Category Algorithmic Codes

Finding LCM

Arunima Mandal Leave a comment

Normal iterative way:

#include <iostream>

using namespace std;

int main()
{
    int a,b,x,i,lcm;
    cout<<"Enter one value: "<<endl;
    cin>>a;
    cout<<"Enter another value: ";
    cin>>b;
    x=max(a,b);
    for(i=x;;i++)
    {
        if(i%a==0 && i%b==0)
        {
            lcm=i;
            break;
        }
    }
    cout<<"LCM is "<<lcm<<endl;

    return 0;
}

Using GCD:
This way has a chance of overflow.

#include <iostream>

using namespace std;

int gcd(int a,int b)
{
    return b==0 ? a : gcd(b,a%b);
}

int main()
{
    int c,d,lcm;
     for(;;)
    {
        cout<<"Enter any number:"<<endl;
        cin>>c;
        cout<<"Enter another number:"<<endl;
        cin>>d;

        lcm=(c*d)/gcd(c,d);

        cout<<"LCM is "<<gcd(c,d)<<endl<<endl;
    }
    return 0;
}

Using GCD:
This way hasn’t a chance of overflow. It’s the best way.

#include <iostream>

using namespace std;

int gcd(int a,int b)
{
    return b==0 ? a : gcd(b,a%b);
}

int main()
{
    int c,d,lcm;
     for(;;)
    {
        cout<<"Enter any number:"<<endl;
        cin>>c;
        cout<<"Enter another number:"<<endl;
        cin>>d;

        lcm=(c*d)/gcd(c,d);

        cout<<"LCM is "<<gcd(c,d)<<endl<<endl;
    }
    return 0;
}

Finding GCD

Arunima Mandal Leave a comment

Iterative way:

#include <iostream>

using namespace std;

int main()
{
    int a,b,x,gcd;
    cout<<"Enter one value: "<<endl;
    cin>>a;
    cout<<"Enter another value: ";
    cin>>b;
    if(a<b)
    {
        x=a;
    }
    else
    {
        x=b;
    }
    for(;x>=1;x--)
    {
        if(a%x==0 && b%x==0)
        {
            gcd=x;
            break;
        }
    }
    cout<<"GCD is "<<gcd<<endl;


    return 0;
}

 

Euclidian algorithm ( Recursive way):

#include <iostream>

using namespace std;


int main()
{
    int a,b,remainder,gcd;
    cout<<"Enter one value: "<<endl;
    cin>>a;
    cout<<"Enter another value: "<<endl;
    cin>>b;

    // Assuming a>b always

    while(remainder!=0)
    {
        remainder=a%b;
        if(remainder==0)
        {
            gcd=b;
            cout<<"GCD is "<<gcd<<endl;
        }
        a=b;
        b=remainder;
    }
    return 0;
}

The above code can be written further in a shortcut as follows:

#include <iostream>

using namespace std;

int gcd(int a,int b)
{
    return b==0 ? a : gcd(b,a%b);
}

int main()
{
    int c,d;

    for(;;)
    {
        cout<<"Enter any number:"<<endl;
        cin>>c;
        cout<<"Enter another number:"<<endl;
        cin>>d;

        cout<<"GCD is "<<gcd(c,d)<<endl<<endl;
    }


    return 0;
}

Trailling zeroes in N! at any base

Arunima Mandal Leave a comment 
#include <bits/stdc++.h>

#define pf                  printf
#define sf(a)               scanf("%d",&a)
#define sfl(a)              scanf("%lld",&a)
#define sff(a,b)            scanf("%d %d",&a,&b)
#define sffl(a,b)           scanf("%lld %lld",&a,&b)
#define sfff(a,b,c)         scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c)        scanf("%lld %lld %lld",&a,&b,&c)
#define sffff(a,b,c,d)      scanf("%d %d %d %d",&a,&b,&c,&d)
#define sffffl(a,b,c,d)     scanf("%lld %lld %lld %lld",&a,&b,&c,&d)
#define sfffff(a,b,c,d,e)   scanf("%d %d %d %d %d",&a,&b,&c,&d,&e)
#define sfffffl(a,b,c,d,e)  scanf("%lld %lld %lld %lld %lld",&a,&b,&c,&d,&e)
#define ms(a,b)             memset(a,b,sizeof(a))
#define pb(a)               push_back(a)
#define pbp(a,b)            push_back({a,b})
#define db                  double
#define ft                  float
#define ll                  long long
#define ull                 unsigned long long
#define ff                  first
#define ss                  second
#define sz(x)               x.size()
#define qu                  queue
#define pqu                 priority_queue
#define vc                  vector
#define vi                  vector<int>
#define vll                 vector<long long>
#define pii                 pair<int,int>
#define pis                 pair<int,string>
#define psi                 pair<string,int>
#define all(x)              x.begin(),x.end()
#define CIN                 ios_base::sync_with_stdio(0); cin.tie(0)
#define max3(a, b, c)       max(a, b) > max(b, c) ? max(a, b) : max(b, c)
#define min3(a, b, c)       min(a, b) < min(b, c) ? min(a, b) : min(b, c)
#define loop0(i,n)          for(int i=0;i<n;i++)
#define loop1(i,n)          for(int i=1;i<=n;i++)
#define loopab(i,a,b)       for(int i=a;i<=b;i++)
#define stlloop(x)          for(__typeof(x.begin()) it=x.begin();it!=x.end();it++)
#define gcd(a, b)           __gcd(a, b)
#define lcm(a, b)           ((a)*((b)/gcd(a,b)))
#define case1(z)            cout<<"Case "<<z<<": "
#define case2(z)            printf("Case %d: ",z)
#define PI                  3.14159265358979323846264338328
#define valid(tx,ty)        tx>=0 && tx<r && ty>=0 && ty<c
#define intlim              2147483648
#define MAX                 1000000
#define inf                 10000000

/*------------------------------Graph Moves----------------------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*---------------------------------------------------------------------*/

using namespace std;

bool p[MAX+2];
vector<int>prime;

void sieve()
{
    p[0]=p[1]=1;
    int root=sqrt(MAX);
    for(int i=2; i<=root; i++)
    {
        if(p[i]==0)
        {
            for(int j=i*i; j<=MAX; j+=i)
            {
                p[j]=1;
                if(i%2==1) j+=i;
            }
        }
    }
    for(int i=2; i<=MAX; i++)
    {
        if(p[i]==0) prime.push_back(i);
    }
}

int trail_zero(int n,int b)
{
    int ans=n;
    int root=sqrt(b);
    int k=b;
    int c,sum;
    for(int i=0; prime[i]<=root; i++)
    {
        if(k%prime[i]==0)
        {
            c=0;
            while(k%prime[i]==0)
            {
                k/=prime[i];
                c++;
            }
            root=sqrt(k);

            sum=0;
            int m=n;
            while(m!=0)
            {
                sum+=m/prime[i];
                m=m/prime[i];
            }
            ans=min(ans,sum/c);
        }
    }

    if(k>1)
    {
        sum=0;
        int m=n;
        while(m!=0)
        {
            sum+=m/k;
            m=m/k;
        }
        ans=min(ans,sum);
    }
    return ans;
}

int main()
{
    //CIN;
//    freopen("in.txt","r",stdin);
//    freopen("out.txt","w",stdout);
    sieve();
    int n,b;
    while(cin>>n>>b)
    {
        cout<<"No. of trailling zeroes in "<<n<<"! at base "<<b<<" is "<<trail_zero(n,b)<<endl;
    }
    return 0;
}

Trailing zeroes in N!

Arunima Mandal Leave a comment 
#include <bits/stdc++.h>

#define pf                  printf
#define sf(a)               scanf("%d",&a)
#define sfl(a)              scanf("%lld",&a)
#define sff(a,b)            scanf("%d %d",&a,&b)
#define sffl(a,b)           scanf("%lld %lld",&a,&b)
#define sfff(a,b,c)         scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c)        scanf("%lld %lld %lld",&a,&b,&c)
#define sffff(a,b,c,d)      scanf("%d %d %d %d",&a,&b,&c,&d)
#define sffffl(a,b,c,d)     scanf("%lld %lld %lld %lld",&a,&b,&c,&d)
#define sfffff(a,b,c,d,e)   scanf("%d %d %d %d %d",&a,&b,&c,&d,&e)
#define sfffffl(a,b,c,d,e)  scanf("%lld %lld %lld %lld %lld",&a,&b,&c,&d,&e)
#define ms(a,b)             memset(a,b,sizeof(a))
#define pb(a)               push_back(a)
#define db                  double
#define ft                  float
#define ll                  long long
#define ull                 unsigned long long
#define ff                  first
#define ss                  second
#define sz(x)               x.size()
#define qu                  queue
#define pqu                 priority_queue
#define vc                  vector
#define vi                  vector<int>
#define vll                 vector<long long>
#define pii                 pair<int,int>
#define pis                 pair<int,string>
#define psi                 pair<string,int>
#define all(x)              x.begin(),x.end()
#define CIN                 ios_base::sync_with_stdio(0); cin.tie(0)
#define max3(a, b, c)       max(a, b) > max(b, c) ? max(a, b) : max(b, c)
#define min3(a, b, c)       min(a, b) < min(b, c) ? min(a, b) : min(b, c)
#define loop0(i,n)          for(int i=0;i<n;i++)
#define loop1(i,n)          for(int i=1;i<=n;i++)
#define loopab(a,b)         for(int i=a;i<=b;i++)
#define stlloop(x)          for(__typeof(x.begin()) it=x.begin();it!=x.end();it++)
#define gcd(a, b)           __gcd(a, b)
#define lcm(a, b)           ((a)*((b)/gcd(a,b)))
#define case1(z)            cout<<"Case "<<z<<": "
#define case2(z)            printf("Case %d: ",z)
#define PI                  3.14159265358979323846264338328
#define valid(tx,ty)        tx>=0 && tx<r && ty>=0 && ty<c
#define intlim              2147483648
#define MAX                 1000000
#define inf                 10000000

/*------------------------------Graph Moves----------------------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*---------------------------------------------------------------------*/

using namespace std;

int trail_zero(int n)
{
    int sum=0;
    while(n!=0)
    {
        sum+=n/5;
        n=n/5;
    }
    return sum;
}

int main()
{
    //CIN;
    //freopen("in.txt","r",stdin);
    //freopen("out.txt","w",stdout);
    int n;
//    for(int i=5;i<=200;i+=5)
//    {
//        cout<<i<<"="<<trail_zero(i)<<endl;
//    }
    cin>>n;
    cout<<"No. of trailling zeroes in "<<n<<" is "<<trail_zero(n)<<endl;
    return 0;
}

Prime factorization of N!

Arunima Mandal Leave a comment 
#include <bits/stdc++.h>

#define pf                  printf
#define sf(a)               scanf("%d",&a)
#define sfl(a)              scanf("%lld",&a)
#define sff(a,b)            scanf("%d %d",&a,&b)
#define sffl(a,b)           scanf("%lld %lld",&a,&b)
#define sfff(a,b,c)         scanf("%d %d %d",&a,&b,&c)
#define sfffl(a,b,c)        scanf("%lld %lld %lld",&a,&b,&c)
#define sffff(a,b,c,d)      scanf("%d %d %d %d",&a,&b,&c,&d)
#define sffffl(a,b,c,d)     scanf("%lld %lld %lld %lld",&a,&b,&c,&d)
#define sfffff(a,b,c,d,e)   scanf("%d %d %d %d %d",&a,&b,&c,&d,&e)
#define sfffffl(a,b,c,d,e)  scanf("%lld %lld %lld %lld %lld",&a,&b,&c,&d,&e)
#define ms(a,b)             memset(a,b,sizeof(a))
#define pb(a)               push_back(a)
#define db                  double
#define ft                  float
#define ll                  long long
#define ull                 unsigned long long
#define ff                  first
#define ss                  second
#define sz(x)               x.size()
#define qu                  queue
#define pqu                 priority_queue
#define vc                  vector
#define vi                  vector<int>
#define vll                 vector<long long>
#define pii                 pair<int,int>
#define pis                 pair<int,string>
#define psi                 pair<string,int>
#define all(x)              x.begin(),x.end()
#define CIN                 ios_base::sync_with_stdio(0); cin.tie(0)
#define max3(a, b, c)       max(a, b) > max(b, c) ? max(a, b) : max(b, c)
#define min3(a, b, c)       min(a, b) < min(b, c) ? min(a, b) : min(b, c)
#define loop0(i,n)          for(int i=0;i<n;i++)
#define loop1(i,n)          for(int i=1;i<=n;i++)
#define loopab(a,b)         for(int i=a;i<=b;i++)
#define stlloop(x)          for(__typeof(x.begin()) it=x.begin();it!=x.end();it++)
#define gcd(a, b)           __gcd(a, b)
#define lcm(a, b)           ((a)*((b)/gcd(a,b)))
#define case1(z)            cout<<"Case "<<z<<": "
#define case2(z)            printf("Case %d: ",z)
#define PI                  3.14159265358979323846264338328
#define valid(tx,ty)        tx>=0 && tx<r && ty>=0 && ty<c
#define intlim              2147483648
#define MAX                 1000000
#define inf                 10000000

/*------------------------------Graph Moves----------------------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*---------------------------------------------------------------------*/

using namespace std;

bool p[MAX+2];
vector<int> prime,v;

void sieve()
{
    p[0]=p[1]=1;
    int root=sqrt(MAX);
    for(int i=2; i<=root; i++)
    {
        if(p[i]==0)
        {
            prime.pb(i);
            for(int j=i*i; j<=MAX; j+=i)
            {
                p[j]=1;
                if(i%2==1) j+=i;
            }
        }
    }
}

void factorial_fact(int n)
{
    for(int i=0; prime[i]<=n && i<sz(prime); i++)
    {
        int k=n;
        int h=0;
        while(k!=0)
        {
            h=h+k/prime[i];
            k=k/prime[i];
        }
        v.pb(prime[i]);
        v.pb(h);
    }
}

int main()
{
    //CIN;
//    freopen("in.txt","r",stdin);
//    freopen("out.txt","w",stdout);
    int t;
    sf(t);
    sieve();
    loop1(z,t)
    {
        int n;
        sf(n);
        case2(z);
        pf("%d = ",n);
        factorial_fact(n);
        pf("%d (%d)",v[0],v[1]);
        for(int i=2;i<sz(v)-1;i+=2)
        {
            pf(" * %d (%d)",v[i],v[i+1]);
        }
        pf("\n");
        v.clear();
    }

    return 0;
}