Butchering Farmer John's cows always yields the best prime rib. You can tell prime ribs by looking at the digits lovingly stamped across them, one by one, by FJ and the USDA. Farmer John ensures that a purchaser of his prime ribs gets really prime ribs because when sliced from the right, the numbers on the ribs continue to stay prime right down to the last rib, e.g.:
7 3 3 1
The set of ribs denoted by 7331 is prime; the three ribs 733 are prime; the two ribs 73 are prime, and, of course, the last rib, 7, is prime. The number 7331 is called a superprime of length 4.
Write a program that accepts a number N 1 <=N<=8 of ribs and prints all the superprimes of that length.
The number 1 (by itself) is not a prime number.
PROGRAM NAME: sprime
INPUT FORMAT
A single line with the number N.
SAMPLE INPUT (file sprime.in)
4
OUTPUT FORMAT
The superprime ribs of length N, printed in ascending order one per line.
SAMPLE OUTPUT (file sprime.out)
2333 2339 2393 2399 2939 3119 3137 3733 3739 3793 3797 5939 7193 7331 7333 7393
/*
ID:nealgav1
PROG:sprime
LANG:C++
*/
#include<cstdio>
#include<cmath>
int m;
bool isprim(int num)//判断质数
{
if(num==2)return 1;
if(num&1)
{
int n=(int)sqrt(num);
for(int i=3;i<=n;i+=2)
if(!(num%i))
return 0;
return 1;
}
return 0;
}
void dfs(int num,int n)
{
int ans;
if(m==n)
{
printf("%d\n",num);
return;
}
for(int i=1;i<=9;i+=2)
{
ans=num*10+i;
if(isprim(ans))
dfs(ans,n+1);
}
}
int main()
{
freopen("sprime.out","w",stdout);
freopen("sprime.in","r",stdin);
scanf("%d",&m);
dfs(2,1);dfs(3,1);dfs(5,1);dfs(7,1);
}
USER: Neal Gavin Gavin [nealgav1] TASK: sprime LANG: C++ Compiling... Compile: OK Executing... Test 1: TEST OK [0.000 secs, 3344 KB] Test 2: TEST OK [0.000 secs, 3344 KB] Test 3: TEST OK [0.000 secs, 3344 KB] Test 4: TEST OK [0.000 secs, 3344 KB] Test 5: TEST OK [0.000 secs, 3344 KB] All tests OK.
Your program ('sprime') produced all correct answers! This is your submission #2 for this problem. Congratulations!
Here are the test data inputs:
------- test 1 ---- 4 ------- test 2 ---- 5 ------- test 3 ---- 6 ------- test 4 ---- 7 ------- test 5 ---- 8Keep up the good work!
Thanks for your submission!
We use a recursive search to build superprimes of length n from superprimes of length n-1 by adding a 1, 3, 7, or 9. (Numbers ending in any other digit are divisible by 2 or 5.) Since there are so few numbers being tested, a simple primality test suffices.
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <assert.h>
FILE *fout;
int
isprime(int n)
{
int i;
if(n == 2)
return 1;
if(n%2 == 0)
return 0;
for(i=3; i*i <= n; i+=2)
if(n%i == 0)
return 0;
return 1;
}
/* print all sprimes possible by adding ndigit digits to the number n */
void
sprime(int n, int ndigit)
{
if(ndigit == 0) {
fprintf(fout, "%d\n", n);
return;
}
n *= 10;
if(isprime(n+1))
sprime(n+1, ndigit-1);
if(isprime(n+3))
sprime(n+3, ndigit-1);
if(isprime(n+7))
sprime(n+7, ndigit-1);
if(isprime(n+9))
sprime(n+9, ndigit-1);
}
void
main(void)
{
int n;
FILE *fin;
fin = fopen("sprime.in", "r");
assert(fin != NULL);
fout = fopen("sprime.out", "w");
assert(fout != NULL);
fscanf(fin, "%d", &n);
sprime(2, n-1);
sprime(3, n-1);
sprime(5, n-1);
sprime(7, n-1);
exit (0);
}
