"Algorithm design and Analysis basis" large integer multiplication

#include <iostream> #include <string> #include <time.h> #include <stdlib.h> #include < Sstream>using namespace Std;class bigdecimal{private:int max (int a,int b) {//Get maximum value in two numbers return a^ ((a^b) &-(A&LT;B) );} public:string N; BigDecimal () {n= "0";} void SetString (string n) {this->n=n;} BigDecimal (string n) {this->n=n;} BigDecimal operator + (BigDecimal b) {string s,l;//s is Addend, L is addend int temp=0,i,j;//temp record carry, I is used to traverse the s,j to determine which number is longer and longer gives S, Short to Lif (N.length () >=b.n.length ()) {s=n;l=b.n;i=s.length () -1;j=b.n.length ()-1;} Else{s=b.n;l=n;i=s.length () -1;j=n.length ()-1;} Start the addition operation while (j>=0) {s[i]=s[i]+l[j]+temp-48;//Two bits add, plus carry, minus 48 (' 0 ' ascii) if (s[i]> ' 9 ') {//= Two if the add is greater than 10, minus 10 , and then into position 1s[i]-=10;temp=1;} Else{temp=0;} i--;j--;} If l goes through, the carry is still 1, it consumes the carry until it is 0while (i>=0 && temp==1) {s[i]++;if (s[i]>=58) {s[i]-=10;i--;} Else{temp=0;break;}} If there is a carry after reaching the highest bit, the number is preceded by a ' 1 ' if (temp) {s= ' 1 ' +s;} return BigDecimal (s);} BigDecimal operator-(BigDecimal b) {string s,e;//s is meiosis, E is meiosis/** * due to (a1+a0) * (b1+b0)-(A1*B1+A0*B0) = A1 * B0 + a0 * B1 * so the subtraction operation is not negative */s=n; E=b.n;int i=s.length () -1,j=b.n.length () -1,temp=0;//begins the subtraction while (j>=0) {s[i]=s[i]+48-e[j]-temp;//Two-bit subtraction, minus borrow, Plus 48if (s[i]< ' 0 ') {//If not enough minus, add 10, borrow position 1s[i]+=10;temp=1;} Else{temp=0;} i--;j--;} If borrow is still 1, consume borrow until 0while (i>=0 && temp) {s[i]--;if (s[i]< ' 0 ') {s[i]+=10;temp=1;} Else{temp=0;}} i=0;//If the number begins with 0, remove the while (S.length () > 1) {if (s[i]== ' 0 ') {s.erase (0,1);} Else{break;}} Return BigDecimal (S);} BigDecimal Mul (string a,string b) {//int is multiplied by int, int num = atoi (A.C_STR ()) * Atoi (B.C_STR ()), if (num==0) return BigDecimal (); String S;stringstream Ss;ss<<num;ss>>s;return BigDecimal (s);} BigDecimal mul (String a,int N) {if (a== "0") {return BigDecimal ();} Char *k=new char[n+1];memset (k, ' 0 ', n*sizeof (char)); k[n]= ' + '; string Temp;a.append (k);d Elete[]k;return BigDecimal (A );} void Sub (int center,bigdecimal *s1,bigdecimal *s0) {if (N.length () <=center) {//If the large integer does not have enough length to be divided into two halves/** * that a1=0 a0=n * * S0->n=n.substr (0,n.length ());} else{/** * Otherwise it will be divided intoTwo halves */s0->n=n.substr (N.length ()-center,center); S1->n=n.substr (0,n.length ()-center);}} BigDecimal operator * (BigDecimal b) {//If the array length is less than or equal to 4, call the original multiplication if (N.length () <=4 && b.n.length () <=4) {return Mul (N,B.N);} BigDecimal Temp, A1, A0, B1, B0, C2, C1, C0;int Maxbit=max (N.length (), b.n.length ()); Sub (MAXBIT/2, &AMP;A1, &amp ; a0); B.sub (MAXBIT/2, &AMP;B1, &b0); c2 = a1 * B1;c0 = a0 * b0;c1 = (A1 + A0) * (B1 + b0)-(C2 + C0); return Mul (C2.N , maxbit/2*2) + mul (C1.N, MAXBIT/2) + C0;}};    int main () {clock_t start, finish; Double Totaltime;srand ((unsigned int) time (0)), int bit=10;//here to modify the number of bits of two large integers int pos=1;int i,j;string s,m;cout<<bit << ":" <<endl;do{j=rand ()%10+48;} while (j== ' 0 '), s+= (char) j;for (i=0;i<bit-1;i++) {J=rand ()%10+48;s+= (char) J;} Do{j=rand ()%10+48;} while (j== ' 0 '), m+= (char) j;for (i=0;i<bit-1;i++) {J=rand ()%10+48;m+= (char) J;} cout<<s<< "*" <<m<< "=" <<endl; BigDecimal A (s), B (M), C;start=clock (); C=a * B;finish=clock (); Cout<<c.n<<endl;totaltime= (double) (Finish-start)/clocks_per_sec;cout<< "This program runs for" << totaltime<< "Seconds!   "<<endl; return 0;}

If you need to do it faster, you need to write a primitive multiplication yourself and then

BigDecimal operator * (BigDecimal b) {
If the array length is less than or equal to 4, the original multiplication is called directly
if (N.length () <=4 && b.n.length () <=4) {
Return Mul (N,B.N);
}
BigDecimal Temp, A1, A0, B1, B0, C2, C1, C0;
int Maxbit=max (N.length (), b.n.length ());
Sub (MAXBIT/2, &AMP;A1, &a0);
B.sub (MAXBIT/2, &AMP;B1, &b0);
c2 = A1 * B1;
C0 = a0 * B0;
C1 = (A1 + A0) * (B1 + b0)-(C2 + C0);
Return Mul (C2.N, maxbit/2*2) + mul (C1.N, MAXBIT/2) + C0;
}

Modified in

if (N.length () <=4 && b.n.length () <=4) {
Return Mul (N,B.N);
}

4 is 600, then change Mul (N,B.N) to your original multiplication function mul (string,string)

Explanation and analysis of large integer algorithm ppt:http://download.csdn.net/detail/u013580497/8888515

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"Algorithm design and Analysis basis" large integer multiplication