[搜索]USACO-1.5-Prime Palindromes

最新推荐文章于 2025-08-13 19:36:32 发布

AimCorder

最新推荐文章于 2025-08-13 19:36:32 发布

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文章标签： c/c++

本文介绍了一种高效找出指定范围内所有回文素数的方法。通过深度优先搜索预先生成回文数，并利用二分查找确定范围边界，最后验证并输出该区间内的所有回文素数。

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Prime Palindromes

The number 151 is a prime palindrome because it is both a prime number and a palindrome (it is the same number when read forward as backward). Write a program that finds all prime palindromes in the range of two supplied numbers a and b (5 <= a < b <= 100,000,000); both a and b are considered to be within the range .

PROGRAM NAME: pprime

INPUT FORMAT

Line 1:

Two integers, a and b

SAMPLE INPUT (file pprime.in)

5 500

OUTPUT FORMAT

The list of palindromic primes in numerical order, one per line.

SAMPLE OUTPUT (file pprime.out)

1 101

151

131 181

353

191 313 373

383

给定一个范围，输出在这个范围内（包含边界）的所有回文素数. 注意以后有回文数的情况，尽量先用DFS生成回文数表，然后在做处理，不要去枚举产生回文数. 这里打出回文数表以后先排序，然后二分查出上下界，把该范围中的所有素数输出即可。

代码：

/*
ID:yfr_1992
PROG:pprime
LANG:C++
*/
#include<iostream>
#include<cstdio>
#include<cstring>
#include<vector>
#include<cstdlib>
#include<algorithm>
#include<cmath>
using namespace std;
vector<int> plist;
int temp[10],sz;
void dfs(int cur,int limit){
    if(cur>((limit-1)>>1)){
        int sum = 0;
        for(int i=0;i<limit;i++)sum = sum*10 + temp[i];
        plist.push_back(sum);
        return;
    }
    for(int i=0;i<10;i++){
        temp[cur] = i,temp[limit-1-cur] = i;
        dfs(cur+1,limit);
    }
}
bool isPrime(int x){
    for(int i=2;i<=(int)sqrt(x)+1;i++){
        if((x%i)==0)return false;
    }
    return true;
}
int bs_lower(int x){
    int l = 0, r = sz-1 , m ;
    while(l<=r){
        m = (l+r)>>1;
        if(plist[m]>=x)r = m-1;
        else l = m+1;
    }
    return l;
}
int bs_upper(int x){
    int l = 0, r = sz-1 , m ;
    while(l<=r){
        m = (l+r)>>1;
        if(plist[m]>x)r = m-1;
        else l = m+1;
    }
    return r;
}
int main(){
    freopen("pprime.in","r",stdin);
    freopen("pprime.out","w",stdout);
    for(int i=1;i<=8;i++)dfs(0,i);
    sort(plist.begin(),plist.end());
    sz = 1;
    for(int i=1;i<(int)plist.size();i++){
        if(plist[i]!=plist[i-1])plist[sz++] = plist[i];
    }
    int a,b;
    scanf("%d%d",&a,&b);
    int s = bs_lower(a), e = bs_upper(b);
    for(int i=s;i<=e;i++){
        if(isPrime(plist[i]))printf("%d\n",plist[i]);
    }
    return 0;
}