{"id":83,"date":"2010-07-12T18:29:14","date_gmt":"2010-07-12T10:29:14","guid":{"rendered":"http:\/\/comzyh.tk\/blog\/?p=83"},"modified":"2011-05-07T21:03:23","modified_gmt":"2011-05-07T13:03:23","slug":"p49-%e5%8a%a0%e5%88%86%e4%ba%8c%e5%8f%89%e6%a0%91-%e9%a2%98%e8%a7%a3","status":"publish","type":"post","link":"https:\/\/comzyh.com\/blog\/archives\/83\/","title":{"rendered":"P49 \u52a0\u5206\u4e8c\u53c9\u6811 \u9898\u89e3"},"content":{"rendered":"

\u9898\u76ee\u4e2d\u8bf4\u4e8c\u53c9\u6811\u7684\u4e2d\u5e8f\u904d\u5386\u662f\u987a\u5e8f\u7684\uff0c\u8fd9\u8bf4\u660e\uff1a\u5bf9\u4e8e\u533a\u95f4[i,j]\u5176\u6839root\u6ee1\u8db3i<=root<=j<\/p>\n

\u4e5f\u5c31\u662f\u8bf4\uff0c\u5bf9\u4e8e\u533a\u95f4[i,j]\u5176\u6700\u5927\u52a0\u5206\u4e3a\u9009\u53d6\u5176\u4e2d\u4e00\u4e2a\u4f5c\u4e3a\u6839R\uff0c\u5176\u5de6\u8fb9[i,R-1]\u7684\u6700\u5927\u52a0\u5206\u4e58\u4ee5[R+1,j]\u533a\u95f4\u6700\u5927\u52a0\u5206+Value[R]\uff0c\u5bf9\u4e8e\u6240\u6709\u53ef\u80fd\u7684R\u53d6\u8868\u8fbe\u5f0f\u6700\u5927\u503c.\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\uff1a<\/p>\n

\\(f[i][j] = Max\\left\\{ {f[i,k – 1] \\times f[k + 1][j] + v[k] ~|~ k = i~to~j} \\right\\}\\)\u6ce8\u610f\uff1a\u9898\u76ee\u8981\u6c42\u82e5\u4e00\u68f5\u6811\u6ca1\u6709\u5de6\u6216\u8005\u53f3\u5b50\u6811\uff0c\u5219\u5176\u52a0\u5206\u4e3a\u5b58\u5728\u7684\u90a3\u68f5\u5b50\u6811<\/span><\/p>\n

\u521d\u59cb\u503cfor i=1 to n f[i][i]=v[i];<\/p>\n

\u8f93\u51fa\u4fbf\u5229\u7684\u65b9\u6cd5\u662f\uff1a\u6bcf\u6b21\u8bb0\u5f55\u53d6\u5230\u6700\u5927\u503c\u65f6\u7684\u6839\u8282\u70b9\u7f16\u53f7\uff0c\u8bbeNode[i][j]=x\u8868\u793a\u5728[i][j]\u533a\u95f4\u53d6\u5230\u6700\u5927\u52a0\u5206\u7684\u6570\u7684\u6839\u8282\u70b9\u4e3ax
\n<\/p>\n

\r\n#include \r\nint n;\r\nint v[40];\r\n__int64 arr[40][40];\/\/\u8868\u793a\u4ecei\u5230j\u7684\u6700\u5927\u52a0\u5206 \r\nint nod[40][40];\/\/\u8868\u793a[i,j]\u533a\u95f4\u6839 \r\n__int64 gm(int b,int e){\/\/Get Max\r\n    int i;__int64 x;\r\n    if (arr[b][e]>0 ) return arr[b][e];\/\/\u8bb0\u5fc6\u5316\u641c\u7d22\r\n     \/\/\u7f3a\u5c11\u5de6\u6216\u53f3\u5b50\u6811\u7684\u60c5\u51b5 \r\n    if (e-b<2) {nod[b][e]=b;arr[b][e]=v[b]+v[e];return arr[b][e];}\r\n\r\n    for (i=b+1;iarr[b][e]){\r\n                         arr[b][e]=x;\r\n                         nod[b][e]=i;\r\n                         }\r\n        }\r\n    return arr[b][e];\r\n    }\r\nvoid print(int b,int e){\/\/\u8f93\u51fa\u5148\u5e8f\u904d\u5386 \r\n     if (b==e ){printf(\"%d \",b);return;}\r\n     printf(\"%d \",nod[b][e]);\r\n     if (nod[b][e]!=b)print(b,nod[b][e]-1);\r\n     if (nod[b][e]!=e)print(nod[b][e]+1,e);\r\n     }\r\nint main(){\r\n    int i,j;\r\n    scanf(\"%d\",&n);\r\n    for (i=1;i<=n;i++) for (j=1;j<=n;j++) arr[i][j]=-1;\r\n    for (i=1;i<=n;i++){ scanf(\"%d\",&v[i]); arr[i][i]=v[i];\r\n                        nod[i][i]=i;\r\n                        }   \r\n    printf(\"%I64d\\n\",gm(1,n));\r\n    \/\/for (i=1;i<=n;i++){ for (j=1;j<=n;j++)printf(\"%3d\",nod[i][j]);printf(\"\\n\");}\r\n    print(1,n);\r\n    \/\/getch();\r\n    return 0;\r\n    }\r\n\/*\r\n\u4e2d\u5e8f\u904d\u5386\u6709\u5e8f\u8bf4\u660e\u5728[i,j]\u533a\u95f4\u5185\u7684\u6700\u5927\u52a0\u5206\u53ef\u7531\u9009\u62e9\u7684\u4e2d\u95f4\u70b9\u8868\u793a\u72b6\u6001 \r\n*\/\r\n<\/pre>\n
\u9898\u76ee\u63cf\u8ff0<\/h1>\n
\u8bbe\u4e00\u4e2an\u4e2a\u8282\u70b9\u7684\u4e8c\u53c9\u6811tree\u7684\u4e2d\u5e8f\u904d\u5386\u4e3a\uff08l,2,3,\u2026,n\uff09\uff0c\u5176\u4e2d\u6570\u5b571,2,3,\u2026,n\u4e3a\u8282\u70b9\u7f16\u53f7\u3002\u6bcf\u4e2a\u8282\u70b9\u90fd\u6709\u4e00\u4e2a\u5206\u6570\uff08\u5747\u4e3a\u6b63\u6574\u6570\uff09\uff0c\u8bb0\u7b2cj\u4e2a\u8282\u70b9\u7684\u5206\u6570\u4e3adi\uff0ctree\u53ca\u5b83\u7684\u6bcf\u4e2a\u5b50\u6811\u90fd\u6709\u4e00\u4e2a\u52a0\u5206\uff0c\u4efb\u4e00\u68f5\u5b50\u6811subtree\uff08\u4e5f\u5305\u542btree\u672c\u8eab\uff09\u7684\u52a0\u5206\u8ba1\u7b97\u65b9\u6cd5\u5982\u4e0b\uff1a<\/p>\n
subtree\u7684\u5de6\u5b50\u6811\u7684\u52a0\u5206\u00d7 subtree\u7684\u53f3\u5b50\u6811\u7684\u52a0\u5206\uff0bsubtree\u7684\u6839\u7684\u5206\u6570<\/p>\n
\u82e5\u67d0\u4e2a\u5b50\u6811\u4e3a\u4e3b\uff0c\u89c4\u5b9a\u5176\u52a0\u5206\u4e3a1\uff0c\u53f6\u5b50\u7684\u52a0\u5206\u5c31\u662f\u53f6\u8282\u70b9\u672c\u8eab\u7684\u5206\u6570\u3002\u4e0d\u8003\u8651\u5b83\u7684\u7a7a<\/p>\n
\u5b50\u6811\u3002<\/p>\n
\u8bd5\u6c42\u4e00\u68f5\u7b26\u5408\u4e2d\u5e8f\u904d\u5386\u4e3a\uff081,2,3,\u2026,n\uff09\u4e14\u52a0\u5206\u6700\u9ad8\u7684\u4e8c\u53c9\u6811tree\u3002\u8981\u6c42\u8f93\u51fa\uff1b<\/p>\n
\uff081\uff09tree\u7684\u6700\u9ad8\u52a0\u5206<\/p>\n
\uff082\uff09tree\u7684\u524d\u5e8f\u904d\u5386<\/p>\n
\u8f93\u5165\u683c\u5f0f<\/h1>\n
\u7b2c1\u884c\uff1a\u4e00\u4e2a\u6574\u6570n\uff08n\uff1c30\uff09\uff0c\u4e3a\u8282\u70b9\u4e2a\u6570\u3002<\/p>\n
\u7b2c2\u884c\uff1an\u4e2a\u7528\u7a7a\u683c\u9694\u5f00\u7684\u6574\u6570\uff0c\u4e3a\u6bcf\u4e2a\u8282\u70b9\u7684\u5206\u6570\uff08\u5206\u6570\uff1c100\uff09\u3002<\/p>\n
\u8f93\u51fa\u683c\u5f0f<\/h1>\n
\u7b2c1\u884c\uff1a\u4e00\u4e2a\u6574\u6570\uff0c\u4e3a\u6700\u9ad8\u52a0\u5206\uff08\u7ed3\u679c\u4e0d\u4f1a\u8d85\u8fc74,000,000,000\uff09\u3002<\/p>\n
\u7b2c2\u884c\uff1an\u4e2a\u7528\u7a7a\u683c\u9694\u5f00\u7684\u6574\u6570\uff0c\u4e3a\u8be5\u6811\u7684\u524d\u5e8f\u904d\u5386\u3002<\/p>\n
\u6837\u4f8b\u8f93\u5165<\/h1>\n