hdoj 4686 Arc of Dream（矩阵快速幂）

一个不难构造的矩阵快速幂，自己硬是找了两天才找到自己错在细节上的东西。

自己犯得错：

1.指数是long long，自己却传了个int

2.构造单位矩阵前，只是把对角线赋值为1，却忘了memset其他值都为0

希望以后别因为这些小错，耽误那么多的时间！

代码:

#include<bits/stdc++.h>using namespace std;typedef long long ll;const ll mod = 1e9+7;ll a0, ax, ay, b0, bx, by;struct node{    ll s[5][5];    void init()    {        memset(s, 0, sizeof(s));        s[0][0] = s[0][1] = s[4][4] = 1;        s[1][1] = (ax*bx)%mod; s[1][2] = (ax*by)%mod;        s[1][3] =(ay*bx)%mod; s[1][4] = (ay*by)%mod;        s[2][2] = ax%mod; s[2][4] = ay%mod;        s[3][3] = bx%mod; s[3][4] = by%mod;    }};node mul(node a, node b){    node t;    memset(t.s, 0, sizeof(t.s));    for(int i = 0; i < 5; i++)        for(int j = 0; j < 5; j++)            for(int k = 0; k < 5; k++)                t.s[i][j] = (t.s[i][j]+a.s[i][k]*b.s[k][j]%mod)%mod;    return t;}node mt_pow(node p, ll n){    node q;    memset(q.s, 0, sizeof(q.s));    for(int i = 0; i < 5; i++)        q.s[i][i] = 1;    while(n)    {        if(n&1) q = mul(p, q);        p = mul(p, p);        n /= 2;    }    return q;}int main(void){    ll n;    while(~scanf("%lld%lld%lld%lld%lld%lld%lld", &n, &a0, &ax, &ay, &b0, &bx, &by))    {        if(n == 0) { puts("0"); }        else        {            node base;            base.init();            node ans = mt_pow(base, n);            ll p[5] = {0, a0*b0%mod, a0%mod, b0%mod, 1}, res = 0;            for(int i = 0; i < 5; i++)                res = (res + ans.s[0][i]*p[i]%mod)%mod;            printf("%lld\n", res);        }    }    return 0;}

Arc of Dream

Time Limit: 2000/2000 MS (Java/Others)    Memory Limit: 65535/65535 K (Java/Others)
Total Submission(s): 4174    Accepted Submission(s): 1301

Problem Description

An Arc of Dream is a curve defined by following function:

where
a₀ = A0
a_i = a_i-1*AX+AY
b₀ = B0
b_i = b_i-1*BX+BY
What is the value of AoD(N) modulo 1,000,000,007?

 

Input

There 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 BY
N is no more than 10¹⁸, and all the other integers are no more than 2×10⁹.

 

Output

For each test case, 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

 

Author

Zejun Wu (watashi)

 

Source

2013 Multi-University Training Contest 9