{"id":113706,"date":"2026-10-07T07:42:50","date_gmt":"2026-10-06T23:42:50","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/113706.html"},"modified":"2026-10-07T07:42:50","modified_gmt":"2026-10-06T23:42:50","slug":"uva-12656-almost-palindrome","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/113706.html","title":{"rendered":"UVa 12656 Almost Palindrome"},"content":{"rendered":"

\u9898\u76ee\u63cf\u8ff0<\/h3>\n

\u7ed9\u5b9a\u4e00\u884c\u6587\u672c，\u627e\u51fa\u5176\u4e2d\u6700\u957f\u7684 \u201c\u51e0\u4e4e\u56de\u6587\u201d \u5b50\u4e32\u3002\u4e00\u4e2a\u5b57\u7b26\u4e32 SS<\/span><\/span>S<\/span><\/span><\/span><\/span><\/span> \u88ab\u79f0\u4e3a \u201c\u51e0\u4e4e\u56de\u6587\u201d ，\u5982\u679c\u6ee1\u8db3：<\/p>\n

  • SS<\/span><\/span>S<\/span><\/span><\/span><\/span><\/span> \u4ee5\u5b57\u6bcd\u5f00\u5934\u5e76\u4ee5\u5b57\u6bcd\u7ed3\u5c3e；<\/li>\n
  • \u5c06 SS<\/span><\/span>S<\/span><\/span><\/span><\/span><\/span> \u4e2d\u6240\u6709\u975e\u5b57\u6bcd\u5b57\u7b26\u5220\u9664\u5e76\u5c06\u6240\u6709\u5b57\u6bcd\u8f6c\u4e3a\u5c0f\u5199\u540e\u5f97\u5230 a(S)a(S)<\/span><\/span>a<\/span>(<\/span>S<\/span>)<\/span><\/span><\/span><\/span><\/span> ，\u5c06 a(S)a(S)<\/span><\/span>a<\/span>(<\/span>S<\/span>)<\/span><\/span><\/span><\/span><\/span> \u53cd\u8f6c\u540e\u5f97\u5230 b(S)b(S)<\/span><\/span>b<\/span>(<\/span>S<\/span>)<\/span><\/span><\/span><\/span><\/span> ，\u4e24\u8005\u5728\u6700\u591a 2k2k<\/span><\/span>2<\/span>k<\/span><\/span><\/span><\/span><\/span> \u4e2a\u4f4d\u7f6e\u4e0a\u5b57\u7b26\u4e0d\u540c\u3002<\/li>\n

    \u4f8b\u5982，\u5f53 k=1k = 1<\/span><\/span>k<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u65f6，"Race cat" \u662f\u51e0\u4e4e\u56de\u6587，\u56e0\u4e3a a(S)="racecat"a(S) = \\\\text{"racecat"}<\/span><\/span>a<\/span>(<\/span>S<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>"racecat"<\/span><\/span><\/span><\/span><\/span><\/span> ，b(S)="tacecar"b(S) = \\\\text{"tacecar"}<\/span><\/span>b<\/span>(<\/span>S<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>"tacecar"<\/span><\/span><\/span><\/span><\/span><\/span> ，\u5b83\u4eec\u6b63\u597d\u6709 22<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u4e2a\u4f4d\u7f6e\u4e0d\u540c\u3002<\/p>\n

    \u8f93\u5165\u683c\u5f0f<\/h3>\n

    \u8f93\u5165\u5305\u542b\u6700\u591a 2525<\/span><\/span>25<\/span><\/span><\/span><\/span><\/span> \u4e2a\u6d4b\u8bd5\u7528\u4f8b\u3002\u6bcf\u4e2a\u6d4b\u8bd5\u7528\u4f8b\u4e24\u884c：<\/p>\n

      \n
    • \u7b2c\u4e00\u884c\u662f\u4e00\u4e2a\u6574\u6570 kk<\/span><\/span>k<\/span><\/span><\/span><\/span><\/span>（0\u2264k\u22642000 \\\\le k \\\\le 200<\/span><\/span>0<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>k<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>200<\/span><\/span><\/span><\/span><\/span>）；<\/li>\n
    • \u7b2c\u4e8c\u884c\u662f\u4e00\u4e2a\u5b57\u7b26\u4e32，\u957f\u5ea6\u4e0d\u8d85\u8fc7 10001000<\/span><\/span>1000<\/span><\/span><\/span><\/span><\/span> \u4e2a\u5b57\u7b26（\u4e0d\u542b\u6362\u884c\u7b26），\u81f3\u5c11\u5305\u542b\u4e00\u4e2a\u5b57\u6bcd\u3002\u5b57\u7b26\u4e32\u53ea\u5305\u542b\u5b57\u6bcd\u3001\u7a7a\u683c\u548c\u5176\u4ed6\u53ef\u6253\u5370\u5b57\u7b26（\u5982 , \u6216 . \u7b49），\u4e14\u4e0d\u4f1a\u4ee5\u7a7a\u767d\u5b57\u7b26\u5f00\u5934\u3002<\/li>\n<\/ul>\n

      \u8f93\u51fa\u683c\u5f0f<\/h3>\n

      \u5bf9\u4e8e\u6bcf\u4e2a\u6d4b\u8bd5\u7528\u4f8b，\u8f93\u51fa\u4e00\u884c，\u683c\u5f0f\u4e3a Case x: L P ，\u5176\u4e2d xx<\/span><\/span>x<\/span><\/span><\/span><\/span><\/span> \u662f\u6d4b\u8bd5\u7528\u4f8b\u7f16\u53f7（\u4ece 11<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u5f00\u59cb），LL<\/span><\/span>L<\/span><\/span><\/span><\/span><\/span> \u662f\u6700\u957f\u51e0\u4e4e\u56de\u6587\u5b50\u4e32\u7684\u957f\u5ea6，PP<\/span><\/span>P<\/span><\/span><\/span><\/span><\/span> \u662f\u8be5\u5b50\u4e32\u7684\u8d77\u59cb\u4f4d\u7f6e（\u4ece 11<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u5f00\u59cb\u8ba1\u6570）\u3002\u5982\u679c\u6709\u591a\u4e2a\u957f\u5ea6\u76f8\u540c\u7684\u6700\u957f\u5b50\u4e32，\u8f93\u51fa\u8d77\u59cb\u4f4d\u7f6e\u6700\u5c0f\u7684\u90a3\u4e2a\u3002<\/p>\n

      \u6837\u4f8b<\/h3>\n

      \u8f93\u5165<\/p>\n

      1
      \nWow, it is a Race cat!
      \n0
      \nabcdcfg
      \n0
      \nKitty: Madam, I'm adam.<\/p>\n

      \u8f93\u51fa<\/p>\n

      Case 1: 8 3
      \nCase 2: 1 1
      \nCase 3: 15 8<\/p>\n

      \u9898\u76ee\u5206\u6790<\/h3>\n

      \u672c\u9898\u7684\u6838\u5fc3\u662f：\u5728\u7ed9\u5b9a\u6587\u672c\u4e2d，\u627e\u51fa\u4e00\u4e2a\u5b50\u4e32，\u5176\u5b57\u6bcd\u5e8f\u5217\u4e0e\u53cd\u8f6c\u540e\u7684\u5b57\u6bcd\u5e8f\u5217\u5728\u76f8\u540c\u4f4d\u7f6e\u4e0a\u7684\u4e0d\u540c\u5b57\u7b26\u4e2a\u6570\u4e0d\u8d85\u8fc7 2k2k<\/span><\/span>2<\/span>k<\/span><\/span><\/span><\/span><\/span> \u3002\u5b50\u4e32\u5fc5\u987b\u540c\u65f6\u4ee5\u5b57\u6bcd\u5f00\u5934\u548c\u7ed3\u5c3e，\u4e14\u957f\u5ea6\u4ee5\u5176\u5728\u539f\u6587\u672c\u4e2d\u7684\u5b9e\u9645\u5b57\u7b26\u6570（\u5305\u62ec\u975e\u5b57\u6bcd）\u4e3a\u51c6\u3002<\/p>\n

      \u76f4\u63a5\u679a\u4e3e\u6240\u6709\u5b50\u4e32\u5e76\u5224\u65ad，\u9700\u8981 O(n3)O(n^3)<\/span><\/span>O<\/span>(<\/span>n<\/span><\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> \u6216 O(n2\u22c5L)O(n^2 \\\\cdot L)<\/span><\/span>O<\/span>(<\/span>n<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span><\/span><\/span>L<\/span>)<\/span><\/span><\/span><\/span><\/span> \u7684\u65f6\u95f4，\u5176\u4e2d nn<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span> \u4e3a\u539f\u4e32\u957f\u5ea6（\u22641000\\\\le 1000<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>1000<\/span><\/span><\/span><\/span><\/span>），\u867d\u7136 nn<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span> \u4e0d\u5927，\u4f46 O(n3)O(n^3)<\/span><\/span>O<\/span>(<\/span>n<\/span><\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> \u53ef\u80fd\u8d85\u65f6（\u6700\u574f 10910^9<\/span><\/span>1<\/span>0<\/span><\/span>9<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u91cf\u7ea7）\u3002\u6211\u4eec\u9700\u8981\u66f4\u9ad8\u6548\u7684\u65b9\u6cd5\u3002<\/p>\n

      \u89c2\u5bdf\u56de\u6587\u5224\u65ad\u7684\u672c\u8d28：\u53ea\u5173\u5fc3\u5b57\u6bcd\u5e8f\u5217\u7684\u5bf9\u79f0\u6027\u3002\u56e0\u6b64，\u53ef\u4ee5\u5148\u628a\u6240\u6709\u5b57\u6bcd\u63d0\u53d6\u51fa\u6765，\u8bb0\u5f55\u6bcf\u4e2a\u5b57\u6bcd\u5728\u539f\u4e32\u4e2d\u7684\u4f4d\u7f6e\u3002\u7136\u540e\u95ee\u9898\u8f6c\u5316\u4e3a：\u5728\u5b57\u6bcd\u5e8f\u5217\u4e2d\u627e\u5230\u8fde\u7eed\u533a\u95f4 [l,r][l, r]<\/span><\/span>[<\/span>l<\/span>,<\/span><\/span>r<\/span>]<\/span><\/span><\/span><\/span><\/span> ，\u4f7f\u5f97\u8be5\u533a\u95f4\u4e0e\u5176\u53cd\u8f6c\u7684\u5bf9\u5e94\u4f4d\u7f6e\u4e0d\u540c\u7684\u4e2a\u6570 diff(l,r)\u22642k\\\\textit{diff}(l, r) \\\\le 2k<\/span><\/span>diff<\/span><\/span>(<\/span>l<\/span>,<\/span><\/span>r<\/span>)<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>2<\/span>k<\/span><\/span><\/span><\/span><\/span> ，\u7136\u540e\u8ba1\u7b97\u5176\u5bf9\u5e94\u7684\u539f\u59cb\u957f\u5ea6 pos[r]\u2212pos[l]+1\\\\textit{pos}[r] – \\\\textit{pos}[l] + 1<\/span><\/span>pos<\/span><\/span>[<\/span>r<\/span>]<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>pos<\/span><\/span>[<\/span>l<\/span>]<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> ，\u5e76\u8bb0\u5f55\u6700\u5927\u7684\u539f\u59cb\u957f\u5ea6\u548c\u6700\u5c0f\u7684\u8d77\u59cb\u4f4d\u7f6e\u3002<\/p>\n

      \u89e3\u9898\u601d\u8def<\/h3>\n

      \u63d0\u53d6\u5b57\u6bcd\u4e0e\u4f4d\u7f6e\u6620\u5c04<\/h4>\n

      \u904d\u5386\u539f\u5b57\u7b26\u4e32，\u6bcf\u5f53\u9047\u5230\u5b57\u6bcd\u65f6，\u5c06\u5176\u8f6c\u6362\u4e3a\u5c0f\u5199，\u5b58\u5165\u6570\u7ec4 letters\\\\textit{letters}<\/span><\/span>letters<\/span><\/span><\/span><\/span><\/span><\/span> ，\u540c\u65f6\u5c06\u8be5\u5b57\u7b26\u5728\u539f\u4e32\u4e2d\u7684\u4e0b\u6807（00<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span>\u2011based）\u5b58\u5165\u6570\u7ec4 pos\\\\textit{pos}<\/span><\/span>pos<\/span><\/span><\/span><\/span><\/span><\/span> \u3002\u8fd9\u6837，\u539f\u4e32\u7684\u4efb\u610f\u5b50\u4e32\u82e5\u9996\u5c3e\u90fd\u662f\u5b57\u6bcd，\u5219\u5bf9\u5e94\u4e8e letters\\\\textit{letters}<\/span><\/span>letters<\/span><\/span><\/span><\/span><\/span><\/span> \u4e2d\u7684\u4e00\u6bb5\u8fde\u7eed\u533a\u95f4 [l,r][l, r]<\/span><\/span>[<\/span>l<\/span>,<\/span><\/span>r<\/span>]<\/span><\/span><\/span><\/span><\/span> ，\u5176\u539f\u59cb\u957f\u5ea6\u4e3a pos[r]\u2212pos[l]+1\\\\textit{pos}[r] – \\\\textit{pos}[l] + 1<\/span><\/span>pos<\/span><\/span>[<\/span>r<\/span>]<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>pos<\/span><\/span>[<\/span>l<\/span>]<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> ，\u8d77\u59cb\u4f4d\u7f6e\u4e3a pos[l]+1\\\\textit{pos}[l] + 1<\/span><\/span>pos<\/span><\/span>[<\/span>l<\/span>]<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u3002<\/p>\n

      \u8ba1\u7b97\u533a\u95f4\u5dee\u5f02\u6570<\/h4>\n

      \u6211\u4eec\u9700\u8981\u5feb\u901f\u5f97\u5230\u4efb\u610f\u533a\u95f4 [l,r][l, r]<\/span><\/span>[<\/span>l<\/span>,<\/span><\/span>r<\/span>]<\/span><\/span><\/span><\/span><\/span> \u7684\u5dee\u5f02\u6570 diff(l,r)\\\\textit{diff}(l, r)<\/span><\/span>diff<\/span><\/span>(<\/span>l<\/span>,<\/span><\/span>r<\/span>)<\/span><\/span><\/span><\/span><\/span> ，\u5b9a\u4e49\u4e3a\u533a\u95f4\u5185\u5bf9\u79f0\u4f4d\u7f6e（ii<\/span><\/span>i<\/span><\/span><\/span><\/span><\/span> \u4e0e r\u2212(i\u2212l)r – (i-l)<\/span><\/span>r<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>(<\/span>i<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>l<\/span>)<\/span><\/span><\/span><\/span><\/span> ）\u5b57\u7b26\u4e0d\u540c\u7684\u4e2a\u6570（\u6bcf\u4e2a\u4e0d\u540c\u4f4d\u7f6e\u8d21\u732e 11<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> ，\u6ce8\u610f\u5bf9\u79f0\u7684\u4e24\u4e2a\u4f4d\u7f6e\u5404\u7b97\u4e00\u4e2a，\u6545\u82e5 letters[l+i]\u2260letters[r\u2212i]\\\\textit{letters}[l+i] \\\\ne \\\\textit{letters}[r-i]<\/span><\/span>letters<\/span><\/span>[<\/span>l<\/span><\/span>+<\/span><\/span><\/span><\/span>i<\/span>]<\/span><\/span><\/span>\ue020<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>letters<\/span><\/span>[<\/span>r<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>i<\/span>]<\/span><\/span><\/span><\/span><\/span> ，\u5219\u8fd9\u4e24\u4e2a\u4f4d\u7f6e\u90fd\u4e0d\u540c，\u8d21\u732e 22<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> ）\u3002<\/p>\n

      \u6211\u4eec\u4f7f\u7528\u52a8\u6001\u89c4\u5212\u9884\u5904\u7406\u6240\u6709\u533a\u95f4\u7684\u5dee\u5f02\u6570\u3002\u8bbe dp[l][r]\\\\textit{dp}[l][r]<\/span><\/span>dp<\/span><\/span>[<\/span>l<\/span>]<\/span>[<\/span>r<\/span>]<\/span><\/span><\/span><\/span><\/span> \u8868\u793a\u533a\u95f4 [l,r][l, r]<\/span><\/span>[<\/span>l<\/span>,<\/span><\/span>r<\/span>]<\/span><\/span><\/span><\/span><\/span> \u4e0e\u5176\u53cd\u8f6c\u7684\u5dee\u5f02\u4f4d\u7f6e\u603b\u6570\u3002\u8f6c\u79fb\u5173\u7cfb\u5982\u4e0b：<\/p>\n

        \n
      • \u5f53\u533a\u95f4\u957f\u5ea6 len=1len = 1<\/span><\/span>l<\/span>e<\/span>n<\/span><\/span>=<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u65f6，dp[l][l]=0\\\\textit{dp}[l][l] = 0<\/span><\/span>dp<\/span><\/span>[<\/span>l<\/span>]<\/span>[<\/span>l<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> ；<\/li>\n
      • \u5f53 len\u22652len \\\\ge 2<\/span><\/span>l<\/span>e<\/span>n<\/span><\/span>\u2265<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u65f6，dp[l][r]=dp[l+1][r\u22121]+(letters[l]\u2260letters[r])\u00d72\\\\textit{dp}[l][r] = \\\\textit{dp}[l+1][r-1] + \\\\big( \\\\textit{letters}[l] \\\\ne \\\\textit{letters}[r] \\\\big) \\\\times 2<\/span><\/span>dp<\/span><\/span>[<\/span>l<\/span>]<\/span>[<\/span>r<\/span>]<\/span><\/span>=<\/span><\/span><\/span><\/span>dp<\/span><\/span>[<\/span>l<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span>]<\/span>[<\/span>r<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span>]<\/span><\/span>+<\/span><\/span><\/span><\/span>(<\/span><\/span>letters<\/span><\/span>[<\/span>l<\/span>]<\/span><\/span><\/span>\ue020<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><\/span><\/span><\/span>letters<\/span><\/span>[<\/span>r<\/span>]<\/span>)<\/span><\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> ，\u5176\u4e2d\u5f53 len=2len = 2<\/span><\/span>l<\/span>e<\/span>n<\/span><\/span>=<\/span><\/span><\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u65f6，dp[l+1][r\u22121]\\\\textit{dp}[l+1][r-1]<\/span><\/span>dp<\/span><\/span>[<\/span>l<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span>]<\/span>[<\/span>r<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>1<\/span>]<\/span><\/span><\/span><\/span><\/span> \u89c6\u4e3a 00<\/span><\/span>0<\/span><\/span><\/span><\/span><\/span> \u3002<\/li>\n<\/ul>\n

        \u6309\u533a\u95f4\u957f\u5ea6\u4ece\u5c0f\u5230\u5927\u8ba1\u7b97\u5373\u53ef\u3002\u7531\u4e8e\u5b57\u6bcd\u4e2a\u6570 mm<\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> \u4e0d\u8d85\u8fc7 10001000<\/span><\/span>1000<\/span><\/span><\/span><\/span><\/span> ，\u4e8c\u7ef4\u6570\u7ec4\u5927\u5c0f\u4e3a m\u00d7mm \\\\times m<\/span><\/span>m<\/span><\/span>\u00d7<\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> ，\u65f6\u95f4\u548c\u7a7a\u95f4\u5747\u53ef\u884c\u3002<\/p>\n

        \u679a\u4e3e\u6240\u6709\u5408\u6cd5\u533a\u95f4<\/h4>\n

        \u5bf9\u4e8e\u6bcf\u4e00\u5bf9 0\u2264l\u2264r<m0 \\\\le l \\\\le r < m<\/span><\/span>0<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>l<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>r<\/span><\/span><<\/span><\/span><\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> ，\u82e5 dp[l][r]\u22642k\\\\textit{dp}[l][r] \\\\le 2k<\/span><\/span>dp<\/span><\/span>[<\/span>l<\/span>]<\/span>[<\/span>r<\/span>]<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>2<\/span>k<\/span><\/span><\/span><\/span><\/span> ，\u5219\u8be5\u533a\u95f4\u5bf9\u5e94\u7684\u539f\u4e32\u5b50\u4e32\u662f\u4e00\u4e2a\u5408\u6cd5\u5019\u9009\u3002\u8ba1\u7b97\u5176\u539f\u59cb\u957f\u5ea6 curLen=pos[r]\u2212pos[l]+1\\\\textit{curLen} = \\\\textit{pos}[r] – \\\\textit{pos}[l] + 1<\/span><\/span>curLen<\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>pos<\/span><\/span>[<\/span>r<\/span>]<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>pos<\/span><\/span>[<\/span>l<\/span>]<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> \u548c\u8d77\u59cb\u4f4d\u7f6e curStart=pos[l]+1\\\\textit{curStart} = \\\\textit{pos}[l] + 1<\/span><\/span>curStart<\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>pos<\/span><\/span>[<\/span>l<\/span>]<\/span><\/span>+<\/span><\/span><\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> ，\u5e76\u66f4\u65b0\u5168\u5c40\u6700\u4f18\u89e3：\u4f18\u5148\u6bd4\u8f83\u957f\u5ea6，\u957f\u5ea6\u76f8\u540c\u65f6\u53d6\u8d77\u59cb\u4f4d\u7f6e\u66f4\u5c0f\u8005\u3002<\/p>\n

        \u6700\u7ec8\u8f93\u51fa\u6700\u4f18\u957f\u5ea6\u548c\u8d77\u59cb\u4f4d\u7f6e\u3002<\/p>\n

        \u590d\u6742\u5ea6\u5206\u6790<\/h4>\n
          \n
        • \u63d0\u53d6\u5b57\u6bcd：O(n)O(n)<\/span><\/span>O<\/span>(<\/span>n<\/span>)<\/span><\/span><\/span><\/span><\/span> ，\u5176\u4e2d nn<\/span><\/span>n<\/span><\/span><\/span><\/span><\/span> \u4e3a\u539f\u4e32\u957f\u5ea6\u3002<\/li>\n
        • DP \u8ba1\u7b97：O(m2)O(m^2)<\/span><\/span>O<\/span>(<\/span>m<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> ，mm<\/span><\/span>m<\/span><\/span><\/span><\/span><\/span> \u4e3a\u5b57\u6bcd\u4e2a\u6570，\u6700\u5927 10001000<\/span><\/span>1000<\/span><\/span><\/span><\/span><\/span> ，\u7ea6 10610^6<\/span><\/span>1<\/span>0<\/span><\/span>6<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u6b21\u64cd\u4f5c\u3002<\/li>\n
        • \u679a\u4e3e\u533a\u95f4：O(m2)O(m^2)<\/span><\/span>O<\/span>(<\/span>m<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> \u3002<\/li>\n
        • \u603b\u65f6\u95f4\u590d\u6742\u5ea6：O(n+m2)O(n + m^2)<\/span><\/span>O<\/span>(<\/span>n<\/span><\/span>+<\/span><\/span><\/span><\/span>m<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> ，\u7a7a\u95f4\u590d\u6742\u5ea6：O(m2)O(m^2)<\/span><\/span>O<\/span>(<\/span>m<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/span><\/span><\/span><\/span><\/span> ，\u5b8c\u5168\u53ef\u4ee5\u6ee1\u8db3\u9898\u76ee\u9650\u5236（\u6700\u591a 2525<\/span><\/span>25<\/span><\/span><\/span><\/span><\/span> \u4e2a\u6d4b\u8bd5\u7528\u4f8b）\u3002<\/li>\n<\/ul>\n

          \u4ee3\u7801\u5b9e\u73b0<\/h3>\n

          \/\/ Almost Palindrome<\/span>
          \n\/\/ UVa ID: 12656<\/span>
          \n\/\/ Verdict: Accepted<\/span>
          \n\/\/ Submission Date: 2026-06-24<\/span>
          \n\/\/ UVa Run Time: 0.020s<\/span>
          \n\/\/<\/span>
          \n\/\/ \u7248\u6743\u6240\u6709（C）2026，\u90b1\u79cb\u3002metaphysis # yeah dot net<\/span><\/p>\n

          #<\/span>include<\/span> <bits\/stdc++.h><\/span><\/span>
          \nusing<\/span> namespace<\/span> std;<\/span><\/p>\n

          int<\/span> main<\/span>(<\/span>)<\/span> {<\/span>
          \n ios::<\/span>sync_with_stdio<\/span>(<\/span>false<\/span>)<\/span>;<\/span>
          \n cin.<\/span>tie<\/span>(<\/span>nullptr<\/span>)<\/span>;<\/span><\/p>\n

          int<\/span> caseNo =<\/span> 0<\/span>,<\/span> k;<\/span>
          \n string line;<\/span>
          \n while<\/span> (<\/span>cin >><\/span> k)<\/span> {<\/span>
          \n getline<\/span>(<\/span>cin,<\/span> line)<\/span>;<\/span> \/\/ \u6d88\u8017\u6389 k \u540e\u7684\u6362\u884c\u7b26<\/span>
          \n getline<\/span>(<\/span>cin,<\/span> line)<\/span>;<\/span> \/\/ \u8bfb\u53d6\u539f\u5b57\u7b26\u4e32（\u53ef\u80fd\u542b\u7a7a\u683c）<\/span><\/p>\n

          vector<<\/span>char<\/span>><\/span> letters;<\/span> \/\/ \u5c0f\u5199\u5b57\u6bcd\u5e8f\u5217<\/span>
          \n vector<<\/span>int<\/span>><\/span> pos;<\/span> \/\/ \u6bcf\u4e2a\u5b57\u6bcd\u5728\u539f\u4e32\u4e2d\u7684\u4f4d\u7f6e（0\u2011based）<\/span>
          \n for<\/span> (<\/span>int<\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> (<\/span>int<\/span>)<\/span>line.<\/span>size<\/span>(<\/span>)<\/span>;<\/span> ++<\/span>i)<\/span>
          \n if<\/span> (<\/span>isalpha<\/span>(<\/span>line[<\/span>i]<\/span>)<\/span>)<\/span> {<\/span>
          \n letters.<\/span>push_back<\/span>(<\/span>tolower<\/span>(<\/span>line[<\/span>i]<\/span>)<\/span>)<\/span>;<\/span>
          \n pos.<\/span>push_back<\/span>(<\/span>i)<\/span>;<\/span>
          \n }<\/span><\/p>\n

          int<\/span> m =<\/span> letters.<\/span>size<\/span>(<\/span>)<\/span>;<\/span>
          \n vector<<\/span>vector<<\/span>int<\/span>>><\/span> dp<\/span>(<\/span>m,<\/span> vector<\/span><<\/span>int<\/span>><\/span><\/span><\/span>(<\/span>m,<\/span> 0<\/span>)<\/span>)<\/span>;<\/span><\/p>\n

          \/\/ \u6309\u957f\u5ea6\u9012\u589e\u8ba1\u7b97 dp[l][r]（\u5dee\u5f02\u4f4d\u7f6e\u603b\u6570）<\/span>
          \n for<\/span> (<\/span>int<\/span> len =<\/span> 1<\/span>;<\/span> len <=<\/span> m;<\/span> ++<\/span>len)<\/span>
          \n for<\/span> (<\/span>int<\/span> l =<\/span> 0<\/span>;<\/span> l +<\/span> len –<\/span> 1<\/span> <<\/span> m;<\/span> ++<\/span>l)<\/span> {<\/span>
          \n int<\/span> r =<\/span> l +<\/span> len –<\/span> 1<\/span>;<\/span>
          \n if<\/span> (<\/span>len ==<\/span> 1<\/span>)<\/span> dp[<\/span>l]<\/span>[<\/span>r]<\/span> =<\/span> 0<\/span>;<\/span>
          \n else<\/span> {<\/span>
          \n int<\/span> inner =<\/span> (<\/span>len ==<\/span> 2<\/span>)<\/span> ?<\/span> 0<\/span> :<\/span> dp[<\/span>l +<\/span> 1<\/span>]<\/span>[<\/span>r –<\/span> 1<\/span>]<\/span>;<\/span>
          \n dp[<\/span>l]<\/span>[<\/span>r]<\/span> =<\/span> inner +<\/span> (<\/span>letters[<\/span>l]<\/span> !=<\/span> letters[<\/span>r]<\/span> ?<\/span> 2<\/span> :<\/span> 0<\/span>)<\/span>;<\/span>
          \n }<\/span>
          \n }<\/span><\/p>\n

          int<\/span> bestLen =<\/span> 0<\/span>,<\/span> bestStart =<\/span> INT_MAX;<\/span>
          \n int<\/span> limit =<\/span> 2<\/span> *<\/span> k;<\/span>
          \n for<\/span> (<\/span>int<\/span> l =<\/span> 0<\/span>;<\/span> l <<\/span> m;<\/span> ++<\/span>l)<\/span>
          \n for<\/span> (<\/span>int<\/span> r =<\/span> l;<\/span> r <<\/span> m;<\/span> ++<\/span>r)<\/span>
          \n if<\/span> (<\/span>dp[<\/span>l]<\/span>[<\/span>r]<\/span> <=<\/span> limit)<\/span> {<\/span>
          \n int<\/span> curLen =<\/span> pos[<\/span>r]<\/span> –<\/span> pos[<\/span>l]<\/span> +<\/span> 1<\/span>;<\/span> \/\/ \u539f\u4e32\u4e2d\u8be5\u5b50\u4e32\u7684\u5b9e\u9645\u957f\u5ea6<\/span>
          \n int<\/span> curStart =<\/span> pos[<\/span>l]<\/span> +<\/span> 1<\/span>;<\/span> \/\/ \u8d77\u59cb\u4f4d\u7f6e（1\u2011based）<\/span>
          \n if<\/span> (<\/span>curLen ><\/span> bestLen ||<\/span> (<\/span>curLen ==<\/span> bestLen &&<\/span> curStart <<\/span> bestStart)<\/span>)<\/span> {<\/span>
          \n bestLen =<\/span> curLen;<\/span>
          \n bestStart =<\/span> curStart;<\/span>
          \n }<\/span>
          \n }<\/span><\/p>\n

          cout <<<\/span> "Case "<\/span> <<<\/span> ++<\/span>caseNo <<<\/span> ": "<\/span> <<<\/span> bestLen <<<\/span> " "<\/span> <<<\/span> bestStart <<<\/span> "\\\\n"<\/span>;<\/span>
          \n }<\/span>
          \n return<\/span> 0<\/span>;<\/span>
          \n}<\/span><\/p>\n

          \u603b\u7ed3<\/h3>\n

          \u672c\u9898\u7684\u5173\u952e\u5728\u4e8e：<\/p>\n

        • \u5c06\u975e\u5b57\u6bcd\u5b57\u7b26\u4e0e\u5b57\u6bcd\u5206\u79bb，\u53ea\u5173\u5fc3\u5b57\u6bcd\u5e8f\u5217，\u5e76\u8bb0\u5f55\u539f\u4f4d\u7f6e，\u4fbf\u4e8e\u8ba1\u7b97\u539f\u59cb\u5b50\u4e32\u957f\u5ea6\u548c\u8d77\u59cb\u4f4d\u7f6e\u3002<\/li>\n
        • \u4f7f\u7528\u52a8\u6001\u89c4\u5212\u9884\u5904\u7406\u6240\u6709\u533a\u95f4\u7684\u5dee\u5f02\u6570，\u907f\u514d\u91cd\u590d\u8ba1\u7b97，\u5c06\u5224\u65ad\u590d\u6742\u5ea6\u964d\u4e3a O(1)O(1)<\/span><\/span>O<\/span>(<\/span>1<\/span>)<\/span><\/span><\/span><\/span><\/span> \u6bcf\u4e2a\u533a\u95f4\u3002<\/li>\n
        • \u6ce8\u610f\u5dee\u5f02\u6570\u7684\u5b9a\u4e49：\u5bf9\u79f0\u7684\u4e24\u4e2a\u4e0d\u540c\u5b57\u7b26\u8d21\u732e 22<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> \u4e2a\u4e0d\u540c\u4f4d\u7f6e，\u800c\u975e 11<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span> ，\u8fd9\u662f\u5bb9\u6613\u51fa\u9519\u7684\u5730\u65b9\u3002<\/li>\n
        • \u679a\u4e3e\u6240\u6709\u5408\u6cd5\u533a\u95f4\u5e76\u66f4\u65b0\u7b54\u6848，\u540c\u65f6\u6ee1\u8db3\u957f\u5ea6\u4f18\u5148\u3001\u8d77\u59cb\u4f4d\u7f6e\u6b21\u4e4b\u7684\u6392\u5e8f\u8981\u6c42\u3002<\/li>\n

          \u8be5\u89e3\u6cd5\u5728 n\u22641000n \\\\le 1000<\/span><\/span>n<\/span><\/span>\u2264<\/span><\/span><\/span><\/span>1000<\/span><\/span><\/span><\/span><\/span> \u7684\u60c5\u51b5\u4e0b\u975e\u5e38\u9ad8\u6548，\u4ee3\u7801\u7b80\u6d01，\u6613\u4e8e\u5b9e\u73b0\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

          \u9898\u76ee\u63cf\u8ff0
          \n\u7ed9\u5b9a\u4e00\u884c\u6587\u672c，\u627e\u51fa\u5176\u4e2d\u6700\u957f\u7684 \u201c\u51e0\u4e4e\u56de\u6587\u201d \u5b50\u4e32\u3002\u4e00\u4e2a\u5b57\u7b26\u4e32 SSS \u88ab\u79f0\u4e3a \u201c\u51e0\u4e4e\u56de\u6587\u201d ，\u5982\u679c\u6ee1\u8db3：
          \nSSS \u4ee5\u5b57\u6bcd\u5f00\u5934\u5e76\u4ee5\u5b57\u6bcd\u7ed3\u5c3e；\u5c06 SSS \u4e2d\u6240\u6709\u975e\u5b57\u6bcd\u5b57\u7b26\u5220\u9664\u5e76\u5c06\u6240\u6709\u5b57\u6bcd\u8f6c\u4e3a\u5c0f\u5199\u540e\u5f97\u5230 a(S)a(S)a(S) ，\u5c06 a(S)a(S)a(S) \u53cd\u8f6c\u540e\u5f97\u5230 b(S)b(S)b(S) ，\u4e24\u8005\u5728\u6700\u591a 2k2k2k \u4e2a\u4f4d\u7f6e\u4e0a\u5b57\u7b26\u4e0d\u540c\u3002
          \n\u4f8b\u5982，\u5f53 k1k 1k1 \u65f6<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[55,427,4405],"topic":[],"class_list":["post-113706","post","type-post","status-publish","format-standard","hentry","category-server","tag-c","tag-427","tag-4405"],"yoast_head":"\nUVa 12656 Almost Palindrome - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/113706.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"UVa 12656 Almost Palindrome - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"\u9898\u76ee\u63cf\u8ff0 \u7ed9\u5b9a\u4e00\u884c\u6587\u672c，\u627e\u51fa\u5176\u4e2d\u6700\u957f\u7684 \u201c\u51e0\u4e4e\u56de\u6587\u201d \u5b50\u4e32\u3002\u4e00\u4e2a\u5b57\u7b26\u4e32 SSS \u88ab\u79f0\u4e3a \u201c\u51e0\u4e4e\u56de\u6587\u201d ，\u5982\u679c\u6ee1\u8db3： SSS \u4ee5\u5b57\u6bcd\u5f00\u5934\u5e76\u4ee5\u5b57\u6bcd\u7ed3\u5c3e；\u5c06 SSS \u4e2d\u6240\u6709\u975e\u5b57\u6bcd\u5b57\u7b26\u5220\u9664\u5e76\u5c06\u6240\u6709\u5b57\u6bcd\u8f6c\u4e3a\u5c0f\u5199\u540e\u5f97\u5230 a(S)a(S)a(S) ，\u5c06 a(S)a(S)a(S) \u53cd\u8f6c\u540e\u5f97\u5230 b(S)b(S)b(S) ，\u4e24\u8005\u5728\u6700\u591a 2k2k2k \u4e2a\u4f4d\u7f6e\u4e0a\u5b57\u7b26\u4e0d\u540c\u3002 \u4f8b\u5982，\u5f53 k1k 1k1 \u65f6\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.wsisp.com\/helps\/113706.html\" \/>\n<meta property=\"og:site_name\" content=\"\u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"article:published_time\" content=\"2026-10-06T23:42:50+00:00\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u4f5c\u8005\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u9884\u8ba1\u9605\u8bfb\u65f6\u95f4\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 \u5206\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.wsisp.com\/helps\/113706.html\",\"url\":\"https:\/\/www.wsisp.com\/helps\/113706.html\",\"name\":\"UVa 12656 Almost Palindrome - 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