Topic 1016: Prime Ring Problem

Problem DescriptionA ring is compose of n circles as shown in digoal. put natural number 1, 2 ,..., n into each circle separately, and the sum of numbers in two adjacent circles shoshould be a prime. note: the number of first circle shoshould always be 1. inputn (0 <n <20 ). outputThe output format is shown as sample below. each row represents a series of circle numbers in the ring beginning from 1 clo Ckwisely and anticlockwisely. the order of numbers must satisfy the above requirements. print solutions in lexicographical order. you are to write a program that completes abve process. print a blank line after each case. sample Input68 Sample OutputCase 1:1 4 3 2 5 61 6 5 2 3 4 Case 2:1 2 3 8 5 6 7 41 2 5 8 3 4 7 61 4 7 6 5 3 21 6 7 4 3 8 5 2 SourceAsia 1996, shanghai (Mainland China) Recommen DJGShining [cpp]/********************************* date: * Author: SJF0115 * question: HDU question 1016: Prime Ring Problem * Source: http://acm.hdu.edu.cn/showproblem.php? Pid = 1016 * result: AC * Source: Asia 1996, Shanghai (Mainland China) * Summary: * *********************************/# include <stdio. h> # include <string. h> int prime [] = {, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0}; int visited [21]; int value [21]; int n; void DFS (int step) {int I; // The last number also needs to be added to 1 to determine if it is a prime number. if (step = n + 1) {if (prime [value [step-1] + 1]) {// output prime ring for (I = 1; I <= n; I ++) {printf ("% d % c", value [I], I = n? '\ N': '') ;}} else {for (I = 2; I <= n; I ++) {// This data has not been used and is added to the previous number as the prime number if (! Visited [I] & prime [I + value [step-1]) {// mark accessed visited [I] = 1; value [step] = I; DFS (step + 1); visited [I] = 0 ;}}} int main () {int caseNum = 1; while (scanf ("% d ", & n )! = EOF) {memset (visited, 0, n); printf ("Case % d: \ n", caseNum ); // The first number of prime ring is always 1 value [1] = 1; DFS (2); printf ("\ n"); caseNum ++;} return 0 ;} /********************************** Date: * Author: SJF0115 * question: HDU question 1016: Prime Ring Problem * Source: http://acm.hdu.edu.cn/showproblem.php? Pid = 1016 * result: AC * Source: Asia 1996, Shanghai (Mainland China) * Summary: * *********************************/# include <stdio. h> # include <string. h> int prime [] = {, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0}; int visited [21]; int value [21]; int n; void DFS (int step) {int I; // The last number also needs to be added to 1 to determine if it is a prime number. if (step = n + 1) {if (prime [value [step-1] + 1]) {// output prime ring for (I = 1; I <= n; I ++) {print F ("% d % c", value [I], I = n? '\ N': '') ;}} else {for (I = 2; I <= n; I ++) {// This data has not been used and is added to the previous number as the prime number if (! Visited [I] & prime [I + value [step-1]) {// mark accessed visited [I] = 1; value [step] = I; DFS (step + 1); visited [I] = 0 ;}}} int main () {int caseNum = 1; while (scanf ("% d ", & n )! = EOF) {memset (visited, 0, n); printf ("Case % d: \ n", caseNum ); // The first number of prime ring is always 1 value [1] = 1; DFS (2); printf ("\ n"); caseNum ++;} return 0 ;}