Prime RingProblem素环问题 14
2015-11-25 20:21
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Prime RingProblem素环问题
Problem Description
A ring is composeof n circles as shown in diagram. Put natural number 1, 2, ..., n into eachcircle separately, and the sum of numbers in two adjacent circles should be aprime.
Note: the number of first circle should always be 1.
环是组合成n个圆圈所示的图。把自然数1,2,...,n为进分别各圈,和数字中的两个相邻圈之和应该是一个素数。
注意:第一圈的数量始终应为1。
Input
n (0 < n <20).
Output
The output formatis shown as sample below. Each row represents a series of circle numbers in thering beginning from 1 clockwisely and anticlockwisely. The order of numbersmust 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.
输出格式如下图所示的样品。每一行代表一个系列的圆形数字的环从1开始顺时针和按逆时针方向。号的顺序,必须满足上述要求。在字典顺序打印解决方案。
请你写一个程序,完成上述过程。
打印每个案例后,一个空行。
Sample Input
6
8
Sample Output
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
代码如下:
Problem Description
A ring is composeof n circles as shown in diagram. Put natural number 1, 2, ..., n into eachcircle separately, and the sum of numbers in two adjacent circles should be aprime.
Note: the number of first circle should always be 1.
环是组合成n个圆圈所示的图。把自然数1,2,...,n为进分别各圈,和数字中的两个相邻圈之和应该是一个素数。
注意:第一圈的数量始终应为1。
Input
n (0 < n <20).
Output
The output formatis shown as sample below. Each row represents a series of circle numbers in thering beginning from 1 clockwisely and anticlockwisely. The order of numbersmust 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.
输出格式如下图所示的样品。每一行代表一个系列的圆形数字的环从1开始顺时针和按逆时针方向。号的顺序,必须满足上述要求。在字典顺序打印解决方案。
请你写一个程序,完成上述过程。
打印每个案例后,一个空行。
Sample Input
6
8
Sample Output
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
代码如下:
#include <stdio.h> #include <stdlib.h> int num[21],mark[21],n; int prime_num[12] = {2,3,5,7,11,13,17,19,23,29,31,37}; //判断是否是质数,是返回1,不是返回0 int is_prime(int a) { int i; for(i = 0; i < 12;i++) if(a==prime_num[i]) return 1; return 0; } void print_num() { int i; for(i = 1; i < n;i++) printf("%d ",num[i]); printf("%d",num ); } int dfs(int pre,int post,int flag) { //如果不符合,直接返回 int i; if(!is_prime(pre+post))//前+后若不是素数,则返回 0 return 0; num[flag] = post; if(flag==n&&is_prime(post+1)) { print_num(); printf("\n"); return 1; } //使用过了这个数字就标记为0 mark[post] = 0; for( i = 2;i<=n;i++) if(mark[i]!=0 && dfs(post,i,flag+1)) break; //标记位恢复原状 mark[post] = 1; return 0; } int main() { int count,i; count = 1; while(scanf("%d",&n)!=EOF) { for(i = 1; i <= n; i++) mark[i] = i; num[1] = 1; printf("Case %d:\n",count++); if(n==1)printf("1\n"); for(i = 2;i<=n;i++) dfs(1,i,2); printf("\n"); } return 0; }
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