if (a[i])

for (j=a[i];j;t*=i,j--)

if (t*i>DEPTH)

mul(b,t),t=1;

mul(b,t);

}

void combination(bignum_t a,int m,int n){

int* t=new int[m+1];

memset((void*)t,0,sizeof(int)*(m+1));

comp(t,n+1,m,1);

comp(t,2,m-n,-1);

convert(t,m,a);

delete []t;

}

void permutation(bignum_t a,int m,int n){

int i,t=1;

memset(a,0,sizeof(bignum_t));

a[0]=a[1]=1;

for (i=m-n+1;i<=m;t*=i++)

if (t*i>DEPTH)

mul(a,t),t=1;

mul(a,t);

}

#define SGN(x) ((x)>0?1:((x)<0?-1:0))

#define ABS(x) ((x)>0?(x):-(x))

int read(bignum_t a,int &sgn,istream& is=cin){

char str[MAX*DIGIT+2],ch,*buf;

int i,j;

memset((void*)a,0,sizeof(bignum_t));

if (!(is>>str)) return 0;

buf=str,sgn=1;

if (*buf=='-') sgn=-1,buf++;

for (a[0]=strlen(buf),i=a[0]/2-1;i>=0;i--)

ch=buf[i],buf[i]=buf[a[0]-1-i],buf[a[0]-1-i]=ch;

for

(a[0]=(a[0]+DIGIT-1)/DIGIT,j=strlen(buf);j

for (i=1;i<=a[0];i++)

for (a[i]=0,j=0;j

a[i]=a[i]*10+buf[i*DIGIT-1-j]-'0';

for (;!a[a[0]]&&a[0]>1;a[0]--);

if (a[0]==1&&!a[1]) sgn=0;

return 1;

}

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