{"id":2236,"date":"2014-01-17T20:35:05","date_gmt":"2014-01-18T04:35:05","guid":{"rendered":"http:\/\/www.slyar.com\/blog\/?p=2236"},"modified":"2022-07-03T15:43:55","modified_gmt":"2022-07-03T22:43:55","slug":"hdu-1016-c","status":"publish","type":"post","link":"http:\/\/www.slyar.com\/blog\/hdu-1016-c.html","title":{"rendered":"HDU 1016 Prime Ring Problem C\u8bed\u8a00\u7248"},"content":{"rendered":"<p>\u6587\u7ae0\u4f5c\u8005\uff1a<span style=\"color: #0000ff;\">\u59dc\u5357(Slyar) <\/span>\u6587\u7ae0\u6765\u6e90\uff1aSlyar Home (<a title=\"Slyar\" href=\"http:\/\/www.slyar.com\" target=\"_blank\" rel=\"noopener\">www.slyar.com<\/a>) \u8f6c\u8f7d\u8bf7\u6ce8\u660e\uff0c\u8c22\u8c22\u5408\u4f5c\u3002<\/p>\n<p>\u975e\u5e38\u5178\u578b\u975e\u5e38\u987a\u624b\u7684\u6df1\u5ea6\u4f18\u5148\u641c\u7d22(DFS)\u9898\uff0c\u5199\u8d77\u6765\u975e\u5e38\u75db\u5feb\u3002<\/p>\n<p><!--more--><\/p>\n<p><span style=\"color: #0000ff;\">Description<\/span><\/p>\n<p>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.<\/p>\n<p>Note: the number of first circle should always be 1.<\/p>\n<p><span style=\"color: #0000ff;\">Input<\/span><\/p>\n<p>n (0 < n < 20).\n\n<span style=\"color: #0000ff;\">Output<\/span><\/p>\n<p>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.<\/p>\n<p>You are to write a program that completes above process.<\/p>\n<p>Print a blank line after each case.<\/p>\n<p><span style=\"color: #0000ff;\">Sample Input<\/span><\/p>\n<p>6<br \/>\n8<\/p>\n<p><span style=\"color: #0000ff;\">Sample Output<\/span><\/p>\n<p>Case 1:<br \/>\n1 4 3 2 5 6<br \/>\n1 6 5 2 3 4<\/p>\n<p>Case 2:<br \/>\n1 2 3 8 5 6 7 4<br \/>\n1 2 5 8 3 4 7 6<br \/>\n1 4 7 6 5 8 3 2<br \/>\n1 6 7 4 3 8 5 2<\/p>\n<p><span style=\"color: #ff0000;\">Slyar:\u5927\u610f\u662f\u7ed9\u51faN\uff0c\u6c42\u6240\u6709\u75311-N\u7ec4\u6210\u7684\u9996\u4f4d\u4e3a1\u73af\u5f62\u5e8f\u5217\uff0c\u8981\u6c42\u76f8\u90bb\u4e24\u6570\u7684\u548c\u4e3a\u7d20\u6570\u3002\u7d20\u6570\u5224\u65ad\u4e0d\u8bf4\u4e86\uff0c\u56e0\u4e3aN\u5c0f\u4e8e20\uff0c\u6240\u4ee5\u53ef\u4ee5\u9884\u5148\u5c06\u7d20\u6570\u6253\u8868\u4fdd\u5b58\u4f9b\u540e\u9762\u67e5\u8be2\u3002\u56e0\u4e3a\u89c4\u5b9a\u4e86\u9996\u4f4d\u4e3a1\uff0c\u6240\u4ee5\u4ece1\u5f00\u59cb\u641c\u7d22\u6240\u6709\u7684\u53ef\u80fd\uff0c\u7528visit[]\u6807\u8bb0\u8bbf\u95ee\u8fc7\u7684\u6570\u5b57\uff0c\u6bcf\u6b21\u641c\u5230\u6df1\u5ea6\u7b49\u4e8eN\u7684\u65f6\u5019\u5c31\u53ef\u4ee5\u6253\u5370\u7ed3\u679cpath[]\u4e86\u3002\u6ca1\u6709\u7ed3\u679c\u7684\u4e5f\u5c31\u7a7a\u7740\u8f93\u51fa\u5c31\u597d\u4e86\uff0c\u683c\u5f0f\u65b9\u9762\u6ce8\u610f\u6bcf\u884c\u7ed3\u679c\u7684\u6700\u540e\u4e00\u4e2a\u6570\u5b57\u540e\u9762\u6ca1\u6709\u7a7a\u683c\u3002<\/span><\/p>\n<pre lang=\"c\" line=\"1\">\r\n#include <stdio.h>\r\n#include <stdlib.h>\r\n#include <string.h>\r\n#include <math.h>\r\n#define MAX 51\r\n\r\nint n;\r\nint path[MAX];\r\nint visit[MAX];\r\nint prime[MAX];\r\n\r\nint isPrime(int x)\r\n{\r\n\tint i;\r\n\tfor (i = 2; i <= sqrt(x*1.0); i++)\r\n\t{\r\n\t\tif (x % i == 0) return 0;\r\n\t}\r\n\treturn 1;\r\n}\r\n\r\nvoid dfs(int x)\r\n{\r\n\tint i;\r\n\tif ((x == n) && prime[path[1] + path[n]])\r\n\t{\r\n\t\tfor (i = 1; i < n; i++)\r\n\t\t{\r\n\t\t\tprintf(\"%d \", path[i]);\r\n\t\t}\r\n\t\tprintf(\"%d\\n\", path[n]);\r\n\t\treturn;\r\n\t}\r\n\telse\r\n\t{\r\n\t\tfor (i = 2; i <= n; i++)\r\n\t\t{\r\n\t\t\tif (!visit[i] && prime[path[x] + i])\r\n\t\t\t{\r\n\t\t\t\tpath[x+1] = i;\r\n\t\t\t\tvisit[i] = 1;\r\n\t\t\t\tdfs(x+1);\r\n\t\t\t\tvisit[i] = 0;\r\n\t\t\t}\r\n\t\t}\r\n\t}\r\n}\r\n\r\nint main()\r\n{\r\n\tint i, t;\r\n\t\r\n\t\/\/ \u6253\u8868 \r\n\tfor (i = 1; i < MAX; i++)\r\n\t{\r\n\t\tif (isPrime(i)) prime[i] = 1;\r\n\t\telse prime[i] = 0;\r\n\t}\r\n\t\r\n\t\/\/ \u8f93\u51fa \r\n\tt = 0;\r\n\twhile(scanf(\"%d\", &n) != EOF)\r\n\t{\r\n\t\tprintf(\"Case %d:\\n\", ++t);\r\n\t\tmemset(visit, 0, sizeof(visit));\r\n\t\tpath[1] = 1;\r\n\t\tvisit[1] = 1;\r\n\t\tdfs(1);\r\n\t\tprintf(\"\\n\");\r\n\t}\r\n\t\/\/system(\"pause\");\r\n\treturn 0;\r\n}\r\n<\/pre>\n<p>\u8f6c\u8f7d\u8bf7\u6ce8\u660e\uff1a<a href=\"http:\/\/www.slyar.com\/blog\">Slyar Home<\/a> &raquo; <a href=\"http:\/\/www.slyar.com\/blog\/hdu-1016-c.html\">HDU 1016 Prime Ring Problem C\u8bed\u8a00\u7248<\/a><\/p>","protected":false},"excerpt":{"rendered":"<p>\u6587\u7ae0\u4f5c\u8005\uff1a\u59dc\u5357(Slyar) \u6587\u7ae0\u6765\u6e90\uff1aSlyar Home (www.slyar.com) \u8f6c\u8f7d\u8bf7\u6ce8\u660e\uff0c\u8c22\u8c22\u5408\u4f5c\u3002 \u975e\u5e38\u5178\u578b\u975e\u5e38\u987a\u624b\u7684\u6df1\u5ea6\u4f18\u5148\u641c\u7d22(DFS)\u9898\uff0c\u5199\u8d77\u6765\u975e\u5e38\u75db\u5feb\u3002 \u8f6c\u8f7d\u8bf7\u6ce8\u660e\uff1aSlyar Home &raquo; HDU 1016 P [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1103],"tags":[],"class_list":["post-2236","post","type-post","status-publish","format-standard","hentry","category-acm-oj-solution"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.2.1 - 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