USACO section 1.5 Superprime Rib（深搜）

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本文深入探讨了技术领域的超级质数与超质数肋骨的概念，通过递归搜索算法构建长度为n的超质数肋骨，并详细解释了算法背后的数学原理与实现细节。

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Superprime Rib

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)

OUTPUT FORMAT

The superprime ribs of length N, printed in ascending order one per line.

SAMPLE OUTPUT (file sprime.out)

/*
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 ----
8

Keep up the good work!

Thanks for your submission!

Super Prime RibRuss Cox

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);
}