【HDU2815】【拓展BSGS】Mod Tree

Problem Description

  The picture indicates a tree, every node has 2 children.
  The depth of the nodes whose color is blue is 3; the depth of the node whose color is pink is 0.
  Now out problem is so easy, give you a tree that every nodes have K children, you are expected to calculate the minimize depth D so that the number of nodes whose depth is D equals to N after mod P.

 

 

Input

The input consists of several test cases.
Every cases have only three integers indicating K, P, N. (1<=K, P, N<=10^9)

 

 

Output

The minimize D.
If you can’t find such D, just output “Orz,I can’t find D!”

 

 

Sample Input

3 78992 453 4 1314520 65536 5 1234 67

 

 

Sample Output

Orz,I can’t find D! 8 20

 

Author

AekdyCoin

 

Source

HDU 1st “Old-Vegetable-Birds Cup” Programming Open Contest

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【分析】

普通的BSGS是只能够解决A^x = B(mod C),其中C为素数的形式，而通过网上的消元的方法能够解决这种问题。

同样BSGS直接解决C为素数的形式也是可以的.

 1 /*

 2 宋代晏几道

 3 《生查子·狂花顷刻香》

 4 狂花顷刻香，晚蝶缠绵意。天与短因缘，聚散常容易。

 5 传唱入离声，恼乱双蛾翠。游子不堪闻，正是衷肠事。 

 6 */ 

 7 #include <iostream>

 8 #include <cstdio>

 9 #include <ctime>

10 #include <cmath>

11 #include <algorithm>

12 #include <cstring>

13 #include <string>

14 #include <map>

15 #include <set>

16 #include <vector> 

17 #define LOCAL

18 const int MAXN = 1000 + 10;

19 const int INF = 0x7fffffff;

20 using namespace std;

21 typedef long long LL;

22 

23 int gcd(int a, int b ){return b == 0 ? a : gcd(b, a % b);}

24 int ext_gcd(int a, int b, int &x, int &y){

25     if (b == 0) {x = 1; y = 0; return a;}

26     int tmp = ext_gcd(b, a % b, y, x);

27     y -= x * (a / b);

28     return tmp;

29 }

30 //求解 

31 int Inval(int a, int  b, int n){

32     int x, y, e;

33     ext_gcd(a, n, x, y);

34     e = (LL) x * b % n;//小心超出int 的范围,因为a,n是互质的，因此求解出来的结果就是ax + ny = 1，乘以b才正确的答案 

35     return e < 0 ? e + n : e; 

36 }

37 // k s m

38 int pow_mod(LL a, int b, int c){

39     if (b == 1) return a % c;

40     LL tmp = pow_mod(a, b / 2, c);

41     if (b % 2 == 0) return (tmp * tmp) % c;

42     else return (((tmp * tmp) % c) * a) % c;

43 }

44 int BSGS(int A, int B, int C){

45     map<int, int> H;//hash

46     LL buf = 1 % C, D = buf, K;

47     int d = 0, tmp;

48     //小步

49     for (int i = 0; i <= 100; buf = buf * A % C, i++)

50     if (buf == B) return i;

51     //消因子 

52     while ((tmp = gcd(A, C)) != 1){

53           if (B % gcd(A, C) != 0) return -1;//为了解不定方程

54           d++;

55           C /= tmp;

56           B /= tmp;

57           D = D * A / tmp % C; 

58     }

59     H.clear();

60     int M = (int)ceil(sqrt(C * 1.0));

61     buf = 1 % C; 

62     for (int i = 0; i <= M; buf = buf * A % C, i++)

63     if (H.find((int)buf) == H.end()) H[(int)buf] = i;//Hash

64     

65     K = pow_mod ((LL) A, M, C);

66     for (int i = 0; i <= M; D = D * K % C, i++){

67         tmp = Inval((int) D ,B, C);//D和C是互质的 

68         //一定不要忘了最后的d 

69         if (tmp >= 0 && H.find(tmp) != H.end()) return i * M + H[tmp] + d;

70     } 

71     return -1;//找不到 

72 } 

73 int main(){

74     

75     //转换为A^x = B(mod C)的形式 

76     int A, B, C;

77     while (scanf("%d%d%d", &A, &C, &B) != EOF){

78           if (B >= C) {printf("Orz,I can’t find D!\n"); continue;}//233

79           int tmp = BSGS(A, B, C);

80           if (tmp < 0) printf("Orz,I can’t find D!\n");

81           else printf("%d\n", tmp);

82     }

83     return 0;

84 }

85 

86  

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