有趣的数学题

http://csustacm.com:4803/problem/1106

 

 1 #include<bits/stdc++.h>
 2 using namespace std;
 3 #define lson l,mid,rt<<1
 4 #define rson mid+1,r,rt<<1|1
 5 #define IT set<ll>::iterator
 6 #define pb push_back
 7 #define eb emplace_back
 8 #define maxn 200005
 9 #define eps 1e-6
10 #define PI acos(-1.0)
11 #define rep(k,i,j) for(int k=i;k<j;k++)
12 typedef long long ll;
13 typedef pair<int,int> pii;
14 typedef pair<ll,ll>pll;
15 typedef pair<ll,int> pli;
16 typedef pair<pair<int,string>,pii> ppp;
17 typedef unsigned long long ull;
18 const long long MOD=1000000007;
19 const double oula=0.57721566490153286060651209;
20 using namespace std;
21 
22 inline char nc()
23 {
24     static char buf[10000000], *p1 = buf, *p2 = buf;
25     return p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 10000000, stdin), p1 == p2) ? EOF : *p1++;
26 }
27 inline int read()
28 {
29     int res = 0;
30     char ch;
31     do ch = nc(); while (ch < 48 || ch > 57);
32     do res = res * 10 + ch - 48, ch = nc(); while (ch >= 48 && ch <= 57);
33     return res;
34 }
35 
36 typedef vector<ll> vec;
37 typedef vector<vec> mat;
38 
39 mat mul(mat &a,mat &b,ll mod){
40     mat c(a.size(),vec(b[0].size()));
41     for(int i=0;i<a.size();i++){
42         for(int k=0;k<b.size();k++){
43             if(a[i][k]){
44                 for(int j=0;j<b[0].size();j++){
45                     c[i][j]=(c[i][j]+a[i][k]*b[k][j]%mod+mod)%mod;
46                 }
47             }
48         }
49     }
50     return c;
51 }
52 
53 mat ksm(mat a,ll n,ll mod){
54     mat b(a.size(),vec(a.size()));
55     b[0][0]=2;
56     b[1][0]=b[2][0]=1;
57     while(n){
58         if(n&1){
59             b=mul(a,b,mod);
60         }
61         a=mul(a,a,mod);
62         n>>=1;
63     }
64     return b;
65 }
66 
67 int main(){
68     std::ios::sync_with_stdio(false);
69     ll n,m,x,y;
70     cin>>n>>m>>x>>y;
71     ll gcd=__gcd(n+m,x+y);
72     if(gcd==1||gcd==2) cout<<1<<endl;
73     else{
74         mat a(3,vec(3));
75         a[0][0]=a[0][1]=a[1][0]=a[2][1]=1;
76         mat ans=ksm(a,gcd-3,1e9+7);
77         cout<<ans[0][0]<<endl;
78     }
79 }
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posted on 2019-04-16 16:45  Fighting_sh  阅读(234)  评论(0)  编辑  收藏  举报

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