{"id":97367,"date":"2020-05-10T01:39:22","date_gmt":"2020-05-09T17:39:22","guid":{"rendered":"http:\/\/4563.org\/?p=97367"},"modified":"2020-05-10T01:39:22","modified_gmt":"2020-05-09T17:39:22","slug":"%e4%b8%80%e9%81%93%e7%ae%97%e6%b3%95%e9%9d%a2%e8%af%95%e9%a2%98","status":"publish","type":"post","link":"http:\/\/4563.org\/?p=97367","title":{"rendered":"\u4e00\u9053\u7b97\u6cd5\u9762\u8bd5\u9898"},"content":{"rendered":"
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\u4e00\u9053\u7b97\u6cd5\u9762\u8bd5\u9898 <\/h1>\n

<\/p>\n

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\u8cc7\u6df1\u5927\u4f6c : leolin <\/span> <\/i> 55<\/span> <\/div>\n
<\/div>\n<\/p><\/div>\n<\/p><\/div>\n<\/p><\/div>\n
<\/p>\n

\u7f16\u7a0b\uff1a\u6570\u503c\u589e\u6b96\uff0c\u7ed9\u4e00\u4e2a\u6570\u5b57\u6bd4\u5982 4\uff0c\u589e\u6b96\u4e00\u6b21\u6210 1 2 3 4\uff0c\u518d\u589e\u6b96\u4e00\u6b21\u5c31\u662f\u6309\u7167\u6bcf\u4e2a\u6570\u5b57\uff0c\u518d\u62d3\u5c55\u6210 1 \u5230 X \u7684\u6570\u5217\uff08 1 1 2 1 2 3 1 2 3 4 \uff09\uff0c\u7136\u540e\u95ee\u7b2c K \u6b21\u5f62\u6210\u7684\u5e8f\u5217\u91cc\u7b2c P \u4f4d\u662f\u591a\u5c11\uff1f<\/p>\n<\/p><\/div>\n

\u5927\u4f6c\u6709\u8a71\u8aaa<\/b> (14<\/span>) <\/div>\n
<\/div>\n<\/p><\/div>\n<\/p><\/div>\n
    \n
  • \n
    \n
    \n
    \u8cc7\u6df1\u5927\u4f6c : ppyybb <\/span> <\/div>\n
    <\/i> <\/span> <\/div>\n<\/p><\/div>\n
    \u6211\u7ed9\u4e00\u4e2a\u601d\u8def\u5427\uff0c\u4e0d\u77e5\u662f\u5426\u53ef\u884c\uff1a
    1. \u5206\u89e3\u95ee\u9898\uff0c\u4ee4 f \uff08 x\uff0ck \uff09\u4ee3\u8868\u4ece\u6570\u5b57 x \u8fdb\u884c\u53d8\u6362 k \u6b21\u4e4b\u540e\u7684\u6570\u5217\u957f\u5ea6\uff0ck \u4ece 0 \u5f00\u59cb<\/p>\n

    2. f \u7684\u52a8\u6001\u89c4\u5212\u65b9\u7a0b\u53ef\u4ee5\u8fd9\u6837\uff1a
    f \uff08 x\uff0ck \uff09= f \uff08 1\uff0ck – 1 \uff09+ f \uff08 2\uff0ck -1 \uff09+ … f \uff08 x – 1\uff0ck – 1 \uff09
    f \uff08 x-1\uff0ck \uff09= f \uff08 1\uff0ck-1 \uff09+ … f \uff08 x-1\uff0ck-1 \uff09
    \u6240\u4ee5\u6709 f \uff08 x\uff0ck \uff09= f \uff08 x-1\uff0ck \uff09+ f \uff08 x\uff0ck-1 \uff09
    \u8ba1\u7b97\u51fa\u6765\u7684\u590d\u6742\u5ea6\u662f O \uff08 xk \uff09\uff0c\u8fd9\u662f\u9884\u5904\u7406\u7684\u8fc7\u7a0b\u3002<\/p>\n

    3. \u5047\u8bbe\u9700\u8981\u67e5\u8be2\u4f4d\u7f6e p\uff0c\u4ee4 g \uff08 x\uff0ck\uff0cp \uff09\u4e3a\u9898\u76ee\u6240\u6c42\uff0c\u5373\u53d8\u5316\u540e\u7684\u6570\u5217\u7684\u7b2c p \u9879\uff0c\u8fd9\u4e2a\u65f6\u5019\u904d\u5386 f \uff08 1\uff0ck-1 \uff09\uff0cf \uff08 2\uff0ck-1 \uff09… f \uff08 x\uff0ck-1 \uff09\u5e76\u7ef4\u62a4\u5f53\u524d\u6570\u5217\u7684\u957f\u5ea6\uff08\u4e5f\u5c31\u662f sum \uff09
    \u627e\u5230 p \u6240\u5728\u7684\u4f4d\u7f6e t\uff0c\u5047\u8bbe\u524d\u9762\u957f\u5ea6\u4e3a sum\uff0c\u5219\u95ee\u9898\u53ef\u4ee5\u76f4\u63a5\u89c4\u7ea6\u5230 g \uff08 t\uff0ck-1\uff0cp – sum \uff09
    \u8fd9\u4e00\u6b65\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f O \uff08 x \uff09<\/p>\n

    4. \u4e0d\u65ad\u9012\u964d\u53ef\u4ee5\u5c06 k \u964d\u4f4e\u5230 1\uff0c\u4e00\u5171\u9700\u8981 k \u6b21\uff0c\u56e0\u6b64\u603b\u590d\u6742\u5ea6\u662f O \uff08 xk \uff09<\/p>\n

    5. \u5bf9\u4e8e k \u4e3a 1 \u7684\u60c5\u51b5\uff0c\u7ed3\u679c\u662f\u663e\u7136\u7684\u3002 <\/p>\n

    6. \u7b2c\u4e09\u6b65\u7684\u590d\u6742\u5ea6\u53ef\u4ee5\u8fdb\u4e00\u6b65\u964d\u4f4e\uff0c\u901a\u8fc7\u9884\u5904\u7406\u6c42\u51fa f \u6570\u5217\u524d\u7f00\u548c\uff0c\u90a3\u4e48\u53ef\u4ee5\u8fdb\u884c\u4e8c\u5206\u67e5\u627e\u627e\u5230\u7b2c\u4e00\u4e2a\u5927\u4e8e p \u7684\u4e00\u9879\uff0c\u964d\u4f4e\u4e3a logx <\/p><\/div>\n<\/p><\/div>\n<\/li>\n

  • \n
    \n
    \n
    \u8cc7\u6df1\u5927\u4f6c : LzyRapx <\/span> <\/div>\n
    <\/i> <\/span> <\/div>\n<\/p><\/div>\n
    \u7528\u4e24\u4e2a\u4e8c\u5206\u5c31\u53ef\u4ee5\u4e86\u3002<\/p>\n

    \u8fed\u4ee3 K \u6b21\u53ef\u4ee5\u770b\u6210\u5f62\u6210 K \u5757\uff0c\u6bcf\u5757\u7684\u957f\u5ea6\u4e3a i(1,2,3,4,5,….n), \u56e0\u4e3a\u524d i+1 \u5757\u7684\u548c\u80af\u5b9a\u662f\u5927\u4e8e\u524d i \u5757\u7684\u548c\u7684\uff0c\u4e5f\u5c31\u662f\u8bf4\u662f\u5355\u8c03\u9012\u589e\u7684\uff0c\u4e8c\u5206\u51fa\u662f\u5c5e\u4e8e\u54ea\u4e00\u5757\u3002\u6700\u540e\u5728\u8fd9\u4e00\u5757\u91cc\u8fdb\u884c\u4e8c\u5206\u627e\u51fa\u90a3\u4e00\u4f4d\u6570\u5b57\u5c31\u53ef\u4ee5\u4e86\u3002<\/p>\n

    \u7b80\u5355\u5c31\u662f\uff1a\u5c06\u627e 112123123412345…\u7684\u7b2c P \u4f4d\u8f6c\u5316\u4e3a\u627e 1234567891011…\u7684\u7b2c P \u4f4d\u3002
    \u590d\u6742\u5ea6\u5c31\u662f\uff1aO(logn * logn) <\/div>\n<\/p><\/div>\n<\/li>\n

  • \n
    \n
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    \u8cc7\u6df1\u5927\u4f6c : firemiles <\/span> <\/div>\n
    <\/i> <\/span> <\/div>\n<\/p><\/div>\n
    @ppyybb #1 \u8fd9\u4e2a\u53ef\u884c\uff0c\u8981\u662f\u9012\u63a8\u516c\u5f0f\u80fd\u6c42\u51fa\u901a\u9879\u516c\u5f0f\u5c31\u66f4\u597d\u4e86 <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
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    \u8cc7\u6df1\u5927\u4f6c : LzyRapx <\/span> <\/div>\n
    <\/i> <\/span> <\/div>\n<\/p><\/div>\n
    \u65e0\u804a\u5199\u5199\uff0c\u5927\u6982\u5c31\u662f\u8fd9\u6837\u3002<\/p>\n

    https:\/\/paste.ubuntu.com\/p\/fN8FkhWkbJ\/ <\/p><\/div>\n<\/p><\/div>\n<\/li>\n

  • \n
    \n
    \n
    \u8cc7\u6df1\u5927\u4f6c : ssynhtn <\/span> <\/div>\n
    <\/i> <\/span> <\/div>\n<\/p><\/div>\n
    \u8fd9\u9898\u5728\u9762\u8bd5\u7684\u65f6\u5019\u662f\u51e0\u4e4e\u4e0d\u53ef\u80fd\u5f53\u573a\u60f3\u51fa\u6765\u7684…
    \u4e00\u4e2a\u6570 a \u5728\u7ecf\u8fc7 K \u6b21\u589e\u6b96\u540e\u5f62\u6210\u7684\u6570\u5217\u957f\u5ea6\u4e3a C(a+K-1, K) \/\/ a+K-1 \u4e2d\u9009 K \u4e2a\u6570
    1: \u5bf9\u4e8e\u8f93\u5165 X, \u5982\u679c X == C(j+K-1, K), \u90a3\u4e48\u7ed3\u679c\u5c31\u662f j
    2: \u5426\u5219 let X = X – C(j+K-1, K), let K = K-1, \u7ee7\u7eed\u9012\u5f52\u76f4\u5230 1 \u6210\u7acb\u4e3a\u6b62 <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
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    \u8cc7\u6df1\u5927\u4f6c : ssynhtn <\/span> <\/div>\n
    <\/i> <\/span> <\/div>\n<\/p><\/div>\n
    https:\/\/paste.ubuntu.com\/p\/HGfttZMCw8\/ <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
    \n
    \u8cc7\u6df1\u5927\u4f6c : ppyybb <\/span> <\/div>\n
    <\/i> <\/span> <\/div>\n<\/p><\/div>\n
    @ssynhtn \u5982\u679c\u53ea\u505a\u5230\u6211\u5728\u4e00\u7ed9\u51fa\u6765\u7684\u7a0b\u5ea6\u662f\u5b8c\u5168\u53ef\u4ee5\u7684\u3002
    \u63a8\u4e86\u4e0b\u8fd9\u4e2a\u516c\u5f0f\uff0c\u5927\u6982\u601d\u8def\u662f\u8054\u60f3\u5230\u7c7b\u4f3c\u6768\u8f89\u4e09\u89d2\u7684\u6027\u8d28\uff0c\u7136\u540e\u5f15\u5165\u7ec4\u5408\u6570\u7684\u6027\u8d28 c \uff08 n\uff0ck \uff09= c \uff08 n-1\uff0ck \uff09+ c \uff08 n-1\uff0ck-1 \uff09\uff0c\u7c7b\u4f3c\u4e8e\u4e00 f \u7684\u9012\u63a8\u516c\u5f0f\uff0c\u7136\u540e\u60f3\u529e\u6cd5\u628a n \u548c i \u51d1\u5230\u8fd9\u4e2a\u7ec4\u5408\u6570\u4e0a\u9762\u6765\u5c31\u5f97\u5230\u4e86\u7ed3\u679c\u3002\u4f46\u662f\u6574\u4e2a\u601d\u8def\u6709\u70b9\u7c7b\u4f3c\u4e8e\u9760\u731c\u60f3\u548c\u51d1\u7684\u601d\u8def\uff0c\u4e0d\u77e5\u9053\u6b63\u89e3\u63a8\u5bfc\u7684\u601d\u8def\u662f\u5565\uff08\u786c\u7b97\uff1f\uff09 <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
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    \u8cc7\u6df1\u5927\u4f6c : keith1126 <\/span> <\/div>\n
    <\/i> <\/span> <\/div>\n<\/p><\/div>\n
    @ppyybb #7 <\/p>\n

    \u76ee\u6d4b\u53ef\u4ee5\u7528\u6570\u5b66\u5f52\u7eb3\u6cd5\u8bc1\u660e\uff0c\u4e0d\u8fc7\u7ed3\u8bba\u8fd8\u662f\u9760\u89c2\u5bdf\u731c\u51fa\u6765\u7684\u3002 <\/p><\/div>\n<\/p><\/div>\n<\/li>\n

  • \n
    \n
    \n
    \u8cc7\u6df1\u5927\u4f6c : ppyybb <\/span> <\/div>\n
    <\/i> <\/span> <\/div>\n<\/p><\/div>\n
    @keith1126 \u6570\u5b66\u5f52\u7eb3\u6cd5\u5c31\u66f4\u52a0\u9760\u731c\u6d4b\u4e86\uff0c\u76f4\u63a5\u7a0b\u5ea6\u8fd8\u4e0d\u5982\u6211\u4ece\u6768\u8f89\u4e09\u89d2\u8054\u60f3\u5230\u7ec4\u5408\u6570\u7684\u6027\u8d28\u6765\u63a8\u5bfc\uff0c\u81f3\u5c11\u4e0d\u592a\u8df3\u8dc3\u3002 <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
    \n
    \u8cc7\u6df1\u5927\u4f6c : LzyRapx <\/span> <\/div>\n
    <\/i> <\/span> <\/div>\n<\/p><\/div>\n
    \u80fd\u4e0d\u80fd\u5728\u77ed\u65f6\u95f4\u5185\u60f3\u51fa\u6765\uff0c\u4e0d\u662f\u770b\u9762\u8bd5\u5b98\u7ed9\u7684 P \u7684\u8303\u56f4\u5417\uff1f P <= 10^9 \u548c P <= 10^18 \u5b8c\u5168\u53ef\u4ee5\u662f\u4e0d\u4e00\u6837\u7684\u505a\u6cd5\u3002 <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
    \n
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    \u8cc7\u6df1\u5927\u4f6c : ssynhtn <\/span> <\/div>\n
    <\/i> <\/span> <\/div>\n<\/p><\/div>\n
    @ppyybb
    \u5b9e\u9645\u4e0a\u6211\u662f\u901a\u8fc7 f(a, k) = Sum(f(j, k-1), 1<=j<=a)\u8fde\u7eed\u5957\u7528 k \u6b21
    \u5f97\u5230 k \u4e2a\u4e0b\u6807\u7684\u6c42\u548c\u5f0f f(a, k) = Sum(1, 1<=j_1<=j_2<=j_3…<=j_k<=a)\u7136\u540e\u5f97\u5230\u7684<\/p>\n

    \u5982\u679c\u662f\u9012\u63a8\u7684\u8bdd, \u5bf9 K \u662f 1,2,3 \u7684\u60c5\u51b5\u8ba1\u7b97\u51fa\u516c\u5f0f\u540e, \u7ed3\u5408\u9012\u63a8\u5f0f, \u719f\u6089\u7ec4\u5408\u6570\u7684\u6027\u8d28\u7684\u8bdd\u4e5f\u80fd\u76f4\u63a5\u5c31\u80fd\u770b\u51fa\u957f\u5ea6\u516c\u5f0f <\/p><\/div>\n<\/p><\/div>\n<\/li>\n

  • \n
    \n
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    \u8cc7\u6df1\u5927\u4f6c : ppyybb <\/span> <\/div>\n
    <\/i> <\/span> <\/div>\n<\/p><\/div>\n
    \u76f4\u89c2\u4e0a\u7684\u7406\u89e3\u4f3c\u4e4e\u662f a \u4e2a\u5143\u7d20\u53d6 k \u4e2a\u6570\uff0c\u4f46\u662f\u8fd9 k \u4e2a\u6570\u53c8\u662f\u53ef\u4ee5\u91cd\u590d\u7684\u4e14\u5b58\u5728\u5168\u5e8f\u5173\u7cfb\uff0c\u56e0\u6b64\u9664\u4e86\u7b2c\u4e00\u4e2a\u6570\uff0c\u518d\u589e\u52a0 k-1 \u4e2a\u6570\uff0c\u4ee3\u8868\u5f53\u6bcf\u4e00\u4e2a\u6570\u9700\u8981\u9009\u7684\u548c\u524d\u4e00\u4e2a\u6570\u4e00\u6837\u7684\u90a3\u79cd\u53ef\u80fd\uff1f\u611f\u89c9\u4e0d\u592a\u4e25\u683c\uff0c\u867d\u7136\u7ed3\u679c\u80af\u5b9a\u662f\u5bf9\u7684 <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
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    \u8cc7\u6df1\u5927\u4f6c : charlie21 <\/span> <\/div>\n
    <\/i> <\/span> <\/div>\n<\/p><\/div>\n
    \u76f4\u63a5\u4e0a\u6570\u5b66\u5f52\u7eb3\u6cd5\u641e\u51fa\u516c\u5f0f\u5b8c\u4e8b <\/div>\n<\/p><\/div>\n<\/li>\n
  • \n
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    \u8cc7\u6df1\u5927\u4f6c : xiadong1994 <\/span> <\/div>\n
    <\/i> <\/span> <\/div>\n<\/p><\/div>\n
    \u9762\u8bd5\u91cc\u8fd9\u79cd x \u53d8\u6362\u4e4b\u540e\u6c42 y \u4f4d\u4e00\u822c\u5c31\u662f\u4e24\u79cd\u529e\u6cd5\uff0c\u8981\u4e48\u662f\u6709\u901a\u9879\u516c\u5f0f\u7684\u7eaf\u6570\u5b66\u95ee\u9898\uff0c\u8981\u4e48\u662f\u52a8\u6001\u89c4\u5212 \/\u9012\u63a8\u3002<\/p>\n

    \u8fd9\u9898\u5199\u51e0\u4e2a\u4f8b\u5b50\u5c31\u5f88\u5bb9\u6613\u60f3\u5230\u7b2c k \u5c42\u7684\u957f\u5ea6\u662f\u7b2c k-1 \u5c42\u5143\u7d20\u7684\u548c\uff0c\u90a3\u4e48\u5c31\u53ef\u4ee5\u7528\u524d\u7f00\u548c\u7b97\u51fa\u7b2c k \u5c42\u7684 p \u4f4d\u662f\u7b2c k-1 \u5c42\u7684\u54ea\u4e00\u4f4d\uff08\u5047\u8bbe\u4e3a p_{k-1})\u6269\u5c55\u800c\u6765\u5e76\u4e14\u53ef\u77e5\u662f p_{k-1}\u6269\u5c55\u540e\u7684\u7b2c\u51e0\u4f4d\u3002\u63a5\u4e0b\u6765\u95ee\u9898\u5c31\u662f\u7b2c k-1 \u5c42\u7684\u7b2c p_{k-1}\u4f4d\u662f\u4ec0\u4e48\uff0c\u4ee5\u6b64\u7c7b\u63a8\u3002<\/p>\n

    \u800c\u6c42\u6bcf\u4e00\u5c42\u7684\u5206\u5757\u957f\u5ea6\u5c31\u662f\u57fa\u672c\u7684\u4e8c\u7ef4 DP\uff0c\u7b2c k \u5c42\u7684\u5143\u7d20\u53ef\u4ee5\u5206\u6210\u7b2c 1 \u5c42\uff08\u7b2c\u4e00\u6b21\u589e\u6b96\u540e\uff09\u4e2d\u5143\u7d20\uff08 1,2,3…n \uff09\u5206\u522b\u589e\u6b96 k-1 \u6b21\u800c\u6765\uff0c\u56e0\u6b64 k \u5c42 i \u5757\u957f\u5ea6\u5c31\u662f sum(dp[k-1][0], dp[k-1][1],…,dp[k-1][i])\uff0c\u56e0\u4e3a\u662f\u524d\u7f00\u548c\u6240\u4ee5\u53ef\u4ee5\u7b80\u5316\u4e3a sum(dp[k-1][i], dp[k][i-1])\u3002 <\/p><\/div>\n<\/p><\/div>\n<\/li>\n

  • \n","protected":false},"excerpt":{"rendered":"

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