Codeforces Round #315 (Div. 2) C. Primes or Palindromes? 暴力
3 seconds
256 megabytes
standard input
standard output
Rikhail Mubinchik believes that the current definition of prime numbers is obsolete as they are too complex and unpredictable.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 n, rub(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).
The input consists of two positive integers p, q, the numerator and denominator of the fraction that is the value of A (,
).
If such maximum number exists, then print it. Otherwise, print "Palindromic tree is better than splay tree" (without the quotes).
1 1
40
1 42
1
6 4
172
题意:不大于n的素数的个数<=A*不大于n的回文数的个数;求最大的n
思路:暴力;
#include<bits/stdc++.h>
using namespace std;
int a[];
int check(int x)
{
int ji=;
while(x)
{
a[ji++]=x%;
x/=;
}
for(int i=;i<ji/;i++)
{
if(a[i]!=a[ji--i])
return ;
}
return ;
}
int prime(int n)
{
if(n<=)
return ;
if(n==)
return ;
if(n%==)
return ;
int k, upperBound=n/;
for(k=; k<=upperBound; k+=)
{
upperBound=n/k;
if(n%k==)
return ;
}
return ;
}
#define ll __int64
const int N=2e6+;
ll p[N],h[N];
int main()
{
for(ll i=;i<=;i++)
{
p[i]=p[i-];
h[i]=h[i-];
if(prime(i))
p[i]++;
if(check(i))
h[i]++;
}
ll u,v;
scanf("%I64d%I64d",&u,&v);
for(int i=;i>;i--)
if(v*p[i]<=u*h[i])
{
printf("%d\n",i);
return ;
}
printf("Palindromic tree is better than splay tree\n");
return ;
}
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