UVA12169 Disgruntled Judge

嘟嘟嘟

 

枚举a, 求出b，然后代入看a和b是否是对的。

具体方法：通过x1和x3可以求出b ：

　　x2 = (a * x1 + b) % mod　　　　(1)

　　x3 = (a * x2 + b) % mod　　　　(2)

把(2)代入(1)得

　　x3 = (a2 * x1 + a * b + b) % mod

整理得

　　x3 + k * mod = a2 * x1 + b * (a + 1)

于是得到了一个只有两个参数的不定方程，用exgcd求解即可。

 1 #include<cstdio>
 2 #include<iostream>
 3 #include<algorithm>
 4 #include<cmath>
 5 #include<cstring>
 6 #include<cstdlib>
 7 #include<cctype>
 8 #include<stack>
 9 #include<queue>
10 #include<vector>
11 using namespace std;
12 #define enter puts("")
13 #define space putchar(' ')
14 #define Mem(a, x) memset(a, x, sizeof(a))
15 #define rg register
16 typedef long long ll;
17 typedef double db;
18 const int INF = 0x3f3f3f3f;
19 const db eps = 1e-8;
20 const int maxn = 1e5 + 5;
21 const int mod = 10001;
22 inline ll read()
23 {
24     ll ans = 0;
25     char ch = getchar(), las = ' ';
26     while(!isdigit(ch)) las = ch, ch = getchar();
27     while(isdigit(ch)) ans = ans * 10 + ch - '0', ch = getchar();
28     if(las == '-') ans = -ans;
29     return ans;
30 }
31 inline void write(ll x)
32 {
33     if(x < 0) putchar('-'), x = -x;
34     if(x >= 10) write(x / 10);
35     putchar(x % 10 + '0');
36 }
37 
38 int n;
39 ll f[maxn], g[maxn];
40 
41 void exgcd(ll a, ll b, ll &x, ll &y, ll &d)
42 {
43     if(!b) d = a, x = 1, y = 0;
44     else exgcd(b, a % b, y, x, d), y -= a / b * x;
45 }
46 
47 bool judge(ll a, ll b)
48 {
49     g[1] = (a * f[1] + b) % mod;
50     for(int i = 2; i <=n; ++i)
51     {
52         int tp = (a * g[i - 1] + b) % mod;
53         if(tp != f[i]) return 0;
54         g[i] = (a * tp + b) % mod;
55     }
56     return 1;
57 }
58 
59 int main()
60 {
61     n = read();
62     for(int i = 1; i <= n; ++i) f[i] = read();
63     for(int i = 1; i < mod; ++i)
64     {
65     ll x, y, a = i + 1, b = mod, d = f[2] - i * i * f[1], Gcd;
66     exgcd(a, b, x, y, Gcd);
67     if(d % Gcd) continue;
68     x = x * d / Gcd % mod;
69     if(judge(i, x))
70     {
71         for(int j = 1; j <= n; ++j) write(g[j]), enter;
72         return 0;
73     } 
74     }
75     return 0;
76 }
View Code

 

posted @ 2018-10-08 11:53  mrclr  阅读(148)  评论(0)  编辑  收藏  举报