Clever Y
| Time Limit: 5000MS | Memory Limit: 65536K | |
| Total Submissions: 5744 | Accepted: 1376 |
Description
Little Y finds there is a very interesting formula in mathematics:
XY 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.
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 33 2 4 3 0 0 0
Sample Output
9 No Solution
这题数据不强。第二种类型，C是任意的非负整数。
这个时候要用到的，不断地缩小，直到互质。代码...可以当一个模板用。 详细的报告：http://blog.csdn.net/tsaid/article/details/7354716
1 #include<iostream> 2 #include<cstdio> 3 #include<cstdlib> 4 #include<cstring> 5 #include<cmath> 6 using namespace std; 7 const int MAX=499991; 8 typedef __int64 LL; 9 LL A,B,C; 10 bool Hash[MAX]; 11 LL val[MAX]; 12 LL idx[MAX]; 13 14 LL gcd(LL a,LL b) 15 { 16 if(b==0) 17 return a; 18 return gcd(b,a%b); 19 } 20 21 void Ex_gcd(LL a,LL b,LL &x,LL &y) 22 { 23 if(b==0) 24 { 25 x=1; 26 y=0; 27 return ; 28 } 29 Ex_gcd(b,a%b,x,y); 30 LL hxl=x-a/b*y; 31 x=y; 32 y=hxl; 33 return ; 34 } 35 36 void Insert(LL id,LL num)//哈希建立 37 { 38 LL k=num%MAX; 39 while(Hash[k] && val[k]!=num) 40 { 41 k++; if(k==MAX) k=k-MAX; 42 } 43 if(!Hash[k]) 44 { 45 Hash[k]=true; 46 val[k]=num; 47 idx[k]=id; 48 } 49 return; 50 } 51 52 LL found(LL num)//哈希查询 53 { 54 LL k=num%MAX; 55 while(Hash[k] && val[k]!=num) 56 { 57 k++; 58 if(k==MAX) k=k-MAX; 59 } 60 if(Hash[k]) 61 { 62 return idx[k]; 63 } 64 return -1; 65 } 66 67 LL baby_step(LL a,LL b,LL c) 68 { 69 LL temp=1; 70 for(LL i=0;i<=100;i++) 71 { 72 if(temp==b%c) return i; 73 temp=(temp*a)%c; 74 } 75 LL tmp,D=1,count=0; 76 memset(Hash,false,sizeof(Hash)); 77 memset(val,-1,sizeof(val)); 78 memset(idx,-1,sizeof(idx)); 79 80 while( (tmp=gcd(a,c))!=1 ) 81 { 82 if(b%tmp) return -1; 83 c=c/tmp; 84 b=b/tmp; 85 D=D*a/tmp%c; 86 count++; 87 } 88 LL cur=1; 89 LL M=ceil(sqrt(c*1.0)); 90 for(LL i=1;i<=M;i++) 91 { 92 cur=cur*a%c; 93 Insert(i,cur); 94 } 95 LL x,y; 96 for(LL i=0;i<M;i++) 97 { 98 Ex_gcd(D,c,x,y); 99 x=x*b%c; 100 x=(x%c+c)%c; 101 LL k=found(x); 102 if(k!=-1) 103 { 104 return i*M+k+count; 105 } 106 D=D*cur%c; 107 } 108 return -1; 109 110 } 111 112 int main() 113 { 114 while(scanf("%I64d%I64d%I64d",&A,&C,&B)>0) 115 { 116 if(A==0&&B==0&&C==0)break; 117 LL cur=baby_step(A,B,C); 118 if(cur==-1) 119 { 120 printf("No Solution "); 121 } 122 else printf("%I64d ",cur); 123 } 124 return 0; 125 }