【数论】Acwing1303.斐波那契数论前n项和(快速幂求斐波那契)

题目

题解

#include <iostream>
#include <cstring>

using namespace std;
typedef long long LL;
const int N = 3;
int n, m;
void mult(int c[], int a[], int b[][N])
{
    int temp[N] = {0};
    for(int i = 0; i < N; ++i)
        for(int j = 0; j < N; ++j)
            temp[i] = (temp[i] + (LL)a[j] * b[j][i]) % m;
    memcpy(c, temp, sizeof temp);
}

void mult(int c[][N], int a[][N], int b[][N])
{
    int temp[N][N] = {0};
    
    for(int i = 0; i < N; ++i)
    for(int j = 0; j < N; ++j)
    {
        for(int k = 0; k < N; ++k)
        {
            temp[i][j] = (temp[i][j] + (LL)a[i][k] * b[k][j]) % m;
        }
    }
    
    memcpy(c, temp, sizeof temp);
}

int main()
{
    cin >> n >> m;
    
    int f1[N] = {1, 1, 1};
    int A[N][N] = {{0,1,0},{1,1,1},{0,0,1}};
    
    n --;
    
    while(n)
    {
        if(n & 1) mult(f1, f1, A); //res *= a
        mult(A, A, A);
        n >>= 1;
    }
    
    cout << f1[2] << endl;
    return 0;
}