POJ 3243 Clever Y BSGS

Clever Y

Time Limit: 5000MS Memory Limit: 65536KTotal Submissions: 6861 Accepted: 1676

Description

Little Y finds there is a very interesting formula in mathematics:

X^Y mod Z = K

Given X, Y, Z, we all know how to figure out K fast. However, given X, Z, K, could you figure out Y fast?

Input

Input data consists of no more than 20 test cases. For each test case, there would be only one line containing 3 integers X, Z, K (0 ≤ X, Z, K ≤ 10⁹). 
Input file ends with 3 zeros separated by spaces. 

Output

For each test case output one line. Write "No Solution" (without quotes) if you cannot find a feasible Y (0 ≤ Y < Z). Otherwise output the minimum Y you find.

Sample Input

5 58 332 4 30 0 0

Sample Output

9No Solution

Source

POJ Monthly--2007.07.08, Guo, Huayang

/* ***********************************************Author        :CKbossCreated Time  :2015年03月31日 星期二 20时02分38秒File Name     :POJ3243.cpp************************************************ */#include <iostream>#include <cstdio>#include <cstring>#include <algorithm>#include <string>#include <cmath>#include <cstdlib>#include <vector>#include <queue>#include <set>#include <map>using namespace std;typedef long long int LL;const int MOD=76543;int hs[MOD],head[MOD],next[MOD],id[MOD],top;void insert(int x,int y){int k=x%MOD;hs[top]=x; id[top]=y;next[top]=head[k]; head[k]=top++;}int find(int x){int k=x%MOD;for(int i=head[k];~i;i=next[i])if(hs[i]==x) return id[i];return -1;}int BSGS(int a,int b,int n){memset(head,-1,sizeof(head));top=1;if(b==1) return 0;int m=sqrt(n*1.0),j;LL x=1,p=1;for(int i=0;i<m;i++,p=p*a%n) insert(p*b%n,i);for(LL i=m;;i+=m){if((j=find(x=x*p%n))!=-1) return i-j;if(i>n) break;}return -1;}int main(){    //freopen("in.txt","r",stdin);    //freopen("out.txt","w",stdout);int a,b,n;while(scanf("%d%d%d",&a,&n,&b)!=EOF){if(a==0&&b==0&&n==0) break;int ans=BSGS(a,b,n);if(ans==-1) puts("No Solution");else printf("%d\n",ans);}        return 0;}