Cod sursa(job #1210375)

Utilizator daniel.amarieiDaniel Amariei daniel.amariei Data 19 iulie 2014 18:19:40
Problema Al k-lea termen Fibonacci Scor 0
Compilator cpp Status done
Runda Arhiva educationala Marime 1.54 kb
#include <fstream>
#define M 666013
using namespace std;

int k;
int Z[2][2] = {{0, 1}, {1, 1}};


ifstream ifs("kfib.in");
ofstream ofs("kfib.out");

int fib1(int k)
{
    if (k == 0) return 0;
    if (k == 1) return 1;
    return fib1(k-1) + fib1(k-2) % M;
}

int fib2(int k)
{
    if (k < 2) return k;
    
    int a = 0;
    int b = 1;
    for (int i = 2; i <= k; ++i)
    {
        int c = (a + b) % M;
        a = b;
        b = c;
    }
    
    return b;
}

void mul_matrix(int A[][2], int B[][2], int C[][2])
{
    for (int i = 0; i < 2; ++i)
    {
        for (int j = 0; j < 2; ++j)
        {
            int sum = 0;
            for (int k = 0; k < 2; ++k)
            {
                sum = (sum + 1LL * A[i][k] * B[k][j]) % M;
            }
            
            C[i][j] = sum;
        }
    }
}


void pow_matrix(int A[][2], int C[][2], int k)
{
    if (k == 1) 
    { 
        for (int i = 0; i < 2; ++i)
            for (int j = 0; j < 2; ++j)
                C[i][j] = A[i][j]; 
    } 
    else
    {
        int B[2][2];
        if (k%2 == 0)
        {
            mul_matrix(A, A, B);
            pow_matrix(B, C, k/2);
        }
        else
        {
            mul_matrix(A, A, B);

            int D[2][2];
            pow_matrix(B, D, k/2);

            mul_matrix(A, D, C);
        }
    }
}


int fib3(int k)
{
    if (k < 2) return k;

    int C[2][2];
    pow_matrix(Z, C, k-1);
    
    return C[1][1];
}

int main()
{
    ifs >> k;
    
    for(int i = 1; i < 11; ++i)
    ofs << i << " " << fib2(i) << " " << fib3(i) << endl;

    return 0;
}