A. Primes or Palindromes?
Time Limit: 20 Sec

Memory Limit: 256 MB

题目连接

http://poj.org/problem?id=3261

Description

Rikhail Mubinchik believes that the current definition of prime numbers is obsolete as they are too complex and unpredictable. A palindromic number is another matter. It is aesthetically pleasing, and it has a number of remarkable properties. Help Rikhail to convince the scientific community in this!

Let us remind you that a number is called prime if it is integer larger than one, and is not divisible by any positive integer other than itself and one.

Rikhail calls a number a palindromic if it is integer, positive, and its decimal representation without leading zeros is a palindrome, i.e. reads the same from left to right and right to left.

One problem with prime numbers is that there are too many of them. Let's introduce the following notation: π(n) — the number of primes no larger than nrub(n) — the number of palindromic numbers no larger than n. Rikhail wants to prove that there are a lot more primes than palindromic ones.

He asked you to solve the following problem: for a given value of the coefficient A find the maximum n, such that π(n) ≤ A·rub(n).

Input

The input consists of two positive integers pq, the numerator and denominator of the fraction that is the value of A ().

Output

If such maximum number exists, then print it. Otherwise, print "Palindromic tree is better than splay tree" (without the quotes).

Sample Input

1 1

Sample Output

40

HINT

题意

给你p,q,A=p/q

π(n)表示1-n中素数的个数

rub(n)表示1-n中回文数的个数

求最大的n,满足π(n) ≤ A·rub(n).

题解

CF测评姬很快,1e7直接上暴力就好了

暴力算出极限数据大概是1.5*1e6的样子,所以1e7很稳

代码:

//qscqesze
#include <cstdio>
#include <cmath>
#include <cstring>
#include <ctime>
#include <iostream>
#include <algorithm>
#include <set>
#include <vector>
#include <sstream>
#include <queue>
#include <typeinfo>
#include <fstream>
#include <map>
#include <stack>
typedef long long ll;
using namespace std;
//freopen("D.in","r",stdin);
//freopen("D.out","w",stdout);
#define sspeed ios_base::sync_with_stdio(0);cin.tie(0)
#define maxn 10050000
#define mod 10007
#define eps 1e-9
int Num;
char CH[20];
//const int inf=0x7fffffff;   //нчоч╢С
const int inf=0x3f3f3f3f;
inline ll read()
{ll x=0,f=1;char ch=getchar();while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}return x*f;
}
//**************************************************************************************
bool flag[maxn];
int primes[maxn], pi;
int pa[maxn];
void GetPrime()
{int i, j;pi = 0;memset(flag, false, sizeof(flag));for (i = 2; i < maxn; i++){primes[i]+=primes[i-1];if (!flag[i]){primes[i] ++ ;for (j = i; j < maxn; j += i)flag[j] = true;}}
}
int check_Pa(int x)
{int X=x;int x2=0;while(X){x2*=10;x2+=X%10;X/=10;}return x2==x?1:0;
}
void GetPa()
{for(int i=1;i<maxn;i++){pa[i]+=pa[i-1];if(check_Pa(i))pa[i]++;}
}
int main()
{GetPrime();GetPa();double p,q;cin>>p>>q;double A=p/q;int ans=0;for(int i=1;i<maxn;i++){if(A*pa[i]*1.0>=primes[i]*1.0)ans=i;}if(ans==0)cout<<"Palindromic tree is better than splay tree"<<endl;elsecout<<ans<<endl;
}

转载于:https://www.cnblogs.com/qscqesze/p/4719862.html

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