【九度】题目1459：Prime ring problem

题目1459：Prime ring problem

时间限制：2 秒内存限制：128 兆特殊判题：否提交：826解决：334

题目描述：

A ring is compose of n circles as shown in diagram. Put natural number 1, 2, ..., n into each circle separately, and the sum of numbers in two adjacent circles should be a prime.

Note: the number of first circle should always be 1.



输入：

n (1 < n < 17).

输出：

The output format is shown as sample below. Each row represents a series of circle numbers in the ring beginning from 1 clockwisely and anticlockwisely. The order of numbers must satisfy the above requirements. Print solutions in lexicographical order.

You are to write a program that completes above process.

Print a blank line after each case.

样例输入：

6

8

样例输出：

Case 1:

1 4 3 2 5 6

1 6 5 2 3 4

Case 2:

1 2 3 8 5 6 7 4

1 2 5 8 3 4 7 6

1 4 7 6 5 8 3 2

1 6 7 4 3 8 5 2

提示：

用printf打印输出。

【解题思路】

1、求解出17以内的所有素数。

2、针对从1开始，判断相邻的两个数是否为素数。

3、dfs求解打印结果，注意每两个case之间有一行空行。

Java AC

import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.StreamTokenizer;
import java.util.ArrayList;
import java.util.List;
 
public class Main {
    /*
     * 1459 2014年6月29日12:07:05
     */
    private static int len;
    private static List<Integer> primeList;
    public static void main(String[] args) throws Exception {
        len = 60;
        initPrimeList();
        int seq = 1;
        StreamTokenizer st = new StreamTokenizer(new BufferedReader(
                new InputStreamReader(System.in)));
        while (st.nextToken() != StreamTokenizer.TT_EOF) {
            int n = (int) st.nval;
            System.out.println("Case "+seq+":");
            int visit[] = new int[n+1];
            int array[] = new int[n+1];
            array[1] = 1;
            dfs(array, visit, 2, n);
            System.out.println();
            seq++;
        }
    }
    private static void dfs(int[] array, int[] visit, int start, int n) {
        if (start == n+1) {
            StringBuffer sb = new StringBuffer();
            if (primeList.contains(1 + array
)) {
                for (int i = 1; i < n; i++) {
                    sb.append(array[i]+" ");
                }
                sb.append(array
);
                System.out.println(sb);
            }
            return;
        }
        for (int i = 2; i < n+1; i++) {
            if (visit[i] == 0 && primeList.contains(i + array[start - 1])) {
                visit[i] = 1;
                array[start] = i;
                dfs( array, visit, start+1,n);
                visit[i] = 0;
            }
        }
    }
    private static void initPrimeList() {
        int array[] = new int[len];
        for (int i = 1; i < len; i++) {
            if (i % 2 == 0) {
                array[i] = 0;
            } else {
                array[i] = 1;
            }
        }
        array[1] = 0;
        array[2] = 1;
        for (int i = 3; i < len; i++) {
            if (array[i] == 1) {
                for (int j = 2 * i; j < len; j += i) {
                    array[j] = 0;
                }
            }
        }
        primeList = new ArrayList<Integer>();
        for (int i = 1; i < len; i++) {
            if (array[i] == 1) {
                primeList.add(i);
            }
        }
    }
}
 
/**************************************************************
    Problem: 1459
    User: wzqwsrf
    Language: Java
    Result: Accepted
    Time:1590 ms
    Memory:105052 kb
****************************************************************/

C++ AC

#include <stdio.h>
#include <string.h>
const int len = 60;
const int maxN = 20;
int array[len];
int primeArr[len];
int numArr[maxN];
int visit[maxN];
int n;
 
void initArray(){
    int i, j;
    for(i = 1; i < len; i++){
        if(i % 2 == 0){
            array[i] = 0;
        }else{
            array[i] = 1;
        }
    }
    array[1] = 0;
    array[2] = 1;
    for(i = 3; i < len; i++){
        if(array[i] == 1){
            for(j = 2 * i; j < len; j += i){
                array[j] = 0;
            }
        }
    }
    memset(primeArr, 0, sizeof(primeArr));
    int k = 0;
    for(i = 1; i < len; i++){
        if(array[i] == 1){
            primeArr[i] = 1;
        }
    }
}
 
void dfs(int start, int n){
    int i, j;
     
    if(start == n + 1){
        if(primeArr[1+numArr
] == 1){
            for(i = 1; i < n; i++){
                printf("%d ", numArr[i]);
            }
            printf("%d\n", numArr
);
        }
        return;
    }
    for(i = 2; i < n+1; i++){
        if(visit[i] == 0 && primeArr[i + numArr[start - 1]] == 1){
            visit[i] = 1;
            numArr[start] = i;
            dfs(start+1, n);
            visit[i] = 0;
        }
    }
}
 
int main(){
    initArray();
    int seq = 1;
    while(scanf("%d", &n) != EOF){
        printf("Case %d:\n", seq);
        memset(numArr, 0, sizeof(numArr));
        memset(visit, 0, sizeof(visit));
        numArr[1] = 1;
        dfs(2, n);
        printf("\n");
        seq++;
         
    }
    return 0;
}
/**************************************************************
    Problem: 1459
    User: wzqwsrf
    Language: C++
    Result: Accepted
    Time:400 ms
    Memory:1020 kb
****************************************************************/