HDU 2815 扩展baby step giant step 算法

题目大意就是求 a^x = b(mod c) 中的x

用一般的baby step giant step 算法会超时

这里参考的是http://hi.baidu.com/aekdycoin/item/236937318413c680c2cf29d4

map平衡树查找值

 1 #include <cstdio>
 2 #include <cstring>
 3 #include <iostream>
 4 #include <cmath>
 5 #include <map>
 6 using namespace std;
 7 #define ll long long
 8 
 9 int q_pow(int a , int b , int mod)
10 {
11     ll ans = 1;
12     while(b)
13     {
14         if(b&1) ans =((ll)ans*a)%mod;
15         a = ((ll)a*a)%mod;
16         b>>=1;
17     }
18     return ans;
19 }
20 
21 int gcd(int a , int b)
22 {
23     if(b == 0)return a;
24     else return gcd(b,a%b);
25 }
26 
27 int ex_gcd(int a , int &x , int b , int &y)
28 {
29     if(b == 0){
30         x=1 , y=0;
31         return a;
32     }
33     int ans = ex_gcd(b , x , a%b , y);
34     int t = x;
35     x=y , y = t-a/b*y;
36     return ans;
37 }
38 
39 int inv(int a , int b , int mod)
40 {
41     int x , y , d;
42     d = ex_gcd(a , x , mod , y);
43     int e = (ll)x*b%mod;
44     return e<0?e+mod:e;
45 }
46 
47 int BabyStep(int A,int B,int C){
48     map<int,int> Hash;
49     ll buf=1%C,D=buf,K;
50     int i,d=0,tmp;
51     for(i=0;i<=100;buf=buf*A%C,++i)
52         if(buf==B) return i;
53     while((tmp=gcd(A,C))!=1)
54     {
55         if(B%tmp)return -1;
56         ++d;
57         C/=tmp;
58         B/=tmp;
59         D=D*A/tmp%C;
60     }
61     Hash.clear();
62     int M=(int)ceil(sqrt((double)C));
63     for(buf=1%C,i=0;i<=M;buf=buf*A%C,++i)
64         if(!Hash.count((int)buf))Hash[(int)buf]=i;
65     for(i=0,K=q_pow((ll)A,M,C);i<=M;D=D*K%C,++i)
66     {
67         tmp=inv(D,B,C);
68         if(tmp>=0&&Hash.count(tmp))return i*M+Hash[tmp]+d;
69     }
70     return -1;
71 }
72 int main()
73 {
74    // freopen("a.in" ,"r" , stdin);
75     int k , p , n;
76     while(scanf("%d%d%d" , &k , &p , &n) == 3)
77     {
78         if(n>=p){
79             puts("Orz,I can’t find D!");
80             continue;
81         }
82         int ans = BabyStep(k , n , p);
83         if(ans == -1) puts("Orz,I can’t find D!");
84         else printf("%d\n" , ans);
85     }
86     return 0;
87 }

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