{"id":61,"date":"2011-08-27T05:26:00","date_gmt":"2011-08-26T21:26:00","guid":{"rendered":"http:\/\/www.shuizilong.com\/house\/?p=61"},"modified":"2022-10-19T05:26:42","modified_gmt":"2022-10-18T21:26:42","slug":"spoj-9392-play-with-sequence","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/spoj-9392-play-with-sequence\/","title":{"rendered":"SPOJ 9392. Play With Sequence"},"content":{"rendered":"

\uff08\u7531\u4e8e\u88ab fgd BS \u4e86\u82f1\u6587\u3002\u3002\u6211\u628a\u9898\u76ee\u80cc\u666f\u90fd\u5220\u4e86\u3002\u3002\uff09<\/del><\/p>\n

Brief description :<\/h3>\n

You are given a sequence A[1], A[2],…, A[N]. On this sequence you have to apply M operations: Add all the elements whose value are in range [l, r] by d or, ask for a query how many element are in range [l, r].
\n( 1\u2264 N \u2264 250,000, M \u2264 50,000), |A[i]| \u2264 1,000,000,000 .)<\/p>\n

<\/p>\n

Analysis :<\/h3>\n

\u54ce\u3002\u3002\u6211\u73b0\u5728\u5df2\u7ecf\u89c9\u5f97\u8fd9\u4e2a\u9898\u51fa\u7684\u771f\u662f\u5931\u8d25\u554a\u3002\u3002
\n\uff08\u561b\u3002\u3002\u9898\u76ee\u51fa\u6210\u8fd9\u6837\u6211\u4e5f\u6ca1\u6709\u4ec0\u4e48\u53ef\u8fa9\u89e3\u7684\u4e86\u3002\u3002
\n\u3002\u3002\u5f00\u59cb\u89c9\u5f97\u8fd9\u662f\u6570\u636e\u7ed3\u6784 S \u7ea7\u795e\u9898\u7684\u3002\u3002\uff09<\/p>\n

\u539f\u9898\u662f\u5728 \u90a3\u4e2a\u64cd\u4f5c \u7684\u57fa\u7840\u4e0a\u7ef4\u62a4\u7b2c K \u5927\u7684\u6570\u3002\u3002\u3002\u5185\u6d4b\u5f97\u65f6\u5019\u51e0\u4e4e\u65e0\u4eba\u505a\u3002\u3002\u56e0\u6b64\u7b80\u5316\u6210\u4e86\u7edf\u8ba1\u67d0\u4e2a\u533a\u95f4\u5185\u6570\u7684\u591a\u5c11\u3002\u3002\u3002\u6c42\u7b2c K \u5927\u7684\u8bdd\u5728\u8fd9\u4e2a\u57fa\u7840\u4e0a\u8fdb\u884c\u4e8c\u5206\u5373\u53ef\uff0c\u56e0\u4e3a\u6ca1\u6709\u76f4\u63a5\u7684\u529e\u6cd5\u3002\u3002<\/p>\n

\u90a3\u4e48\uff0c\u5bf9\u4e8e\u503c\u57df\u5728\u67d0\u4e2a\u533a\u95f4\u5185\u7684\u6570\u8fdb\u884c\u64cd\u4f5c\uff0c\u9996\u5148\u60f3\u5230\u7684\u662f \u4f38\u5c55\u6811\uff0c\u5979\u7684\u4e00\u4e2a\u795e\u6280\u662f\u4e24\u6b21 Splay \u64cd\u4f5c\u5c06\u67d0\u4e2a\u533a\u95f4\u7684\u6240\u6709\u6811\u4f38\u5c55\u5230\u67d0\u4e2a\u5bb9\u6613\u8bbf\u95ee\u7684\u5b50\u6811\u4f4d\u7f6e\u3002<\/p>\n

\u90a3\u4e48\uff0c\u63a5\u4e0b\u6765\uff1f\u3002\u3002\u3002\u3001\u6253\u6807\u8bb0\uff1f<\/p>\n

\u5982\u56fe\u6240\u793a\u3002\u3002\uff08\u3002\u3002\u3002\uff09<\/p>\n

\u8fd9\u4e2a\u64cd\u4f5c\u4f1a\u7834\u574f\u952e\u503c\u3002\u3002\u3002\u4e5f\u662f\u56e0\u4e3a\u540c\u6837\u7684\u539f\u56e0\uff0c\u7ebf\u6bb5\u6811 \u5757\u72b6\u94fe\u8868 \u90fd\u4e0d\u594f\u6548\u3002\u3002<\/p>\n

\u3002\u3002\u3002\u8fd9\u662f\u8fd9\u4e2a\u95ee\u9898\u7684\u96be\u70b9\u6240\u5728\u3002\u3002\u3002\u4e0b\u9762\u5bf9 \u952e\u503c\u5904\u5728\u67d0\u4e2a\u8303\u56f4\u7684\u6570\u6574\u9898\u52a0\u4e0a\u67d0\u4e2a\u6570 \u8fd9\u4e2a\u64cd\u4f5c\u8fdb\u884c\u8fdb\u4e00\u6b65\u7684\u89c2\u5bdf\u3002\u3002<\/p>\n

\u53ef\u4ee5\u5f97\u5230\u4e0b\u9762\u4e24\u4e2a\u6027\u8d28\u3002<\/p>\n

    \n
  1. \u9009\u51fa\u7684\u5e8f\u5217\uff0c\u5728\u64cd\u4f5c\u7684\u524d\u540e\u76f8\u5bf9\u987a\u5e8f\u4e0d\u53d1\u751f\u6539\u53d8\u3002<\/li>\n
  2. \u5728\u4efb\u610f\u65f6\u523b\uff0c\u5982\u679c\u4e24\u4e2a\u6570\u989d\u952e\u503c\u76f8\u540c\uff0c\u90a3\u4e48\u4eca\u540e\uff0c\u5b83\u4eec\u4f1a\u4e00\u76f4\u4f5c\u4e3a\u4e00\u4e2a\u6574\u4f53\u5b58\u5728\u3002<\/li>\n<\/ol>\n

    ….<\/p>\n

    \u4e3a\u4e86\u9632\u6b62\u6709\u4eba\u7528\u7b2c\u4e8c\u4e2a\u6027\u8d28\u4e71\u641e\u3002\u3002\u9898\u76ee Ai \u503c\u7684\u8303\u56f4\u8981\u5c3d\u53ef\u80fd\u7684\u5927\u3002\u3002<\/p>\n

    \u7b2c\u4e00\u4e2a\u6027\u8d28\u3002\u3002\u63d0\u793a\u6211\u4eec\u7528 \u5757\u72b6\u7ed3\u6784 \u6765\u89e3\u51b3\u6389\u8fd9\u4e2a\u95ee\u9898\u3002\u3002\u3002<\/p>\n

    \u6807\u7a0b\u4f7f\u7528\u7684\u662f \u4f38\u5c55\u68ee\u6797 … \u5b57\u9762\u4e0a\u7684\u610f\u601d\uff0c\u4e5f\u5c31\u662f\u7ef4\u62a4\u4e00\u7ec4\u4f38\u5c55\u6811\uff0c\u6bcf\u6b21\u5bf9\u6bcf\u68f5\u4f38\u5c55\u6811\u4f38\u5c55\u51fa\u9009\u5b9a\u7684\u533a\u95f4\uff0c\u7136\u540e\u6253\u4e0a\u6807\u8bb0\u5206\u79bb\u51fa\u6765\uff08\u5580\u5693\uff01\uff09\u3002\u3002<\/p>\n

    \u7b49\u5230\u4f38\u5c55\u6811\u7684\u68f5\u6811\u8fbe\u5230 \u67d0\u4e2a\u503c \uff08\u4e00\u822c\u8bbe\u5b9a\u4e3a sqrt(n) \u7136\u540e\u8003\u8651\u5230 \u5e38\u6570\uff0c\u518d\u51cf\u5c0f\u4e00\u70b9\u3002\u3002\u4e0d\u5224\u65ad\u5757\u6811\u800c\u662f\u6bcf\u9694\u4e00\u6bb5\u65f6\u95f4\u91cd\u6784\u4e00\u6b21\u3002\u3002\u5927\u6982\u7528\u4e00\u4e2a\u5bf9\u6570\u51fd\u6570\u3002\u3002\u3002\uff09
    \n\u7684\u65f6\u5019\u3002\u3002\u63a8\u6389\u91cd\u7ec3\u3002\u3002\uff08\u8fd9\u91cc\u6ce8\u610f\u4e00\u4e2a\u5730\u65b9\u3002\u5b9e\u9645\u4e2d\u91cd\u6784\u7684\u8bdd\u7528 std::sort \u6bd4\u7528\u5806\u7136\u540e\u5206\u5757\u5408\u5e76\u8981\u5feb\u3002\u3002\uff09<\/p>\n

    \u8fd9\u91cc\u7684\u6807\u8bb0\u53ea\u8981\u8bb0\u5f55\u5728\u6839\u8282\u70b9\u5373\u53ef\uff0c\u4e0d\u9700\u8981\u4e0b\u653e\u3002\u3002
    \n\uff08\u4e00\u4e2a\u5bb9\u6613\u51fa\u9519\u7684\u5730\u65b9\u662f\uff0c\u867d\u7136\u6211\u4fdd\u8bc1\u4e2d\u95f4\u7684\u6570\u636e\u4e5f\u4e0d\u4f1a\u7206 int32\uff0c\u4f46\u662f\u5728\u5904\u7406 delta \u7684\u65f6\u5019\u53ef\u80fd\u4f1a\u7206\u3002\u3002\u6240\u4ee5\u5982\u679c\u60f3\u4fdd\u6301\u4e3b\u8981\u7684\u7ed3\u6784\u90fd\u4f7f\u7528 int32 \u7684\u8bdd\u8fd9\u91cc\u8981\u7279\u5224\u4e00\u4e0b\u3002\u3002\uff09<\/p>\n

    \u4e00\u4e2a\u4e25\u91cd\u7684\u95ee\u9898\u5c31\u6b64\u4ea7\u751f\u4e86\uff1a<\/p>\n

    \u4f3c\u4e4e\u4e00\u773c\u770b\u4e0a\u53bb\uff0csplay \u7684\u9897\u6811\u4f1a\u5448\u6307\u6570\u7206\u70b8\uff1f\uff01\u3002\u3002\u3002<\/p>\n

    \u55ef\u55ef\u3002\u3002\u8fd9\u4e2a\u95ee\u9898\u3002\u3002\u6211\u8fd8\u3002\u3002\u4e0d\u77e5\u9053\u600e\u4e48\u8bc1\u660e\u3002\uff08\u4ec0\u4e48\uff01\uff09
    \n\u3002\u3002\u4f46\u662f\u770b\u4e0a\u53bb\u4f3c\u4e4e\uff08\u5bf9\u4e8e\u968f\u673a\u751f\u6210\u7684\u6570\u636e\uff09\u8fd9\u79cd\u60c5\u51b5\u4e0d\u4f1a\u51fa\u73b0 \u3002\u3002<\/p>\n

    \u4e0b\u9762\u6211\u8bd5\u56fe\u8bf4\u4e00\u70b9\u6211\u7684\u60f3\u6cd5\u3002\u3002<\/p>\n

    \u5b9a\u4e49
    \n\/theta = sqrt Sigma i, j sqr(Ai – Aj)
    \n\u4e3a\u4e00\u4e2a\u6570\u96c6\u7684 \u79bb\u6563\u7a0b\u5ea6\u3002\uff08\u6ce8\u610f\u4e0d\u80fd\u76f4\u63a5\u4f7f\u7528\u65b9\u5dee\u3002\u3002\u5427\u3002\u3002\uff09<\/p>\n

    \uff08\u4e8e\u662f\uff0c\u91cd\u65b0\u8003\u5bdf\u524d\u9762\u7684\u6027\u8d282\uff0c\u867d\u7136\u8bf4\u8981\u4e2d\u95f4\u6070\u597d\u76f8\u7b49\u53ef\u80fd\u4e0d\u592a\u4f1a\u51fa\u73b0\u3002
    \n\u4f46\u662f\u6709\u8ff9\u8c61\u8868\u660e\uff0c\u64cd\u4f5c\u8fc7\u540e\u6570\u5217\u53ef\u80fd\u5728\u67d0\u51e0\u4e2a\u4f4d\u7f6e\u96c6\u4e2d\u3002\u3002\u800c\u8fd9\u5c31\u76f8\u5f53\u4e8e\u964d\u4f4e\u4e86 N \u7684\u89c4\u6a21\uff09\u3002\u3002<\/p>\n

    \u5bf9\u4e8e\u67d0\u4e00\u6b21\u64cd\u4f5c\uff0c\u4f1a\u53d1\u751f\u4e0b\u9762\u4e24\u79cd\u4e8b\u60c5\u4e4b\u4e00<\/p>\n

      \n
    1. \u6570\u5217\u7684\u79bb\u6563\u7a0b\u5ea6\u4e0b\u964d\uff0c\u540c\u65f6\uff0c\u5757\u6570\u589e\u591a\u3002<\/li>\n
    2. Nothing happend (\u4ec0\u4e48\u90fd\u6ca1\u6709\u53d1\u751f)\u3002\u3002<\/li>\n<\/ol>\n

      …<\/p>\n

      \u597d\u5427\u3002\u3002\u5927\u6982\u5c31\u662f\u8fd9\u6837\u4e86\u3002\u3002\u3002<\/p>\n

      \uff08\u6211\u4ee5\u540e\u4f1a\u7ee7\u7eed\u8003\u8651\u8fd9\u4e2a\u95ee\u9898\u7684\u3002\u3002\u5982\u679c\u6709\u4e48\u8fdb\u5c55\u7684\u8bdd\u4f1a\u53ca\u65f6\u66f4\u65b0\u3002\u3002\uff09<\/p>\n

      \n

      \u6211\u770b\u5230\u8d5b\u540e\u5f88\u591a\u540c\u5b66\u63d0\u4ea4\u4e86 \u7ebf\u6bb5\u6811 \u7684\u65b9\u6cd5\u3002\u3002\u3002\u672c\u8d28\u4e0a\u90fd\u5dee\u4e0d\u591a\u5427\u3002\u3002<\/p>\n

      \u590d\u6742\u5ea6\u7684\u8bdd\u3002\u3002\u662f<\/p>\n

      P = sqrt(n)
      \nO( (M \/ log P) N log P) = O(NM)..
      \nP \u662f\u5757\u6570\u4e0a\u9650\u3002\u3002 M \/ log P \u662f\u91cd\u6784\u9891\u7387\u3002\u3002\uff08= =\u3002\u3002\u3002\u3002\uff09<\/p>\n

      \u968f\u7740 M \u7684\u589e\u5927\u9010\u6e10\u5411 O(nlogn) \u6536\u655b\uff08\u56e0\u4e3a\u6839\u636e \u89c2\u5bdf \u540e\u671f\u5757\u6570\u5f88\u5c11\u518d\u589e\u52a0\u3002\u3002\uff09
      \n\uff08\u7136\u540e\u8fd8\u4f1a \u5f88\u6162\u5f88\u6162 \u7684 \u5411 O(1) \u6536\u655b \u3002\u3002\u8003\u8651\u6240\u6709\u6570\u7684\u503c\u90fd\u4e00\u6837\u7684\u65f6\u5019\u3002\u3002\u5927\u6982\u968f\u673a\u60c5\u51b5\u4e0b\u8981\u8fdb\u884c\u4e00\u4e2a\u5929\u6587\u6570\u5b57\u6b21\u624d\u53ef\u80fd\u53d1\u751f\u5427\u3002\u54ce\u3002\u3002\u8981\u4f1a\u4e00\u70b9\u6982\u7387\u8bba\u5c31\u597d\u4e86\u554a\u3002\u3002\u3002\u3002\u3002\uff09<\/p>\n

      \n

      \u6211\u628a SPOJ \u7684\u65f6\u9650\u8bbe\u5b9a\u7684\u5f88\u3002\u3002\u3002\u559c\u6b22\u6d4b\u65f6\u95f4\u7684\u540c\u5b66\u8bf7\u79fb\u6b65\u3002\u3002
      \n\u4e0b\u9762\u7ed9\u51fa\u6807\u7a0b\u2461 \u3002\u3002\u3002<\/p>\n

      \u65b9\u6cd5\u662f\u3002\u3002\u3002\u5148\u5bf9\u6574\u4e2a\u6570\u5217\u6392\u4e00\u6b21\u5e8f\u3002\u3002\u7136\u540e\u4f7f\u7528\u4e0b\u9762\u8fd9\u4e2a\u4e1c\u897f\u4fdd\u5b58\u5206\u5757\u3002\u3002\u3002
      \n\u53ef\u4ee5\u652f\u6301\u539f\u5730\u7684\u4e8c\u5206\u67e5\u627e\u3002\u3002<\/p>\n

      \r\nstruct Link{\r\n    int a, b, d;\r\n\r\n    Link(){}\r\n    Link(int _a, int _b, int _d):a(_a), b(_b), d(_d){};\r\n    void Split();\r\n    int Stat();\r\n} L[N]; int sz;\r\n<\/pre>\n
      \u5176\u4e2d a, b \u8868\u793a\u8fd9\u4e2a\u5206\u5757\u7684\u533a\u95f4\uff0c\u5de6\u95ed\u53f3\u5f00 [ )\u3002\u3002
      \n\u3002\u3002\u3002<\/p>\n
      \u7136\u540e\u5c31\u53ef\u4ee5\u7ef4\u62a4\u4e86\u3002\u3002
      \n\u8fd9\u4e2a\u65b9\u6cd5\u5e38\u6570\u5f88\u5c0f\u3002\u3002\u3002\uff08\u4e0d\u8fc7\u5206\u88c2\u7684\u65f6\u5019\u4f3c\u4e4e\u4f1a 3 \u5206\u3002\uff01\uff01\u3002\uff09<\/p>\n
      \u3002\u8fd9\u4e2a \u65b9\u6cd5\u5728 SPOJ \u53ef\u4ee5\u8dd1 14.54 s\u3002\u3002\u3002<\/p>\n
      \r\n\/* .................................................................................................................................. *\/\r\n\r\nconst int N = 250010, M = 1010, C = 1000000000;\r\nint A[N]; char cmd; int cnt;\r\nint n, m, a, b, l, r, d; int *_a, *_b;\r\n\r\nstruct Link{\r\n    int a, b, d;\r\n\r\n    Link(){}\r\n    Link(int _a, int _b, int _d):a(_a), b(_b), d(_d){};\r\n    void Split();\r\n    int Stat();\r\n} L[N]; int sz;\r\n\r\n#define FIX(x) int(x < -C ? -C : x > C ? C : x)\r\n#define GPS _a = lower_bound(A + a, A + b, FIX((LL)::l - d)), _b = upper_bound(A + a, A + b, FIX((LL)::r - d))\r\n\r\nvoid Link::Split(){\r\n\r\n    GPS, ::a = _a - A, ::b = _b - A;\r\n    if (::a == ::b || b < ::a || ::b < a) return;\r\n    int aa = max(::a, a), bb = min(::b, b);\r\n\r\n    if (a < aa) L[sz++] = Link(a, aa, d);\r\n    if (bb < b) L[sz++] = Link(bb, b, d);\r\n    a = aa, b = bb, d += ::d;\r\n}\r\n\r\nint Link::Stat(){\r\n    GPS; return _b - _a;\r\n}\r\n\r\nvoid Rebuild(){\r\n    REP(i, sz) FOR(j, L[i].a, L[i].b) A[j] += L[i].d;\r\n    sort(A, A+n), L[0] = Link(0, n, 0), sz = 1;\r\n}\r\n\r\n\/*\r\nvoid Patch(){\r\n\r\n    REP(i, sz){\r\n        FOR(j, L[i].a, L[i].b)\r\n            cout << A[j] + L[i].d << " ";\r\n    }\r\n    cout << endl;\r\n}*\/\r\n\r\n\r\nint main(){\r\n\r\n    \/\/freopen("in.txt", "r", stdin);\r\n    \/\/freopen("out.txt", "w", stdout);\r\n\r\n    RD(n, m); REP(i, n) RD(A[i]); sort(A, A+n);\r\n    L[0] = Link(0, n, 0), sz = 1;\r\n    int P = sqrt(n) \/ 11;\r\n\r\n    char cmd; REP(j, m){\r\n        scanf(" %c", &cmd);\r\n\r\n        if (cmd == 'C'){\r\n            RD(l, r, d); REP_C(i, sz) L[i].Split();\r\n            if (sz > P) Rebuild();\r\n            \/\/Patch();\r\n        }\r\n        else {\r\n            RD(l, r); cnt = 0; REP(i, sz) cnt += L[i].Stat();\r\n            OT(cnt);\r\n        }\r\n\r\n    }\r\n}\r\n<\/pre>\n
      \u3002\u5982\u4f55\u6784\u9020\u4e00\u4e2a\u6570\u636e\u53ef\u4ee5\u6740\u6389\u6240\u6709 std  \u5462\u3002\u3002
      \n\uff08\u3001\u8fd9\u4e2a\u95ee\u9898\u7559\u7ed9\u8bfb\u8005\u601d\u8003\u3002\u3002\uff09<\/p>\n
      External link :<\/h3>\n
      https:\/\/www.spoj.pl\/problems\/PS11A\/<\/a>
      \n      https:\/\/vjudge.net\/problem\/HDU-3971<\/a><\/p>\n
      http:\/\/acm.hit.edu.cn\/judge\/show.php?Proid=3054<\/a>
      \n      \u5757\u72b6\u7ed3\u6784\u79d2\u6740\u4e00\u5207\uff01 by WJMZBMR <\/a><\/p>\n","protected":false},"excerpt":{"rendered":"
      \uff08\u7531\u4e8e\u88ab fgd BS \u4e86\u82f1\u6587\u3002\u3002\u6211\u628a\u9898\u76ee\u80cc\u666f\u90fd\u5220\u4e86\u3002\u3002\uff09 Brief description : You are given a sequence A[1], A[2],…, A[N]. On this sequence you have to apply M operations: Add all the elements whose value are in range [l, r] by d or, ask for a query how many element are in range [l, r]. ( 1\u2264 N \u2264 250,000, […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[21],"tags":[],"class_list":["post-61","post","type-post","status-publish","format-standard","hentry","category-spoj"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-Z","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/61","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/comments?post=61"}],"version-history":[{"count":0,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/61\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=61"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=61"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=61"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}