Fast mulitplication.cpp

///Status : AC
///Remark :
typedef unsigned long long ull;
typedef long long ll;
typedef long double ld;
#include<bits/stdc++.h>

//MACROS{
#define rep(x,a,b) for(x=a;x<b;x++)
#define reptill(x,a,b) for(x=a;x<=b;x++)

#define scani(x) scanf("%d",&x)
#define scan2i(x,y) scanf("%d %d",&x,&y)
#define scan3i(x,y,z) scanf("%d %d %d",&x,&y,&z)

#define scanfl(x) scanf("%f",&x)
#define scanc(x) scanf("%c",&x)
#define scand(x) scanf("%lf",&x)

#define scanll(x) scanf("%lli",&x)
#define scan2ll(x,y) scanf("%lli %lli",&x,&y)
#define scan3ll(x,y,z) scanf("%lli %lli %lli",&x,&y,&z);

#define scanl(x) scanf("%ld",&x)
#define scans(x) scanf("%s",x)
#define printi(x) printf("%d\n",x)
#define printl(x) printf("%ld\n",x)
#define printll(x) printf("%lli\n",x)
#define printd(x) printf("%lf\n",x)
#define printfl(x) printf("%f\n",x)
#define printc(x) printf("%c\n",x)
#define prints(x) printf("%s\n",x);
#define sloop(x) loop(i,0,strlen(x)-1)
#define nl ("\n")
#define newl cout<<nl
#define FILL(A,value) memset(A,value,sizeof(A))
#define FILL_MAT(x,rrrr,cccc,value) for(int iiii=0;iiii<rrrr;iiii++){for(int jjjj=0;jjjj<cccc;jjjj++) x[iiii][jjjj]=value;}


#define whole(x) x.begin(),x.end()
#define pb push_back
#define in insert
#define mp make_pair
#define get(tp_name,x) (get<x>(tp_name))   ///to access tuple(i)
#define umap unordered_map


#define F first
#define S second
//}END MACROS

using namespace std;


///comparator class for ordering on the basis of 'Second'
/*
class CompareDist
{
public:				///pairType doesn't name a type ,its just to show type of pair object passed in operatorfunction

bool operator()( pairType p1, pairType p2) {
return p1.S>p2.S;
}
};
*/

typedef pair<int,int> II;
typedef pair<ll,ll> LL;
typedef vector<II> VII;
typedef vector<LL> VLL;
typedef vector<int> VI;
typedef vector<bool> VB;
typedef vector<ll> VL;
typedef vector< VI > VVI;
typedef vector< VL > VVL;
typedef vector<string> VS;

//maths
#define PI acos(-1)

#define INTmax numeric_limits<int>::max()
#define INTmin numeric_limits<int>::min()

#define LLmax numeric_limits<ll>::max()
#define LLmin numeric_limits<ll>::min()

#define ULLmax numeric_limits<ull>::max()

typedef priority_queue<II,vector<II>, greater<II> > P_Queue;             ///priority queue contianing II (having vector<II> as underlying container) with greater as functor
															///		heapify on the basis of comparisons of  II.first  values

template<typename type>
void get_arr(type a[],type n)
{
for(type i=0;i<n;i++) cin>>a[i];
}

template<typename type>
void show_arr(type a[],type n=1) {for(type i=0;i<n;i++) cout<<a[i]<<" ";}

template<typename type>
inline type max3(type a,type b,type c){	 return max(max(a,b),c);}

template<typename type>
inline type min3(type a,type b,type c){	 return min(a,min(b,c));}

template<typename type>
inline type min4(type a,type b,type c,type d){	 return min(a,min3(b,c,d));}

template<typename type>
inline type max4(type a,type b,type c,type d){	 return max(a,max3(b,c,d));}


template<typename type>
type modpowIter(type a, type b, type c) { type ans=1;  while(b != 0){ if(b%2 == 1) ans=(ans*a)%c;  a=(a*a)%c; b /= 2; } return ans; }

template<typename type>
type phi(type n){ type result = n;  for (type p=2; p*p<=n; ++p) { if (n % p == 0){ while (n % p == 0)   n /= p; result -= result / p; } } if (n > 1) result -= result / n; return result; }

template<typename type> type gcd(type A,type B){	if(B==0)	return A;	else return gcd(B, A % B);	}

template<class type>
type ncr(type n,type r){  	assert(n>=r); type ans=1,i; 	if(n==r) return 1; if(r==1) return n; if(r>(n-r)) r=n-r; reptill(i,0,r-1) ans=ans*(n-i)/(i+1);	return ans; }

template<typename type>  unsigned long long fact(type x){ ull ans=1; for(type i=1;i<=x;i++){ ans*=i;        /*ans%=MOD;   /Optional*/ } return ans; }

template<typename type>
int Digs(type n){ return (n >= 10) ? 1 + Digs(n/10): 1; }

template<typename type>
type tonum(string s){	type ans=0,i;	rep(i,0,s.size())	ans=ans*10+(s[i]-'0'); return ans; }

template<typename T_> inline bool is_perfsq(T_ n){T_ a=(T_)sqrt((double) n); return (a*a==n || (a+1)*(a+1)==n);/* in case of an off-by-one float error*/}

inline void FAST_IO(){ios_base::sync_with_stdio(false);}


#define printMat(x,r,c) for(int i=0;i<r;i++){ for(int j=0;j<c;j++) cout<<x[i][j]<<" "; newl; }

#define SIZE (int(2e3)+1)
#define MOD
#define debug
#define MAX1
#define MAX2

void append(int z,string &s)
{
	for(int i=0;i<z;i++)
	s.pb('0');
}

string a,b;

string add(string a,string b)
{

	if(a.size()<b.size())
	swap(a,b);

	reverse(whole(a)); reverse(whole(b));

	int diff=a.size()-b.size();

	for(int i=1;i<=diff;i++)
	  b.pb('0');

	string ans;
	int carry=0,sum;
	for(int i=0;i<a.size();i++)
	{
		int x=a[i]-'0';
		int y=b[i]-'0';

		sum=(x+y)+carry;

		if(sum>9)
		{
			sum-=10;
			carry=1;
		}
		else { carry=0;
		}
		ans.pb(sum+'0');

	}
	if(carry) ans.pb('1');
	reverse(whole(ans));

  	return ans;
}



string bigMul(int lx,int rx,int ly,int ry)
{

	if(lx==rx and ly==ry)
	{
		int x= a[lx]-'0';
		int y= b[ly]-'0';

		int p= x*y;

		string aux="";

		if(p%10==p)
		{
			aux+=(p+'0');
		}
		else{

			aux+= (p/10  +'0');
			p=p%10;
			aux+=(p + '0');
		}
		return aux;
	}

	int n = (rx-lx+1);

	int midx= (lx+rx)>>1,midy=(ly+ry)>>1;

	string AC= bigMul(lx,midx,ly,midy) ;

	append(n,AC);

	string AD = bigMul(lx,midx,midy+1,ry);

	append(n/2,AD);

	string BC= bigMul(midx+1,rx,ly,midy) ;

	append(n/2,BC);

	string BD = bigMul(midx+1,rx,midy+1,ry) ;

	string ans =  add(add(AC,AD),add(BC,BD));

	return ans;

}



int main()
{

	FAST_IO();

	#ifndef ONLINE_JUDGE
		ifstream cin("/home/aditya/Documents/ip");
	#endif

	//ofstream cout("/home/aditya/Documents/op");

	//int t;	cin>>t;while(t--){}


	int t;
	cin>>t;

	while(t--)
	{

		cin>>a>>b;

		if(a.size()<b.size())
		swap(a,b);

		int diff= a.size()-b.size();




	string aux(diff,'0');
	aux = aux + b;

	b= aux;

	//till here size of both a and b is equal

	if((a.size() & (a.size()-1))!=0){

		int fac=log2(a.size()) +1;

		int reqsize= pow(2,fac);

		int extra= reqsize - a.size();

		string tempa,tempb;

		for(int i=0;i<extra;i++) tempa.pb('0'),tempb.pb('0');

		tempa += a;
		tempb += b;
		a=tempa;
		b=tempb;
	}




	//cout<<a<<" "<<b<<nl;

	string ans = bigMul(0,a.size()-1,0,b.size()-1);

	//cout<<ans<<" \n";

	string newans;

	int i=0;
	while(i<ans.size() and ans[i]=='0') ++i;

	for(int j=i;j<ans.size();j++) newans.pb(ans[j]);

	if(newans.size()==0) newans= "0";

	cout<<newans<<nl;


	}
}