HDU 4686 arc of Dream (recursive matrix acceleration)

This is to give you a formula that is multiplied by two Recursive formulas, so that you can obtain the result of nth.

Note that this recursive operation requires the formula to be multiplied and then the matrix is constructed.

Arc of dream Time Limit: 2000/2000 MS (Java/others) memory limit: 65535/65535 K (Java/Others)
Total submission (s): 2092 accepted submission (s): 664


Problem descriptionan arc of dream is a curve defined by following function:

Where
A0 = A0
Ai = ai-1 * AX + AY
B0 = b0
Bi = bi-1 * bx +
What is the value of AOD (n) modulo 1,000,000,007?
Inputthere are multiple test cases. process to the end of file.
Each test case contains 7 nonnegative integers as follows:
N
A0 ax ay
B0 BX
N is no more than 1018, and all the other integers are no more than 2 × 109.
Outputfor each test case and output AOD (n) modulo 1,000,000,007.
Sample Input

11 2 34 5 621 2 34 5 631 2 34 5 6

Sample output

41341902

#include <algorithm>#include <iostream>#include <stdlib.h>#include <string.h>#include <iomanip>#include <stdio.h>#include <string>#include <queue>#include <cmath>#include <stack>#include <map>#include <set>#define eps 1e-10///#define M 1000100#define LL __int64///#define LL long long///#define INF 0x7ffffff#define INF 0x3f3f3f3f#define PI 3.1415926535898#define zero(x) ((fabs(x)<eps)?0:x)#define mod 1000000007const int maxn = 210;using namespace std;struct matrix{    LL f[10][10];};matrix mul(matrix a, matrix b, int n){    matrix c;    memset(c.f, 0, sizeof(c.f));    for(int i = 0; i < n; i++)    {        for(int j = 0; j < n; j++)        {            for(int k = 0; k < n; k++) c.f[i][j] += a.f[i][k]*b.f[k][j];            c.f[i][j] %= mod;        }    }    return c;}matrix pow_mod(matrix a, LL b, int n){    matrix s;    memset(s.f, 0 , sizeof(s.f));    for(int i = 0; i < n; i++) s.f[i][i] = 1LL;    while(b)    {        if(b&1) s = mul(s, a, n);        a = mul(a, a, n);        b >>= 1;    }    return s;}matrix Add(matrix a,matrix b, int n) {    matrix c;    for(int i = 0; i < n; i++)    {        for(int j = 0; j < n; j++)        {            c.f[i][j] = a.f[i][j]+b.f[i][j];            c.f[i][j] %= mod;        }    }    return c;}int main(){    LL n;    LL a, ax, ay;    LL b, bx, by;    while(~scanf("%I64d",&n))    {        scanf("%I64d %I64d %I64d",&a, &ax, &ay);        scanf("%I64d %I64d %I64d",&b, &bx, &by);        a %= mod;        ax %= mod;        ay %= mod;        b %= mod;        bx %= mod;        by %= mod;        LL ff = a*b%mod;        LL x = (a*ax+ay)%mod;        LL y = (b*bx+by)%mod;        LL pp = (x*y)%mod;        if(n == 0)        {            puts("0");            continue;        }        matrix c;        memset(c.f, 0 ,sizeof(c.f));        c.f[0][0] = ax*bx%mod;        c.f[0][1] = ax*by%mod;        c.f[0][2] = ay*bx%mod;        c.f[0][3] = ay*by%mod;        ///c.f[0][4] = 1LL;        c.f[1][1] = ax;        c.f[1][3] = ay;        c.f[2][2] = bx;        c.f[2][3] = by;        c.f[3][3] = 1LL;        c.f[4][0] = 1LL;        c.f[4][4] = 1LL;        matrix d = pow_mod(c, n-1LL, 5);        LL sum = 0LL;        sum += ((d.f[4][0]*pp%mod)+(d.f[4][4]*ff%mod))%mod;        sum += ((d.f[4][1]*x%mod) + (d.f[4][2]*y%mod) + d.f[4][3]%mod)%mod;        printf("%I64d\n",(sum+mod)%mod);    }    return 0;}

HDU 4686 arc of Dream (recursive matrix acceleration)