{"id":840,"date":"2013-10-17T13:38:48","date_gmt":"2013-10-17T05:38:48","guid":{"rendered":"http:\/\/www.shuizilong.com\/house\/?p=840"},"modified":"2013-10-17T22:44:57","modified_gmt":"2013-10-17T14:44:57","slug":"codeforces-round-207","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/codeforces-round-207\/","title":{"rendered":"Codeforces Round #207"},"content":{"rendered":"

<\/p>\n

Problem A. Knight Tournament<\/h2>\n

Brief description: <\/h3>\n

\u7565\uff09<\/p>\n

Analysis: <\/h3>\n

\u3002\u3002\u76f4\u63a5\u7ebf\u6bb5\u6811\u4e86\u3002\u3002\uff08\u4f3c\u4e4e\u6709\u7b80\u5355\u4e00\u4e9b\u7684\u65b9\u6cd5\u3002\u3002\u4f46\u662f\u4e0d\u613f\u610f\u52a8\u8111\u7b4b\u3002\u3001\u3001\u3002\u3002
\nhttp:\/\/codeforces.com\/contest\/356\/submission\/4791519<\/a><\/p>\n

Problem B. Xenia and Hamming<\/h2>\n

Brief description: <\/h3>\n

\u7565\uff09<\/p>\n

Analysis: <\/h3>\n

\u65e2\u7136\u8981\u957f\u5ea6\u76f8\u7b49\u3002\u90a3\u4e48\u80af\u5b9a\u662f lcm \u7684\u6574\u6570\u500d\u3002\u3002\u4e5f\u5c31\u662f\u8981\u7edf\u8ba1\u51fa\u4e00\u6bb5 lcm \u7684\u7ed3\u679c\u5c31\u884c\u4e86\u3002\u3002
\n\u8003\u5bdf gcd = 1 \u7684\u65f6\u5019\u3002\u3002\u90a3\u4e48\u663e\u7136\u6bcf\u4e2a\u5b57\u7b26\u4f1a\u8dd1\u904d\u6bcf\u4e00\u4e2a\u4f4d\u7f6e\u3002\u4e4b\u540e\u5c31\u80fd yy \u51fa\u4e00\u822c\u60c5\u51b5\u7684\u505a\u6cd5\u4e86\u3002\u3002\u3002<\/p>\n

\r\nI =->{gets.split.map &:to_i}\r\n\r\nn, m = I[]; a = gets.chomp; b = gets.chomp\r\ndd = a.size.gcd(b.size); mm = a.size.lcm(b.size); nn = a.size*n; ss = 0\r\nc = Array.new(dd){Array.new(128, 0)}\r\n0.upto(a.size-1){|i|c[i%dd][a[i].ord] += 1}\r\n0.upto(b.size-1){|i|ss += c[i%dd][b[i].ord]}\r\np nn-ss*nn\/mm\r\n<\/pre>\n
http:\/\/codeforces.com\/contest\/356\/submission\/4810357<\/a><\/p>\n
Problem C. Compartments<\/h2>\n
Brief description: <\/h3>\n
\u5c0f\u4f19\u4f34\u4eec\u5206\u5e03\u5728\u4e00\u4e9b\u8f66\u53a2\u4e2d\uff0c\u6bcf\u8282\u8f66\u53a2\u91cc\u53ef\u4ee5\u662f 0\u30011\u30012\u30013\u30014<\/code> \u4e2a\u4eba\u3002\u5982\u679c\u4e00\u8282\u8f66\u53a2\u6709 3<\/code> \u6216 4<\/code> \u4e2a\u4eba\u90a3\u4e48\u8fd9\u8282\u8f66\u53a2\u4f1a\u5145\u6ee1\u5feb\u6d3b\u7684\u7a7a\u6c14\u3002\u3002\u3002\u95ee\u81f3\u5c11\u79fb\u52a8\u51e0\u4e2a\u4eba\uff0c\u53ef\u4ee5\u4ee4\u6240\u6709\u8f66\u53a2\u90fd\u5145\u6ee1\u5feb\u6d3b\u7684\u7a7a\u6c14\u3002\u3002\u3002\uff08\u6216\u8005\u65e0\u89e3\u65f6\u8f93\u51fa\u65e0\u89e3\u3002\u3002\uff09<\/p>\n
Analysis: <\/h3>\n
\u663e\u7136 1, 2, 5<\/code> \u65f6\u662f\u65e0\u89e3\u7684\u3002\u3002\u7ecf\u8fc7\u4e00\u756a\u52aa\u529b\u3002\u3002\u6211\u4eec\u53d1\u73b0\u8fd9\u8fd9\u4e9b\u5c31\u662f\u65e0\u89e3\u7684\u5168\u90e8\u60c5\u51b5\u3002\u3002\u663e\u7136\u8981\u4ece\u843d\u5355\u7684\u4eba\u5f00\u59cb\u4e0b\u624b\u3002\u3002
\n\u3002\u3002\u8bbe d = min(c1, c2)<\/code> \u3002\u3002\u663e\u7136\u8fd9 d<\/code> \u4e2a\u4eba\u662f\u4ece c1 -> c2<\/code> \u7684\u3002\u3002\u3002\u4e4b\u540e\u8ba8\u8bba\u3002\u3002
\n\u5982\u679c d == c2<\/code>\u3002\u3002\u90a3\u4e48\u591a\u51fa\u6765\u90a3 c1<\/code> \u4e2a\u4eba\uff0c\u80af\u5b9a\u4e09\u4e2a\u4e09\u4e2a\u914d\u5bf9\u3002\u3002\u82e5\u6709\u4f59\u6570\uff0c\u5982\u679c\u4f59\u6570\u662f 1 \u4e14\u6709 3 \u4eba\u7684\u3002\u3002\u5219\u518d\u52a0\u4e00\u5426\u5219\u52a0\u4e8c\u3002\u3002\u3002
\nd == c1<\/code> \u60c5\u51b5\u7c7b\u4f3c\u3002<\/p>\n
\r\nI =->{gets.split.map &:to_i}\r\n\r\ndef f\t\r\n\tgets; a = I[]; c1 = a.count(1); c2 = a.count(2); c3 = a.count(3); c4 = a.count(4)\r\n\ts = c1+2*c2+3*c3+4*c4; return -1 if (s == 1 || s == 2 || s == 5)\r\n\r\n\tz = d = [c1, c2].min; c1 -= d; c2 -= d; c3 += d\r\n\tif !c1.zero? then\r\n\t\tz += 2*(d=c1\/3); c1 -= d*3; c3 += d\r\n\t\tz += c1.zero? ? 0 : (c1 == 1 && !c3.zero? ? 1 : 2)\r\n\telsif !c2.zero? then\r\n\t\tz += 2*(d=c2\/3); c2 -= d*3\r\n\t\tz += c2.zero? ? 0 : (c2 == 1 && !c4.zero? ? 1 : 2)\r\n\tend\r\n\r\n\treturn z\r\nend\r\n\r\np f()\r\n<\/pre>\n
http:\/\/codeforces.com\/contest\/356\/submission\/4810189<\/a><\/p>\n
Problem D. Bags and Coins<\/h2>\n
Brief description: <\/h3>\n
\u6784\u9020 n<\/code> \u4e2a\u7ed3\u70b9\u7684\u68ee\u6797\uff0c\u4f7f\u5f97\u603b\u7684\u6743\u503c\u548c\u4e3a s<\/code>\u3002\u3002
\n\u5e76\u4e14\u4ee5\u6bcf\u4e2a\u7ed3\u70b9\u4e3a\u6839\u7684\u5b50\u6811\u7684\u6743\u503c\u548c\u6070\u4e3a ai<\/code>\u3002<\/p>\n
Analysis: <\/h3>\n
\u3002\u3002\u3002\u771f\u00b7\u50bb\u903c\u9898\u3002\u3002 \u590d\u6742\u5ea6\u662f O(n2\/32)<\/code> \u3002\u3002\u3002
\n\u3002\u3002\u663e\u7136\u65b9\u6848\u6ee1\u8db3\u6240\u6709\u6839\u7ed3\u70b9\u7684 $$!\\sum_{i=1}^n a_i = s$$\u3002
\n\u3002\u3002\u7136\u540e\u5c31\u662f\u4e00\u4e2a\u80cc\u5305\u3002\u3002\u3002\u56e0\u4e3a\u9700\u8981\u6784\u9020\u65b9\u6848\u3002\u8fd8\u8981\u4e25\u683c\u63a7\u5236\u5e73\u65b9\u540e\u9762\u7684\u5e38\u6570\u3002\u3002\u3002\u6240\u4ee5\u597d\u50cf\u8fde bitset<\/code> \u90fd\u6ca1\u6cd5\u7528\u4e86\u3002\u3002\u53ea\u80fd\u624b\u5199\u3002\u3002\u3002
\n\u3002\u3002\u90a3\u4e9b 40ms \u8fc7\u7684\u3002\u3002\u4f3c\u4e4e\u662f hash \u80cc\u5305 + \u5947\u602a\u7684\u526a\u679d\u3002\u3002\u3002\u3002<\/p>\n
\u6ce8\u610f\u6ce8\u610f\u6ce8\u610f\uff01\u3002\u3002 <\/p>\n
    \n
  1. 1<<31  is undefined \u3002\u3002\uff08so always use 1u << 31<\/li>\n
  2. x>>32 is undefined \u3002\u3002\uff08so \u7279\u5224\u3002\u3002<\/li>\n<\/ol>\n
    http:\/\/codeforces.com\/contest\/356\/submission\/4809700<\/a><\/p>\n
    Problem E. Xenia and String Problem<\/h2>\n
    Brief description: <\/h3>\n
    \u3002\u3002\u4e00\u4e2a\u5b50\u4e32\u88ab\u79f0\u4e3a\u662f G-\u5b50\u4e32<\/code>\u3002\u3002\u5982\u679c.. .<\/p>\n
      \n
    1. odd<\/code>…\uff08\u957f\u5ea6\u4e3a\u5947\u6570 <\/li>\n
    2. GxG<\/code>.. \uff08\u5de6\u53f3\u4e24\u534a\u90fd\u662f G-\u5b50\u4e32<\/code> \u4e14\u76f8\u540c\u3002\u3002\u4e2d\u95f4\u662f\u4e00\u4e2a\u4efb\u610f\u5b57\u7b26\u3002\u3002\u4e8e\u662f\u5176\u5b9e\u6761\u4ef6 1 \u591a\u4f59\u3002\u3002\u3002\u3002<\/li>\n
    3. x<\/code> \u4e0d\u66fe\u5728 G<\/code> \u4e2d\u51fa\u73b0\u3002<\/li>\n<\/ol>\n
      \u3002\u3002\u7ed9\u5b9a\u4e00\u6bb5\u6587\u672c\uff0c\u4f60\u53ef\u4ee5\u81f3\u591a\u4fee\u6539\u5176\u4e2d\u7684\u4e00\u4e2a\u5b57\u7b26\uff0c\u95ee\u6700\u5927\u7684 G-\u5b50\u4e32 \u7684\u957f\u5ea6\u7684\u5e73\u65b9\u548c\u3002<\/p>\n
      Analysis: <\/h3>\n
      .\u9996\u5148\uff0cG-\u5b50\u4e32<\/code> \u7684\u957f\u5ea6\u5448 1\u30013\u30017 … 2^n – 1 \u51e0\u4f55\u589e\u957f\u3002
      \n\u663e\u7136\u53ef\u4ee5\u679a\u4e3e\u957f\u5ea6\u66b4\u529b hash<\/code> \u5148\u628a\u4e0d\u4fee\u6539\u7684\u7edf\u8ba1\u51fa\u6765\u3002\u3002\u3002\uff08\u636e\u51fa\u9898\u4eba\u8bf4\u5b58\u5728\u4e0d\u7528 hash<\/code> \u7684\u65b9\u6cd5\u3002\u3002\u6211\u731c\u662f\u6539 Manacher<\/code>\u3002\u3002\u6709\u5f85\u7814\u7a76\u3002\u3002<\/p>\n
      \u8bbe G[lv][i] \u8868\u793a\u4ee5 i \u4e3a\u4e2d\u5fc3\u662f\u5426\u6784\u6210\u4e00\u4e2a lv \u9636\u7684 G \u5b50\u4e32\u3002\u3002
      \n\u3002\u3002\u8003\u8651\u4fee\u6539\u4e00\u4e2a\u5b57\u7b26\u3002\u3002\u4f1a\u9020\u6210\u4e24\u79cd\u5f71\u54cd\u3002\u3002<\/p>\n
      \u7b2c\u4e00\u79cd\u5bf9\u4e8e\u8de8\u8d8a\u4e86\u8fd9\u4e2a\u5b57\u7b26\u7684\u4e00\u7ec4 G-\u5b50\u4e32\u73b0\u5728\u5c06\u4f1a\u5931\u6548\uff0c\u9700\u8981\u8ba1\u5165\u635f\u5931\u3002
      \n\u3002\u5bf9\u4e8e\u90a3\u4e9b \u51c6-G \u5b50\u4e32\u3002\u3002\u53ef\u80fd\u7ecf\u8fc7\u4e00\u6b21\u4fee\u6539\u53d8\u6210 G-\u5b50\u4e32\uff0c\u5f97\u5230\u6536\u76ca\u3002<\/p>\n
      \u524d\u8005\u662f\u4e00\u4e2a\u533a\u95f4\u4fee\u6539\uff0c\u5355\u70b9\u8be2\u95ee\u7684\u95ee\u9898\u3002\u3002\u4f46\u662f\u53ea\u5728\u6700\u540e\u7edf\u8ba1\uff0c\u53ef\u4ee5\u5f88\u7b80\u5355\u7684\u79bb\u7ebf\u3002
      \n\u5bf9\u4e8e\u540e\u8005\u3002\u3002\u9700\u8981\u5728\u7528 hash \u5f97\u5230 G[][] \u7684\u65f6\u5019\uff0c\u987a\u4fbf\u4e8c\u5206\u51fa\u90a3\u4e24\u4e2a\u4e0d\u76f8\u540c\u7684\u4f4d\u7f6e\u3002\uff08\u5982\u679c\u6070\u6709\u4e00\u4f4d\u4e0d\u76f8\u540c\u7684\u8bdd\u3002\u3002\u3002<\/p>\n
      \r\nconst int N = int(1e5) + 9, C = 27, LN = 18;\r\n\r\nuLL P[N], S[N]; char str[N]; int prd[C][N], suc[C][N]; int n;\r\nLL F[C][N], FF[N]; bool G[LN][N]; LL ans0;\r\n\r\ninline uint h(int l, int r){\r\n    --l; return S[r]-S[l]*P[r-l];\r\n}\r\n\r\ninline bool d1(int l1, int r1, int l2, int r2, int &p1, int &p2){\r\n\r\n    while (l1 < r1){\r\n        int m1 = l1 + r1 >> 1, m2 = l2 + r2 >> 1;\r\n        if (h(l1, m1) != h(l2, m2) && h(m1+1, r1) != h(m2+1, r2)) return 0;\r\n        if (h(l1, m1) != h(l2, m2)) r1 = m1, r2 = m2; else l1 = m1 + 1, l2 = m2 + 1;\r\n    }\r\n\r\n    p1 = l1, p2 = l2;\r\n    return 1;\r\n}\r\n\r\ninline int prdd(int i, int p){\r\n    return prd[str[i]][i] == p ? prd[str[i]][p] : prd[str[i]][i];\r\n}\r\ninline int succ(int i, int p){\r\n    return suc[str[i]][i] == p ? suc[str[i]][p] : suc[str[i]][i];\r\n}\r\n\r\n\r\nint main(){\r\n\r\n#ifndef ONLINE_JUDGE\r\n    freopen("in.txt", "r", stdin);\r\n    \/\/freopen("out.txt", "w", stdout);\r\n#endif\r\n\r\n    ans0 = n = strlen(RS(str+1)), P[0] = 1; REP_1(i, n) str[i] -= 'a', P[i] = P[i-1]*C, S[i] = S[i-1]*C+str[i]+1, G[0][i] = 1;\r\n\r\n    REP(c, C) prd[c][1] = 0; FOR_1(i, 2, n){\r\n        REP(c, C) prd[c][i] = prd[c][i-1];\r\n        prd[str[i-1]][i] = i-1;\r\n    }\r\n\r\n    REP(c, C) suc[c][n] = n+1; DWN(i, n, 1){\r\n        REP(c, C) suc[c][i] = suc[c][i+1];\r\n        suc[str[i+1]][i] = i+1;\r\n    }\r\n\r\n    for (int lv=1,lxl=3,l=1,_l=0,p1,p2;lxl<=n;_l=l,l=lxl,lxl=(l<<1)+1,++lv){\r\n        FOR_1(i0, l+1, n-l){\r\n            int l0 = i0-_1(lv-1), r0=i0+_1(lv-1); LL ll = sqr((LL)lxl);\r\n            if (G[lv-1][l0] && G[lv-1][r0] && h(l0-_l, l0+_l) == h(r0-_l, r0+_l)){\r\n                REP(c, C) if (prd[c][i0] < l0-_l && r0+_l < suc[c][i0]){\r\n                    if (c == str[i0]) G[lv][i0] = 1, ans0 += ll, FF[l0-_l] -= ll, FF[r0+_l+1] += ll;\r\n                    else F[c][i0] += ll;\r\n                }\r\n            }\r\n            else if (d1(l0-_l, l0+_l, r0-_l, r0+_l, p1, p2)){\r\n                if (G[lv-1][r0] && prdd(i0, p1) < l0-_l && r0+_l < suc[str[i0]][i0]){\r\n                    F[str[p2]][p1] += ll;\r\n                }\r\n                if (G[lv-1][l0] && prd[str[i0]][i0] < l0-_l && r0+_l < succ(i0, p2)){\r\n                    F[str[p1]][p2] += ll;\r\n                }\r\n            }\r\n        }\r\n    }\r\n\r\n    \/\/OT(ans0);\r\n\r\n    LL bonus = 0, ff = 0; REP_1(i, n){\r\n        ff += FF[i]; REP(c, C) checkMax(bonus, ff + F[c][i]);\r\n    }\r\n\r\n    OT(ans0 + bonus);\r\n}\r\n\r\n<\/pre>\n
      http:\/\/codeforces.com\/contest\/356\/submission\/4814590<\/a><\/p>\n
      \u7efc\u4e0a\u6240\u8ff0\uff0c\u6211\u4eec\u6574\u7406\u5982\u4e0b\uff1a<\/p>\n
      \u9996\u5148\u5199\u5b57\u7b26\u4e32 hash \u76f8\u5173\u3002\u3002\u518d\u8005\u6211\u4eec\u9700\u8981\u6c42\u6bcf\u4e2a\u4f4d\u7f6e\u524d\u9762\u4e00\u4e2a\u3001\u548c\u540e\u9762\u4e00\u4e2a\u548c\u5b83\u76f8\u540c\u7684\u5b57\u7b26\u7684\u4f4d\u7f6e\u3002\uff08prd\uff0csuc\u3002\u3002
      \n\u3002\u3002\u56e0\u4e3a\u6709\u4fee\u6539\u64cd\u4f5c\uff0c\u8fdb\u4e00\u6b65\u6211\u4eec\u9700\u8981\u6c42\u51fa\u3002\u6bcf\u4e2a\u4f4d\u7f6e\u5982\u679c\u5b83\u662f\u67d0\u4e2a\u5b57\u7b26\u65f6\u524d\u3001\u540e\u548c\u5b83\u76f8\u540c\u7684\u4f4d\u7f6e\u3002\u3002\u3002
      \nans0 \u8868\u793a\u4e0d\u4fee\u6539\u65f6\u7684\u7b54\u6848\uff0cF[][] \u8868\u793a\u4fee\u6539\u5b57\u7b26\u4ea7\u751f\u7684\u6536\u76ca\uff0cFF[] \u7edf\u8ba1\u635f\u5931\u3002<\/p>\n
      d1(l1,r1,l2,r2,p1,p2) \u8868\u793a\u662f\u5426 [l1, r1] \u4e0e [l2, r2] \u8fd9\u4e00\u6bb5\u53ea\u6709\u4e00\u4e2a\u5b57\u7b26\u4e0d\u76f8\u540c\uff0c\u5982\u679c\u662f\uff0c
      \n\u5219\u7528 p1, p2 \u5e26\u51fa\u4e24\u8fb9\u7684\u4e0b\u6807\uff0c\u5728\u8ba8\u8bba p1 \u8986\u76d6 p2 \u548c p2 \u8986\u76d6 p1 \u8fd9\u4e24\u79cd\u60c5\u51b5\u3002
      \n\u6ce8\u610f\u56e0\u4e3a\u66ff\u6362\u4e86\u4e00\u4e2a\u5b57\u7b26\uff0c\u6240\u4ee5 prd \u8981\u7b80\u5355\u8c03\u6574\u3002\u3002<\/p>\n
      \u4ee5 p2 \u8986\u76d6 p1 \u4e3a\u4f8b\uff0c\u8fd9\u91cc\u5199\u505a prdd(i0, p1) \u8868\u793a p1 \u8fd9\u4e2a\u5b57\u7b26\u7684\u4f4d\u7f6e\u5b9e\u9645\u4e0a\u88ab\u66ff\u6362\u4e86\u3002\u3002\u3002
      \n\u6ce8\u610f\u6211\u4eec\u53ea\u662f\u7b80\u5355\u7684\u8003\u8651 p1 \u6240\u5728\u4f4d\u7f6e\u7684\u5b57\u7b26\u88ab\u5220\u53bb\uff0c\u56e0\u4e3a\u8fd9\u4e2a\u65f6\u5019\u5982\u679c\u66ff\u6362\u7684\u5b57\u7b26\u4ea7\u751f\u4e86\u65b0\u7684\u963b\u788d\u90a3\u4e48\u5728\u53f3\u534a\u6bb5\u80af\u5b9a\u5df2\u7ecf\u53d1\u751f\u8fc7\u4e86\u3002<\/p>\n
      External link: <\/h3>\n
      http:\/\/codeforces.com\/contest\/356<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"","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":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[18],"tags":[],"class_list":["post-840","post","type-post","status-publish","format-standard","hentry","category-codeforces"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-dy","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/840","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=840"}],"version-history":[{"count":0,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/840\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=840"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=840"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=840"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}