【BZOJ】【2242】【SDOI2011】计算器

快速幂/扩展欧几里得/BSGS

  经典好例题!!

  三个问题三种算法……

  算法:白书(算法竞赛入门经典——训练指南)全有……

 1 /**************************************************************
 2     Problem: 2242
 3     User: Tunix
 4     Language: C++
 5     Result: Accepted
 6     Time:1824 ms
 7     Memory:2476 kb
 8 ****************************************************************/
 9  
10 //BZOJ 2242
11 #include<map>
12 #include<cmath>
13 #include<cstdio>
14 #include<cstdlib>
15 #include<cstring>
16 #include<iostream>
17 #include<algorithm>
18 #define rep(i,n) for(int i=0;i<n;++i)
19 #define F(i,j,n) for(int i=j;i<=n;++i)
20 #define D(i,j,n) for(int i=j;i>=n;--i)
21 using namespace std;
22  
23 int getint(){
24     int v=0,sign=1; char ch=getchar();
25     while(ch<'0'||ch>'9') {if (ch=='-') sign=-1; ch=getchar();}
26     while(ch>='0'&&ch<='9') {v=v*10+ch-'0'; ch=getchar();}
27     return v*=sign;
28 }
29 /*******************tamplate********************/
30 typedef long long LL;
31 LL x,y,z,P;
32 LL pow(LL a,LL b,LL P){
33     LL r=1,base=a;
34     while(b){
35         if (b&1) r=r*base%P;
36         base=base*base%P;
37         b>>=1;
38     }
39     return r;
40 }
41 void exgcd(LL a,LL b,LL &d,LL &x,LL &y){
42     if (!b) {d=a; x=1; y=0; return;}
43     else{exgcd(b,a%b,d,y,x); y-=x*(a/b);}
44 }
45 LL log_mod(LL a,LL b,LL P){
46     LL m,v,e=1,i;
47     m=ceil(sqrt(P+0.5));//这里需要用ceil……?
48     v=pow(a,P-m-1,P);//inv
49     map<LL,LL> x;
50     x[1]=0;
51     for(int i=1;i<m;++i){
52         e=e*a%P;
53         if (!x.count(e)) x[e]=i;
54     }
55     rep(i,m){
56         if (x.count(b)) return (LL)i*m+x[b];
57         b=b*v%P;
58     }
59     return -1;
60 }
61 int main(){
62     int T=getint(),K=getint();
63     while(T--){
64         y=getint(); z=getint(); P=getint();
65         if (K==1) printf("%lld\n",pow(y,z,P));
66         if (K==2){
67             LL d=0,X=0,Y=0;
68             exgcd(y,P,d,X,Y);
69             if(z%d){ printf("Orz, I cannot find x!\n"); continue; }
70             X*=z/d;
71             LL T=X*d/P;
72             X-=T*P/d;
73             if (X<0) X+=P/d;
74             printf("%lld\n",X);
75         }
76         if (K==3){
77             y%=P; z%=P;
78             if(!y && !z) {printf("1\n"); continue;}
79             if(!y) { printf("Orz, I cannot find x!\n"); continue; }
80             LL ans=log_mod(y,z,P);
81             if (ans==-1){ printf("Orz, I cannot find x!\n"); continue; }
82             printf("%lld\n",ans);
83         }
84     }
85     return 0;
86 }
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posted @ 2015-02-05 23:51  Tunix  阅读(201)  评论(3编辑  收藏  举报