SPOJ: AMR10E – Stocks Prediction

0

Problem Link : http://www.spoj.com/problems/AMR10E/


#include <bits/stdc++.h>

#define pii              pair <int,int>
#define pll              pair <long long,long long>
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cout<<#x " = "<<(x)<<endl
#define VI               vector <int>
#define DBG              pf("Hi\n")
//#define MOD              1000000007
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#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 stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i<n;i++)
#define loop1(i,n)       for(int i=1;i<=n;i++)
#define REP(i,a,b)       for(int i=a;i<b;i++)
#define RREP(i,a,b)      for(int i=a;i>=b;i--)
#define TEST_CASE(t)     for(int z=1;z<=t;z++)
#define PRINT_CASE       printf("Case %d: ",z)
#define LINE_PRINT_CASE  printf("Case %d:\n",z)
#define CASE_PRINT       cout<<"Case "<<z<<": "
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1<<28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;


/*----------------------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
/*------------------------------------------------*/

/*-----------------------Bitmask------------------*/
//int Set(int N,int pos){return N=N | (1<<pos);}
//int reset(int N,int pos){return N= N & ~(1<<pos);}
//bool check(int N,int pos){return (bool)(N & (1<<pos));}
/*------------------------------------------------*/



/*----------------------Matrix-----------------------*/

// int MOD=
ll MOD= 1000000007;

struct matrix
{
    ll mat[11][11];
    int row,col;

    matrix()
    {
        row=col=0;
        memset(mat,0,sizeof mat);
    }
    matrix(int a, int b)
    {
        row=a,col=b;
        memset(mat,0,sizeof mat);
    }

    matrix operator*(const matrix &p) const
    {
        assert(col == p.row);
        matrix temp;
        temp.row = row;
        temp.col = p.col;
        for (int i = 0; i < temp.row; i++)
        {
            for (int j = 0; j < temp.col; j++)
            {
                ll sum = 0;
                for (int k = 0; k <col;  k++)
                {
                    sum += ((mat[i][k]%MOD) * (p.mat[k][j]%MOD))%MOD;
                    sum%=MOD;
                }
                temp.mat[i][j] = sum;
            }
        }
        return temp;
    }
    matrix operator+ (const matrix &p) const
    {
        assert(row==p.row && col==p.col);
        matrix temp;
        temp.row=row;
        temp.col=col;
        for(int i=0; i<temp.row; i++)
        {
            for(int j=0; j<temp.col; j++)
                temp.mat[i][j]=((mat[i][j]%MOD)+(p.mat[i][j]%MOD))%MOD;;
        }
        return temp;
    }

    matrix identity()
    {
        matrix temp;
        temp.row=row;
        temp.col=col;
        for(int i=0; i<row; i++)
            temp.mat[i][i]=1;
        return temp;
    }

    matrix pow(ll pow)
    {
        matrix temp=(*this);
        matrix ret=(*this).identity();
        while(pow)
        {
            if(pow % 2==1)
                ret=ret*temp;
            temp=temp*temp;
            pow/=2;
        }
        return ret;
    }

    void show()
    {
        printf("-----------------------------\n");
        for(int i=0; i<row; i++)
        {
            for(int j=0; j<col; j++)
                printf("%lld ",mat[i][j]);
            printf("\n");
        }
        printf("-----------------------------\n");
    }

};

/*--------------------------Matrix End---------------------*/

matrix identity;

matrix func(matrix m, ll p)
{
//    if(p==0) return identity;
    if(p==1) return identity;
//
//    matrix ret=func(m,p/2);
//
//    matrix temp=m.pow(p/2);

    if(p%2==0)
    {
        return func(m,p/2)*(identity+m.pow(p/2));
    }
    else
    {
        return func(m,p-1)+m.pow(p-1);
    }
}

ll s[15],ara[15];

int main()
{

//    freopen("in.txt","r",stdin);
//	  freopen("out.txt","w",stdout);

    int t;
    sf(t);
    TEST_CASE(t)
    {
        ll n,r,k;

        sfffl(n,r,k);

        matrix base(r,1);

        ms(s,0);
        ms(ara,0);

        for(int i=1; i<=r; i++)
            sfl(s[i]);

        matrix a(r,r);

        for(int i=0; i<r; i++)
        {
            sfl(a.mat[0][i]);
            ara[i+1]=a.mat[0][i];
            if(i+1!=r)
                a.mat[i+1][i]=1;
        }

//        base.show();

//        a.show();

        a=a.pow(k);

//        a.show();

//        base.show();

        identity=a.identity();

        a=func(a,n);

//        a.show();

        ll ans=0;

        if(k>r)
        {
            for(int i=r+1; i<=k; i++)
            {
                for(int j=1; j<=r; j++)
                {
                    s[i]+=s[i-j]*ara[j];
                    s[i]%=MOD;
                }
            }

            for(int i=0; i<r; i++)
            {
                ans=(ans+(s[k-i]*a.mat[0][i])%MOD);
                ans%=MOD;

            }

        }
        else
        {
            for(int i=0; i<r; i++)
            {
                ans=(ans+(a.mat[r-k][r-i-1]*s[i+1])%MOD);
                ans%=MOD;
            }

        }
        pf("%lld\n",ans);

    }

    return 0;
}

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Light OJ: 1070 – Algebraic Problem

0

Problem Link : http://lightoj.com:81/volume/problem/1070

(These solution idea is form : http://blog.csdn.net/u013532224/article/details/46862465
and LightOj forum.)


/*

Solution Idea: 

Meaning of the questions:
You p = a + b, q = ab

Calculating (a ^ n + b ^) mod2 ^ 64

practice:

mod 2 ^ 64 so open unsigned long long, llu on the line, reaches the upper limit will be automatically modulo.

Then the formula is. I was pushing the law found in the formula.

a ^ 2 + b ^ 2 = (a + b) * (a + b) -2 * a * b

a ^ 3 + b ^ 3 = (a ^ 2 + b ^ 2) * (a + b) -a * b (a + b)

a ^ 4 + b ^ 4 = (a ^ 3 + b ^ 3) * (a + b) -a * b (a ^ 2 + b ^ 2)

now --

1.a^n + b^n = (a^(n-1)+b^(n-1))*(a+b) - a*b*(a^(n-2)+b^(n-2))
 
2.  Xn = a^n + b^n

3 . Xn = pXn-1 + qXn-2

    (p q)      (Xn-1)         (pXn-1 + qXn-2)         (Xn  )
4.         x               =                      =
    (1 0)      (Xn-2)         ( Xn-1 +  0  )          (Xn-1)

5 . from this

    (p q)^(n-1)     (X1)     (Xn   )   
                x          =
    (1 0)           (X0)     (Xn-1)

*/


#include <bits/stdc++.h>

#define pii              pair <int,int>
#define pll              pair <long long,long long>
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cout<<#x " = "<<(x)<<endl
#define VI               vector <int>
#define DBG              pf("Hi\n")
#define MOD              1000000007
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#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 stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i<n;i++)
#define loop1(i,n)       for(int i=1;i<=n;i++)
#define REP(i,a,b)       for(int i=a;i<b;i++)
#define RREP(i,a,b)      for(int i=a;i>=b;i--)
#define TEST_CASE(t)     for(int z=1;z<=t;z++)
#define PRINT_CASE       printf("Case %d: ",z)
#define CASE_PRINT       cout<<"Case "<<z<<": "
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1<<28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;


/*----------------------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
/*------------------------------------------------*/

/*-----------------------Bitmask------------------*/
//int Set(int N,int pos){return N=N | (1<<pos);}
//int reset(int N,int pos){return N= N & ~(1<<pos);}
//bool check(int N,int pos){return (bool)(N & (1<<pos));}
/*------------------------------------------------*/

/*----------------------Matrix-----------------------*/

// int MOD=
// ll MOD=

struct matrix
{
    ull mat[2][2];
    int row,col;

    matrix()
    {
        memset(mat,0,sizeof mat);
    }
    matrix(int a, int b)
    {
        row=a,col=b;
        memset(mat,0,sizeof mat);
    }

    matrix operator*(const matrix &p) const
    {
        assert(col == p.row);
        matrix temp;
        temp.row = row;
        temp.col = p.col;
        for (int i = 0; i < temp.row; i++)
        {
            for (int j = 0; j < temp.col; j++)
            {
                ll sum = 0;
                for (int k = 0; k <col;  k++)
                {
                    sum += ((mat[i][k]) * (p.mat[k][j]));
//                    sum%=MOD;
                }
                temp.mat[i][j] = sum;
            }
        }
        return temp;
    }
    matrix operator+ (const matrix &p) const
    {
        assert(row==p.row && col==p.col);
        matrix temp;
        temp.row=row;
        temp.col=col;
        for(int i=0;i<temp.row;i++)
        {
            for(int j=0;j<temp.col;j++)
                temp.mat[i][j]=((mat[i][j])+(p.mat[i][j]));
        }
        return temp;
    }

    matrix identity()
    {
        matrix temp;
        temp.row=row;
        temp.col=col;
        for(int i=0;i<row;i++)
            temp.mat[i][i]=1;
        return temp;
    }

    matrix pow(ll pow)
    {
        matrix temp=(*this);
        matrix ret=(*this).identity();
        while(pow)
        {
            if(pow % 2==1)
                ret=ret*temp;
            temp=temp*temp;
            pow/=2;
        }
        return ret;
    }

    void show()
    {
        printf("-----------------------------\n");
        for(int i=0;i<row;i++)
        {
            for(int j=0;j<col;j++)
                printf("%llu ",mat[i][j]);
            printf("\n");
        }
        printf("-----------------------------\n");
    }

};

/*--------------------------Matrix End---------------------*/


int main()
{

    ///freopen("in.txt","r",stdin);
    ///freopen("out.txt","w",stdout);

    int t;
    sf(t);
    TEST_CASE(t)
    {
        ll p,q,n;
        sfffl(p,q,n);
        matrix base(2,2);
        base.mat[0][0]=p;
        base.mat[0][1]=-q;
        base.mat[1][0]=1;

        matrix temp(2,1);
        temp.mat[0][0]=p;
        temp.mat[1][0]=2;

//        base.show();

        base=base.pow(n-1);
//        base.show();
//        temp.show();
        base=base*temp;
//        ull ans=(base.mat[0][0]*temp.mat[0][0])-(base.mat[0][1]*temp.mat[1][0]);

//        base.show();

        ull ans=base.mat[0][0];
        
        if(n==0) ans=2;
        
        PRINT_CASE;
        printf("%llu\n",ans);

    }

    return 0;
}


Light OJ: 1132 – Summing up Powers

0

Problem Link : http://lightoj.com:81/volume/problem/1132

Soluton Idea:
————–

f(x)=1^k+2^k+3^k+……….+x^k
f(1)=1
f(x+1)=f(x)+(x+1)^k

from Binomial Co efficient we know –
(x+1)^n= nC0 x^n + nC1 x^n-1 + nC2 x^n-2+…………..+ nCn-1 x^1 + nCn x^0

Now make a matrix with co efficient of x so that we can find f(x+1) from f(x).

details: http://lbv-pc.blogspot.com/2012/05/summing-up-powers.html



#include <bits/stdc++.h>

#define pii              pair <int,int>
#define pll              pair <long long,long long>
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cout<<#x " = "<<(x)<<endl
#define VI               vector <int>
#define DBG              pf("Hi\n")
//#define MOD              1000000007
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#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 stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i<n;i++)
#define loop1(i,n)       for(int i=1;i<=n;i++)
#define REP(i,a,b)       for(int i=a;i<b;i++)
#define RREP(i,a,b)      for(int i=a;i>=b;i--)
#define TEST_CASE(t)     for(int z=1;z<=t;z++)
#define PRINT_CASE       printf("Case %d: ",z)
#define CASE_PRINT       cout<<"Case "<<z<<": "
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1<<28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;


/*----------------------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
/*------------------------------------------------*/

/*-----------------------Bitmask------------------*/
//int Set(int N,int pos){return N=N | (1<<pos);}
//int reset(int N,int pos){return N= N & ~(1<<pos);}
//bool check(int N,int pos){return (bool)(N & (1<<pos));}
/*------------------------------------------------*/



/*----------------------Matrix-----------------------*/

// int MOD=
// ll MOD= (1LL)<<32;

struct matrix
{
    unsigned int mat[52][52];
    int row,col;

    matrix()
    {
        memset(mat,0,sizeof mat);
    }
    matrix(int a, int b)
    {
        row=a,col=b;
        memset(mat,0,sizeof mat);
    }

    matrix operator*(const matrix &p) const
    {
        assert(col == p.row);
        matrix temp;
        temp.row = row;
        temp.col = p.col;
        for (int i = 0; i < temp.row; i++)
        {
            for (int j = 0; j < temp.col; j++)
            {
                ll sum = 0;
                for (int k = 0; k <col;  k++)
                {
                    sum += ((mat[i][k]) * (p.mat[k][j]));
//                    sum%=MOD;
                }
                temp.mat[i][j] = sum;
            }
        }
        return temp;
    }
    matrix operator+ (const matrix &p) const
    {
        assert(row==p.row && col==p.col);
        matrix temp;
        temp.row=row;
        temp.col=col;
        for(int i=0;i<temp.row;i++)
        {
            for(int j=0;j<temp.col;j++)
                temp.mat[i][j]=((mat[i][j])+(p.mat[i][j]));;
        }
        return temp;
    }

    matrix identity()
    {
        matrix temp;
        temp.row=row;
        temp.col=col;
        for(int i=0;i<row;i++)
            temp.mat[i][i]=1;
        return temp;
    }

    matrix pow(ll pow)
    {
        matrix temp=(*this);
        matrix ret=(*this).identity();
        while(pow)
        {
            if(pow % 2==1)
                ret=ret*temp;
            temp=temp*temp;
            pow/=2;
        }
        return ret;
    }

    void show()
    {
        printf("-----------------------------\n");
        for(int i=0;i<row;i++)
        {
            for(int j=0;j<col;j++)
                printf("%lld ",mat[i][j]);
            printf("\n");
        }
        printf("-----------------------------\n");
    }

};

/*--------------------------Matrix End---------------------*/

unsigned int nCr[55][55];

void compute_nCr()
{
    nCr[0][0]=nCr[1][1]=1;
    for(int i=1;i<52;i++)
    {
        nCr[i][0]=1;
        for(int j=1;j<52;j++)
            nCr[i][j]=nCr[i-1][j]+nCr[i-1][j-1];
    }
}

int main()
{

//    freopen("in.txt","r",stdin);
    ///freopen("out.txt","w",stdout);

    int t;
    sf(t);
    compute_nCr();

//    int a=5;
//    while(a--)
//    {
//        int a,b;
//        cin>>a>>b;
//        cout<<nCr[a][b]<<endl;
//    }

    TEST_CASE(t)
    {
        ll n,k;
        sffl(n,k);
        matrix base(k+2,k+2);

        base.mat[0][0]=1;

        for(int i=1;i<=k+1;i++)
        {
            base.mat[0][i]=nCr[k][i-1];
            base.mat[1][i]=nCr[k][i-1];
        }
        for(int i=2;i<=k+1;i++)
        {
            for(int j=i;j<=k+1;j++)
                base.mat[i][j]=nCr[k-i+1][j-i];
        }

//        base.show();

        matrix temp(k+2,1);
        for(int i=0;i<=k+1;i++)
            temp.mat[i][0]=1;

        base=base.pow(n-1);
//        base.show();
//        temp.show();
        base=base*temp;
        PRINT_CASE;
        printf("%u\n",base.mat[0][0]);



    }

    return 0;
}


Light OJ: 1131 – Just Two Functions

0

Problem Link : http://lightoj.com:81/volume/problem/1131


#include <bits/stdc++.h>

#define pii              pair <int,int>
#define pll              pair <long long,long long>
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cout<<#x " = "<<(x)<<endl
#define VI               vector <int>
#define DBG              pf("Hi\n")
//#define MOD              1000000007
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#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 stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i<n;i++)
#define loop1(i,n)       for(int i=1;i<=n;i++)
#define REP(i,a,b)       for(int i=a;i<b;i++)
#define RREP(i,a,b)      for(int i=a;i>=b;i--)
#define TEST_CASE(t)     for(int z=1;z<=t;z++)
#define PRINT_CASE       printf("Case %d:\n",z)
#define CASE_PRINT       cout<<"Case "<<z<<": "
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1<<28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;


/*----------------------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
/*------------------------------------------------*/

/*-----------------------Bitmask------------------*/
//int Set(int N,int pos){return N=N | (1<<pos);}
//int reset(int N,int pos){return N= N & ~(1<<pos);}
//bool check(int N,int pos){return (bool)(N & (1<<pos));}
/*------------------------------------------------*/

/*----------------------Matrix-----------------------*/

// int MOD=
 ll MOD;

struct matrix
{
    ll mat[7][7];
    int row,col;

    matrix()
    {
        memset(mat,0,sizeof mat);
    }
    matrix(int a, int b)
    {
        row=a,col=b;
        memset(mat,0,sizeof mat);
    }

    matrix operator*(const matrix &p) const
    {
        assert(col == p.row);
        matrix temp;
        temp.row = row;
        temp.col = p.col;
        for (int i = 0; i < temp.row; i++)
        {
            for (int j = 0; j < temp.col; j++)
            {
                ll sum = 0;
                for (int k = 0; k <col;  k++)
                {
                    sum += ((mat[i][k]%MOD) * (p.mat[k][j]%MOD))%MOD;
                    sum%=MOD;
                }
                temp.mat[i][j] = sum;
            }
        }
        return temp;
    }
    matrix operator+ (const matrix &p) const
    {
        assert(row==p.row && col==p.col);
        matrix temp;
        temp.row=row;
        temp.col=col;
        for(int i=0;i<temp.row;i++)
        {
            for(int j=0;j<temp.col;j++)
                temp.mat[i][j]=((mat[i][j]%MOD)+(p.mat[i][j]%MOD))%MOD;;
        }
        return temp;
    }

    matrix identity()
    {
        matrix temp;
        temp.row=row;
        temp.col=col;
        for(int i=0;i<row;i++)
            temp.mat[i][i]=1;
        return temp;
    }

    matrix pow(ll pow)
    {
        matrix temp=(*this);
        matrix ret=(*this).identity();
        while(pow)
        {
            if(pow % 2==1)
                ret=ret*temp;
            temp=temp*temp;
            pow/=2;
        }
        return ret;
    }

    void show()
    {
        printf("-----------------------------\n");
        for(int i=0;i<row;i++)
        {
            for(int j=0;j<col;j++)
                printf("%lld ",mat[i][j]);
            printf("\n");
        }
        printf("-----------------------------\n");
    }

};

/*--------------------------Matrix End---------------------*/

int main()
{

    ///freopen("in.txt","r",stdin);
    ///freopen("out.txt","w",stdout);

    int t;
    sf(t);
    TEST_CASE(t)
    {
        int a1,b1,c1,a2,b2,c2,f0,f1,f2,g0,g1,g2;
        sfff(a1,b1,c1);
        sfff(a2,b2,c2);
        sfff(f0,f1,f2);
        sfff(g0,g1,g2);
        sfl(MOD);

        matrix base(6,6);
        base.mat[0][0]=a1;
        base.mat[0][1]=b1;
        base.mat[0][5]=c1;
        base.mat[1][0]=1;
        base.mat[2][1]=1;
        base.mat[3][2]=c2;
        base.mat[3][3]=a2;
        base.mat[3][4]=b2;
        base.mat[4][3]=1;
        base.mat[5][4]=1;

        matrix temp(6,1);
        temp.mat[0][0]=f2%MOD;
        temp.mat[1][0]=f1%MOD;
        temp.mat[2][0]=f0%MOD;
        temp.mat[3][0]=g2%MOD;
        temp.mat[4][0]=g1%MOD;
        temp.mat[5][0]=g0%MOD;

        int q;
        sf(q);
        PRINT_CASE;
        while(q--)
        {
            int n;
            sf(n);
            ll ans1,ans2;
            if(n<=2)
            {
                ans1=temp.mat[2-n][0];
                ans2=temp.mat[5-n][0];
            }
            else
            {
                matrix power=base.pow(n-2);
                power = power*temp;
                ans1=power.mat[0][0];
                ans2=power.mat[3][0];
            }
            printf("%lld %lld\n",ans1,ans2);
        }


    }

    return 0;
}

Light OJ: 1096 – nth Term

0

Problem Link : http://lightoj.com:81/volume/problem/1096


#include <bits/stdc++.h>

#define pii              pair <int,int>
#define pll              pair <long long,long long>
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cout<<#x " = "<<(x)<<endl
#define VI               vector <int>
#define DBG              pf("Hi\n")
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#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 stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i<n;i++)
#define loop1(i,n)       for(int i=1;i<=n;i++)
#define REP(i,a,b)       for(int i=a;i<b;i++)
#define RREP(i,a,b)      for(int i=a;i>=b;i--)
#define TEST_CASE(t)     for(int z=1;z<=t;z++)
#define PRINT_CASE       printf("Case %d: ",z)
#define CASE_PRINT       cout<<"Case "<<z<<": "
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1<<28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;


/*----------------------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
/*------------------------------------------------*/

/*-----------------------Bitmask------------------*/
//int Set(int N,int pos){return N=N | (1<<pos);}
//int reset(int N,int pos){return N= N & ~(1<<pos);}
//bool check(int N,int pos){return (bool)(N & (1<<pos));}
/*------------------------------------------------*/

/*----------------------Matrix-----------------------*/

// int MOD=
 ll MOD= 10007;

struct matrix
{
    ll mat[5][5];
    int row,col;

    matrix()
    {
        memset(mat,0,sizeof mat);
    }
    matrix(int a, int b)
    {
        row=a,col=b;
        memset(mat,0,sizeof mat);
    }

    matrix operator*(const matrix &p) const
    {
        assert(col == p.row);
        matrix temp;
        temp.row = row;
        temp.col = p.col;
        for (int i = 0; i < temp.row; i++)
        {
            for (int j = 0; j < temp.col; j++)
            {
                ll sum = 0;
                for (int k = 0; k <col;  k++)
                {
                    sum += ((mat[i][k]%MOD) * (p.mat[k][j]%MOD))%MOD;
                    sum%=MOD;
                }
                temp.mat[i][j] = sum;
            }
        }
        return temp;
    }
    matrix operator+ (const matrix &p) const
    {
        assert(row==p.row && col==p.col);
        matrix temp;
        temp.row=row;
        temp.col=col;
        for(int i=0;i<temp.row;i++)
        {
            for(int j=0;j<temp.col;j++)
                temp.mat[i][j]=((mat[i][j]%MOD)+(p.mat[i][j]%MOD))%MOD;;
        }
        return temp;
    }

    matrix identity()
    {
        matrix temp;
        temp.row=row;
        temp.col=col;
        for(int i=0;i<row;i++)
            temp.mat[i][i]=1;
        return temp;
    }

    matrix pow(ll pow)
    {
        matrix temp=(*this);
        matrix ret=(*this).identity();
        while(pow)
        {
            if(pow % 2==1)
                ret=ret*temp;
            temp=temp*temp;
            pow/=2;
        }
        return ret;
    }

    void show()
    {
        printf("-----------------------------\n");
        for(int i=0;i<row;i++)
        {
            for(int j=0;j<col;j++)
                printf("%lld ",mat[i][j]);
            printf("\n");
        }
        printf("-----------------------------\n");
    }

};

/*--------------------------Matrix End---------------------*/

int main()
{

    ///freopen("in.txt","r",stdin);
    ///freopen("out.txt","w",stdout);

    int t;
    sf(t);
    TEST_CASE(t)
    {
        int n,a,b,c;
        sfff(n,a,b);
        sf(c);
        matrix base(4,4);
        base.mat[0][0]=a;
        base.mat[0][2]=b;
        base.mat[0][3]=1;
        base.mat[1][0]=1;
        base.mat[2][1]=1;
        base.mat[3][3]=1;

        base=base.pow(n-2);

        matrix temp(4,1);
        temp.mat[3][0]=c;
        base=base*temp;
        PRINT_CASE;
        ll ans=base.mat[0][0];
        if(n<=2)
            ans=0;
        pf("%lld\n",ans);

    }

    return 0;
}

Light OJ: 1065 – Number Sequence

0

Problem Link : http://lightoj.com:81/volume/problem/1065


#include <bits/stdc++.h>

#define pii              pair <int,int>
#define pll              pair <long long,long long>
#define sc               scanf
#define pf               printf
#define Pi               2*acos(0.0)
#define ms(a,b)          memset(a, b, sizeof(a))
#define pb(a)            push_back(a)
#define MP               make_pair
#define db               double
#define ll               long long
#define EPS              10E-10
#define ff               first
#define ss               second
#define sqr(x)           (x)*(x)
#define D(x)             cout<<#x " = "<<(x)<<endl
#define VI               vector <int>
#define DBG              pf("Hi\n")
#define CIN              ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0)
#define SZ(a)            (int)a.size()
#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 stlloop(v)       for(__typeof(v.begin()) it=v.begin();it!=v.end();it++)
#define loop(i,n)        for(int i=0;i<n;i++)
#define loop1(i,n)       for(int i=1;i<=n;i++)
#define REP(i,a,b)       for(int i=a;i<b;i++)
#define RREP(i,a,b)      for(int i=a;i>=b;i--)
#define TEST_CASE(t)     for(int z=1;z<=t;z++)
#define PRINT_CASE       printf("Case %d: ",z)
#define CASE_PRINT       cout<<"Case "<<z<<": "
#define all(a)           a.begin(),a.end()
#define intlim           2147483648
#define infinity         (1<<28)
#define ull              unsigned long long
#define gcd(a, b)        __gcd(a, b)
#define lcm(a, b)        ((a)*((b)/gcd(a,b)))

using namespace std;


/*----------------------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
/*------------------------------------------------*/

/*-----------------------Bitmask------------------*/
//int Set(int N,int pos){return N=N | (1<<pos);}
//int reset(int N,int pos){return N= N & ~(1<<pos);}
//bool check(int N,int pos){return (bool)(N & (1<<pos));}
/*------------------------------------------------*/

/*----------------------Matrix-----------------------*/
int MOD;
struct matrix
{
    ll mat[2][2];
    int row,col;

    matrix()
    {
        memset(mat,0,sizeof mat);
    }
    matrix(int a, int b)
    {
        row=a,col=b;
        memset(mat,0,sizeof mat);
    }

    matrix operator*(const matrix &p) const
    {
        assert(col == p.row);
        matrix temp;
        temp.row = row;
        temp.col = p.col;
        for (int i = 0; i < temp.row; i++)
        {
            for (int j = 0; j < temp.col; j++)
            {
                ll sum = 0;
                for (int k = 0; k <col;  k++)
                {
                    sum += ((mat[i][k]%MOD) * (p.mat[k][j]%MOD))%MOD;
                    sum%=MOD;
                }
                temp.mat[i][j] = sum;
            }
        }
        return temp;
    }
    matrix operator+ (const matrix &p) const
    {
        assert(row==p.row && col==p.col);
        matrix temp;
        temp.row=row;
        temp.col=col;
        for(int i=0;i<temp.row;i++)
        {
            for(int j=0;j<temp.col;j++)
                temp.mat[i][j]=((mat[i][j]%MOD)+(p.mat[i][j]%MOD))%MOD;;
        }
        return temp;
    }

    matrix identity()
    {
        matrix temp;
        temp.row=row;
        temp.col=col;
        for(int i=0;i<row;i++)
            temp.mat[i][i]=1;
        return temp;
    }

    matrix pow(ll pow)
    {
        matrix temp=(*this);
        matrix ret=(*this).identity();
        while(pow)
        {
            if(pow % 2==1)
                ret=ret*temp;
            temp=temp*temp;
            pow/=2;
        }
        return ret;
    }

    void show()
    {
        printf("-----------------------------\n");
        for(int i=0;i<row;i++)
        {
            for(int j=0;j<col;j++)
                printf("%lld ",mat[i][j]);
            printf("\n");
        }
        printf("-----------------------------\n");
    }

};

/*--------------------------Matrix End---------------------*/


int main()
{

//    freopen("in.txt","r",stdin);
    ///freopen("out.txt","w",stdout);

    int t;
    sf(t);
    TEST_CASE(t)
    {
        int a,b,n,m;
        sfff(a,b,n);
        sf(m);

        MOD=pow(10*1.0,m);

        matrix base(2,2);
        base.mat[0][0]=base.mat[0][1]=base.mat[1][0]=1;
        base=base.pow(n-1);
        matrix temp(2,1);
        temp.mat[0][0]=b,temp.mat[1][0]=a;
        temp=base*temp;
        ll ans=temp.mat[0][0];
        if(n==0)
            ans=a%MOD;
        else if(n==1)
            ans=b%MOD;
//        PRINT_CASE;
        printf("%lld\n",ans);
    }

    return 0;
}