查找素数环,题目不难,按照递归的方法解决,每次递归地填充一个位置,在判断能用哪个数填充的时候首先判断该数是否使用过了,再判断该数与上一个已经填充的数的和是否为素数,同时,在每次全部填充结束后要判断最后一个数是否与1(也就是第一个位置的数)之和为素数。具体实现见下面的源代码:
#include<iostream>
#include<vector>
#include<string>
#include<set>
#include<stack>
#include<queue>
#include<map>
#include<algorithm>
#include<cmath>
#include<iomanip>
#include<cstring>
#include<sstream>
#include<cstdio>
#include<deque>
using namespace std;
int n;
bool isPrime(int data){
for (int i = 2; i*i <= data; i++){
if (data%i == 0) return false;
}
return true;
}
void putElem(vector<int>& arr,int cur){
if (cur == arr.size()){
if (!isPrime(arr[0]+arr[arr.size()-1])) return;
for (int i = 0; i < arr.size();i++){
cout << arr[i];
if (i != arr.size()-1) cout << " ";
}
cout <<endl;
return;
}
for (int elem = 2; elem <= n; elem++){
bool exist = true;
for (int i = 0; i < cur; i++){
if (arr[i] == elem){
exist = false;
break;
}
}
if (exist&&!isPrime(arr[cur-1]+elem)) exist = false;
if (exist){
arr[cur] = elem;
putElem(arr,cur+1);
}
}
}
int main(){
int Case = 0;
while (cin >> n){
if (Case) cout << endl;
Case++;
vector<int> arr(n);
arr[0] = 1;
cout << "Case " << Case << ":\n";
putElem(arr, 1);
}
return 0;
}