{"id":1576,"date":"2021-03-03T23:58:00","date_gmt":"2021-03-03T15:58:00","guid":{"rendered":"http:\/\/47.101.202.111\/?p=1576"},"modified":"2023-06-01T13:53:34","modified_gmt":"2023-06-01T05:53:34","slug":"%e7%ba%a6%e7%91%9f%e5%a4%ab%e7%8e%af%e9%97%ae%e9%a2%98","status":"publish","type":"post","link":"http:\/\/139.196.114.170\/?p=1576","title":{"rendered":"\u6df1\u5165\u7406\u89e3\u7ea6\u745f\u592b\u73af – \u628a\u63e1\u9012\u63a8\u601d\u60f3"},"content":{"rendered":"

\u8bfb\u8005\u53ef\u80fd\u4f1a\u6709\u7591\u60d1\uff1a\u7ea6\u745f\u592b\u73af\u9012\u63a8\u65f6\uff0c\u662f\u600e\u4e48\u50cf\u6a21\u62df\u6cd5\u90a3\u6837\u8df3\u8fc7\u5df2\u5220\u9664\u4f4d\u7f6e\u7684\uff1f\u672c\u6587\u7740\u91cd\u8bb2\u89e3\u7ea6\u745f\u592b\u73af\u89c4\u5f8b\u63a8\u5bfc\u548c\u9012\u63a8\u601d\u60f3\u89c4\u907f\u8df3\u6b65\u539f\u56e0\uff0c\u5982\u679c\u5e2e\u52a9\u5230\u8bfb\u8005\u52a0\u6df1\u7406\u89e3\u6b22\u8fce\u7559\u8a00\uff0c\u5982\u6709\u9519\u8bef\u6b22\u8fce\u8ba8\u8bba\uff0c\u8f6c\u8f7d\u8bf7\u6ce8\u660e\u51fa\u5904<\/p>\n

<\/p>\n

\u95ee\u9898\u62bd\u8c61 – \u660e\u786e\u7ea6\u745f\u592b\u73af\u95ee\u9898\u76ee\u7684<\/h3>\n

0…N-1 \u5171N\u4e2a\u5143\u7d20\u56f4\u6210\u73af\uff0c\u4ece0\u5f00\u59cb\u8ba1\u6570\uff0c\u6bcf\u8ba1\u6570\u5230M\u5220\u9664\u5e76\u91cd\u65b0\u8ba1\u6570\uff0c\u6c42N-1\u8f6e\u540e\u5269\u4f59\u5143\u7d20\u3002\u5373\u7ea6\u745f\u592b\u73af\u95ee\u9898\u7684\u76ee\u7684\u662f\u6c42\u5f97 \u5269\u4f59\u5143\u7d20\u4e0b\u6807 \u5bf9\u5e94 \u539f\u5e8f\u5217\u7684\u54ea\u4e2a\u4e0b\u6807<\/strong>\uff0c\u82e5\u60f3\u627e\u5230\u6570\u5b66\u89c4\u5f8b\uff0c\u5bb9\u6613\u60f3\u5230\u540e\u6587\u4e24\u79cd\u5206\u6790\u601d\u8def<\/p>\n

\u95ee\u9898\u5206\u6790 – \u5bfb\u6c42\u4e0b\u6807\u4e0e\u539f\u5e8f\u5217\u76f4\u63a5\u5bf9\u5e94\u5173\u7cfb<\/h3>\n

\u6c42\u89e3\u601d\u8def<\/h4>\n

\u56e0\u4e3a\u6bcf\u4e00\u8f6e\u90fd\u8981\u5bf9\u5e94\u5230\u539f\u5e8f\u5217\uff0c\u8fd9\u5c31\u610f\u5473\u7740 \u524d\u8fdb\u91cfM\u9700\u8981\u8df3\u8fc7M\u4e2a\u672a\u5220\u9664\u9879\uff0c\u8fd9\u5c31\u9700\u8981\u8003\u8651\u5230\u539f\u5e8f\u5217\u4e2d\u5df2\u5220\u9664\u7684\u4f4d\u7f6e\uff1a\u524d\u8fdb\u91cf\u662f\u5426\u56ca\u62ec\u5220\u9664\u9879\uff1f\u56ca\u62ec\u51e0\u4e2a\u5220\u9664\u9879\uff1f\u901a\u9879\u516c\u5f0f\u975e\u5e38\u4e0d\u5bb9\u6613\u5206\u6790<\/strong>\u3002\u5bfb\u627e\u4e0b\u6807\u4e0e\u539f\u5e8f\u5217\u76f4\u63a5\u5bf9\u5e94\u5173\u7cfb\u5b9e\u9645\u8fd8\u662f\u6a21\u62df\u6cd5\uff0c\u5faa\u73af\u94fe\u8868\u6a21\u62df\uff0c\u65f6\u95f4 \\scriptsize O(MN)<\/code>\uff0c\u7a7a\u95f4 \\scriptsize O(N)<\/code><\/p>\n

\u5b9e\u73b0\u4ee3\u7801<\/h4>\n
class Solution {\n    class ListNode {\n        int id;\n        ListNode prev;\n        ListNode next;\n\n        public ListNode(int id, ListNode prev, ListNode next) {\n            this.id = id;\n            this.next = next;\n            this.prev = prev;\n        }\n    }\n\n    class LinkedList {\n        ListNode head;\n        ListNode tail;\n        int size;\n\n        public LinkedList() {\n            head = new ListNode(-2, null, null);\n            tail = new ListNode(-1, head, null);\n            head.next = tail;\n        }\n\n        public void addLast(ListNode node) {\n            node.prev = tail.prev;\n            tail.prev.next = node;\n            tail.prev = node;\n            node.next = tail;\n            size++;\n        }\n\n        public void removeNode(ListNode node) {\n            node.prev.next = node.next;\n            node.next.prev = node.prev;\n            node = null; \/\/ help GC\n            size--;\n        }\n    }\n\n    public int lastRemaining(int N, int M) {\n        LinkedList list = new LinkedList();\n        for (int i = 0; i < N; i++) {\n            list.addLast(new ListNode(i, null, null));\n        }\n\n        ListNode node = list.head;\n        while (list.size > 1) {\n            for (int i = 0; i < M; i++) {\n                node = node.next;\n                if (node == list.tail)\n                    node = list.head.next;\n            }\n            list.removeNode(node);\n        }\n\n        return list.head.next.id;\n    }\n}<\/code><\/pre>\n
\u4e0a\u8ff0\u8fc7\u7a0b\u4e2d\u95f4\u9694\u5143\u7d20\u6ca1\u5fc5\u8981\u8bbf\u95ee\uff0c\u76f4\u63a5\u4f7f\u7528\u4e0b\u6807\u8ba1\u7b97\u53ef\u4ee5\u51cf\u5c11\u6210\u672c\uff0c\u6ce8\u610f\u5220\u9664\u5143\u7d20\u64cd\u4f5c\u5e26\u6765\u7684\u95ee\u9898\uff1a\u2460\u6570\u7ec4\u957f\u5ea6\u53d1\u751f\u53d8\u5316 \u2461\u5f53\u524d\u6307\u9488\u6307\u5411\u4e86\u4e0b\u4e00\u5143\u7d20\uff0c\u518d\u8fc7M-1\u9879\u4e3a\u624d\u662f\u4e0b\u4e00\u4e2a\u6b63\u786e\u5220\u9664\u4f4d\u7f6e\u3002\u6b64\u65b9\u6cd5\u5df2\u7ecf\u975e\u5e38\u63a5\u8fd1\u9012\u63a8\u65b9\u6cd5\uff0c\u65f6\u95f4 \\scriptsize O(N)<\/code>\uff0c\u7a7a\u95f4 \\scriptsize O(N)<\/code><\/p>\n
public int lastRemaining(int N, int M) {\n    List<Integer> list = new LinkedList<>();\n    for (int i = 0; i < N; i++) {\n        list.add(i);\n    }\n\n    for (int i = N, pos = 0; i > 1; i--) {\n        list.remove(pos = (pos + M - 1) % i);\n    }\n\n    return list.get(0);\n}<\/code><\/pre>\n
\u95ee\u9898\u5206\u6790 – \u5bfb\u6c42\u4e0b\u6807\u4e0e\u4e0a\u8f6e\u4e0b\u6807\u7684\u5bf9\u5e94\u5173\u7cfb<\/h3>\n
\u6c42\u89e3\u601d\u8def<\/h4>\n
\u6ce8\u610f\u5230\u6bcf\u6b21\u64cd\u4f5c\u662f\u76f8\u540c\u7684\uff0c\u76f8\u90bb\u8f6e\u4e4b\u95f4\u5c31\u53ef\u80fd\u5b58\u5728\u9012\u63a8\u5173\u7cfb\u3002\u5220\u9664\u5143\u7d20\u540e\u7684\u65b0\u4e00\u8f6e\u4ece0\u5f00\u59cb\u91cd\u65b0\u8ba1\u6570\uff0c\u6211\u4eec\u628a\u65b0\u8ba1\u6570\u4f5c\u4e3a\u5143\u7d20\u5728\u65b0\u4e00\u8f6e\u7684\u865a\u6784\u4e0b\u6807\u3002\u5269\u4f59\u5143\u7d20\u6700\u7ec8\u4e0b\u6807\u4e00\u5b9a\u662f0\uff0c\u82e5\u5b58\u5728\u9012\u63a8\u5173\u7cfb\u4f9d\u6b21\u9012\u63a8\u56de\u521d\u59cb\u8f6e\u5373\u53ef\u5f97\u77e5\u5269\u4f59\u5143\u7d20\u7684\u521d\u59cb\u4e0b\u6807<\/p>\n
\u4ece\u76f4\u89c2\u8fc7\u7a0b\u6765\u5bfb\u627e\u89c4\u5f8b\uff0c\u53d6N=5\u3001M=3\uff1a\u6b63\u5411\u6a21\u62df\u4e00\u8f6e\u5220\u9664\u91cd\u65b0\u8ba1\u6570\uff0c\u76f8\u5f53\u4e8e\u6570\u7ec4\u5faa\u73af\u5de6\u79fbM\u4f4d\u540e\u518d\u5220\u9664\u672b\u5c3e\u5143\u7d20<\/strong>\uff0c\u5982\u4e0b\u56fe\u6240\u793a<\/p>\n
\"joseph-ring-1\"<\/p>\n
id(x)\u4e3a\u7b2cx\u8f6e\u7684\u4e0b\u6807\uff0cN(x)\u4e3a\u7b2cx\u8f6e\u7684\u6570\u7ec4\u957f\u5ea6\uff0c\u5219\u9012\u63a8\u56de\u4e0a\u4e00\u8f6e\u7684\u516c\u5f0f\u4e3a<\/p>\n
\\scriptsize\nid(x) =\n\\left \\{\n\\begin{array}{ll}\n(id(x+1) + M) \\mod N(x), & x \\ge 0\\\\\n0,   & x=N-1\\\\\n\\end{array}\n\\right.<\/code><\/pre>\n
\u4ece\u4e24\u8f6e\u7684\u4e0b\u6807\u6765\u5f52\u7eb3\u6620\u5c04\u5173\u7cfb\uff0c\u9012\u63a8\u56de\u4e0a\u4e00\u8f6e\u7684\u516c\u5f0f\u540c\u4e0a\u3002\u4eb2\u81ea\u52a8\u624b\u624d\u80fd\u627e\u5230\u5171\u6027\uff0c\u4e24\u79cd\u65b9\u6cd5\u5747\u627e\u5230\u4e86\u76f8\u90bb\u8f6e\u4e4b\u95f4\u7684\u9012\u63a8\u5173\u7cfb\uff0c\u65f6\u95f4 \\scriptsize O(N)<\/code>\uff0c\u7a7a\u95f4 \\scriptsize O(1)<\/code>
\n\"joseph-ring-2\"<\/p>\n
\u73b0\u5728\u6765\u89e3\u7b54\u6587\u7ae0\u5bfc\u8a00\u63d0\u51fa\u7684\u95ee\u9898\uff1a
\n\u5176\u4e00 \u4e24\u8f6e\u865a\u6784\u4e0b\u6807\u5173\u7cfb\u7684\u63a8\u5bfc\u53ea\u9650\u7528\u4e8e\u7559\u5b58\u5143\u7d20\uff0c\u4e0d\u8003\u8651\u4e24\u8f6e\u4e4b\u95f4\u7684\u5220\u9664\u5143\u7d20\uff0c\u4e0d\u6d89\u53ca\u5220\u9664\u5143\u7d20\u7684\u63a8\u5bfc<\/strong>
\n\u5176\u4e8c \u865a\u6784\u4e0b\u6807\u5173\u7cfb\u662f\u76f8\u90bb\u8f6e\u4e4b\u95f4\u7684\u6620\u5c04\uff0c\u4e0d\u662f\u6bcf\u4e00\u8f6e\u5b9e\u9645\u5750\u6807\u4e0e\u539f\u5e8f\u5217\u7684\u6620\u5c04\uff0c\u4e0e\u539f\u5e8f\u5217\u5750\u6807\u65e0\u5173\uff0c\u4e0d\u9700\u8003\u8651\u539f\u5e8f\u5217\u4e2d\u5220\u9664\u7684\u5143\u7d20
\n\u5176\u4e09 \u4e24\u8f6e\u4e4b\u95f4\u4ec5\u5220\u9664\u5355\u4e2a\u5143\u7d20\uff0c\u4e14\u4e0b\u6807\u5747\u5982\u4e0b\u56fe\u4e2d\u7684 \\scriptsize (M-1)\\mod N(x)<\/code>\uff0c\u89c4\u907f\u4e86\u4e0d\u540c\u8f6e\u4e2d\u5df2\u5220\u5143\u7d20\u6570\u91cf\u4f4d\u7f6e\u4e0d\u540c\u7684\u9ebb\u70e6\uff0c\u5c06\u53d8\u5316\u8f6c\u4e3a\u786e\u5b9a\uff0c\u7edf\u4e00\u4e86\u89c4\u5f8b<\/p>\n
\"joseph-ring-3\"<\/p>\n
\u5b9e\u73b0\u4ee3\u7801<\/h4>\n
public int lastRemaining(int N, int M) {\n    int id = 0;\n    for (int Nx = 2; Nx <= N; Nx++) {\n        id = (id + M) % Nx;\n    }\n    return id;\n}<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
\u8bfb\u8005\u53ef\u80fd\u4f1a\u6709\u7591\u60d1\uff1a\u7ea6\u745f\u592b\u73af\u9012\u63a8\u65f6\uff0c\u662f\u600e\u4e48\u50cf\u6a21\u62df\u6cd5\u90a3\u6837\u8df3\u8fc7\u5df2\u5220\u9664\u4f4d\u7f6e\u7684\uff1f\u672c\u6587\u7740\u91cd\u8bb2\u89e3\u7ea6\u745f\u592b\u73af\u89c4\u5f8b\u63a8\u5bfc\u548c\u9012\u63a8\u601d\u60f3\u89c4 … <\/p>\n
\u7ee7\u7eed\u9605\u8bfb\u201c\u6df1\u5165\u7406\u89e3\u7ea6\u745f\u592b\u73af – \u628a\u63e1\u9012\u63a8\u601d\u60f3\u201d<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[12],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"http:\/\/139.196.114.170\/index.php?rest_route=\/wp\/v2\/posts\/1576"}],"collection":[{"href":"http:\/\/139.196.114.170\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/139.196.114.170\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/139.196.114.170\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/139.196.114.170\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1576"}],"version-history":[{"count":17,"href":"http:\/\/139.196.114.170\/index.php?rest_route=\/wp\/v2\/posts\/1576\/revisions"}],"predecessor-version":[{"id":2848,"href":"http:\/\/139.196.114.170\/index.php?rest_route=\/wp\/v2\/posts\/1576\/revisions\/2848"}],"wp:attachment":[{"href":"http:\/\/139.196.114.170\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1576"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/139.196.114.170\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1576"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/139.196.114.170\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1576"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}