{"id":6,"date":"2025-04-10T20:03:19","date_gmt":"2025-04-10T12:03:19","guid":{"rendered":"http:\/\/120.55.184.7\/?p=6"},"modified":"2025-04-16T00:44:23","modified_gmt":"2025-04-15T16:44:23","slug":"%e3%80%90%e5%8d%95%e8%af%8d%e6%8e%a5%e9%be%99%e3%80%91%e7%8a%b6%e6%80%81%e5%8e%8b%e7%bc%a9dp","status":"publish","type":"post","link":"https:\/\/beijian99.top\/?p=6","title":{"rendered":"\u3010\u5355\u8bcd\u63a5\u9f99\u3011\u72b6\u6001\u538b\u7f29DP"},"content":{"rendered":"\n
\n\n\n\n

\u9898\u76ee\u63cf\u8ff0<\/strong><\/p>\n\n\n\n

\u5355\u8bcd\u63a5\u9f99\uff0c\u7ed9\u5b9aN\u4e2a\u5b57\u7b26\u4e32s1,s2\u2026..sN\uff0c\uff08N<=20, len(s)<=20\uff09\uff0c\u4ece\u4e2d\u9009\u53d6\u82e5\u5e72\u4e2a\u8fdb\u884c\u63a5\u9f99\uff0c\u89c4\u5219\u5982\u4e0b\uff1a<\/p>\n\n\n\n

\u63a5\u9f99\u65f6\uff0c\u540e\u4e00\u5355\u8bcd\u7684\u9996\u5b57\u6bcd\u5fc5\u987b\u4e0e\u524d\u4e00\u4e2a\u5355\u8bcd\u7684\u5c3e\u5b57\u6bcd\u76f8\u540c\u3002<\/p>\n\n\n\n

\u6bcf\u4e2a\u5355\u8bcd\u53ea\u80fd\u4f7f\u7528\u4e00\u6b21\u3002<\/p>\n\n\n\n

\u8d77\u59cb\u5355\u8bcd\u53ef\u4efb\u9009\u3002<\/p>\n\n\n\n

\u5728\u6240\u6709\u53ef\u80fd\u7684\u63a5\u9f99\u8def\u5f84\u4e2d\uff0c\u627e\u5230\u200b\u200b\u6700\u957f\u7684\u5355\u8bcd\u4e32\u200b\u200b\u3002\u82e5\u5b58\u5728\u591a\u4e2a\u6700\u957f\u4e32\uff0c\u8f93\u51fa\u5176\u4e2d\u4efb\u610f\u4e00\u4e2a\u65b9\u6848\u3002<\/p>\n\n\n\n

\u6d4b\u8bd5\u7528\u4f8b 1<\/p>\n\n\n\n

\u8f93\u5165
5
dog cat elephant rat tiger<\/p>\n\n\n\n

\u8f93\u51fa
elephant-tiger-rat<\/p>\n\n\n\n

\u7528\u4f8b\u5206\u6790\u200b\u200b
\u8f93\u5165 [dog, cat, elephant, rat, tiger] \u7684\u6700\u4f18\u89e3\u4e3a elephant-tiger-rat\uff0c\u5176\u8fde\u63a5\u903b\u8f91\u4e3a\uff1a<\/p>\n\n\n\n

elephant\uff08\u5c3e t\uff09\u2192 tiger\uff08\u9996 t\uff09<\/p>\n\n\n\n

tiger\uff08\u5c3e r\uff09\u2192 rat\uff08\u9996 r\uff09<\/p>\n\n\n\n

<\/p>\n\n\n\n

\u7b97\u6cd5\u601d\u8def<\/strong><\/p>\n\n\n\n

\u7531\u4e8e\u5355\u8bcd\u6570\u91cf\u9650\u5236\u4e3a N\u226420\uff0c\u76f4\u63a5\u66b4\u529b\u641c\u7d22\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a O(N!)\uff0c\u663e\u7136\u4e0d\u53ef\u884c\u3002\u6b64\u65f6\u53ef\u4ee5\u91c7\u7528 \u200b\u200b\u72b6\u6001\u538b\u7f29\u52a8\u6001\u89c4\u5212\uff08\u72b6\u538bDP\uff09\u200b \u6765\u9ad8\u6548\u89e3\u51b3\u3002<\/p>\n\n\n\n

\u72b6\u6001\u538b\u7f29DP\u6838\u5fc3\u601d\u60f3<\/p>\n\n\n\n

\u200b\u200b\u72b6\u6001\u8868\u793a\u200b\u200b<\/p>\n\n\n\n

\u4f7f\u7528\u4e8c\u8fdb\u5236\u6570\u8868\u793a\u5355\u8bcd\u7684\u4f7f\u7528\u72b6\u6001\u3002\u4f8b\u5982\uff0ci=1010\uff08\u4e8c\u8fdb\u5236\uff09\u8868\u793a\u7b2c2\u548c\u7b2c4\u4e2a\u5355\u8bcd\u5df2\u88ab\u4f7f\u7528\u3002<\/p>\n\n\n\n

\u5b9a\u4e49 dp[i][j]\uff1a\u72b6\u6001\u4e3a i \u4e14\u6700\u540e\u4e00\u4e2a\u5355\u8bcd\u662f\u7b2c j \u4e2a\u5355\u8bcd\u65f6\uff0c\u63a5\u9f99\u7684\u6700\u5927\u957f\u5ea6\u3002<\/p>\n\n\n\n

\u5c5e\u6027\u4e3a max\uff0c\u8bb0\u5f55\u6700\u5927\u957f\u5ea6\u3002<\/p>\n\n\n\n

\u200b\u200b\u72b6\u6001\u8f6c\u79fb\u200b\u200b<\/p>\n\n\n\n

\u904d\u5386\u6240\u6709\u53ef\u80fd\u7684\u8f6c\u79fb\uff1a\u82e5\u5f53\u524d\u72b6\u6001\u4e3a i\uff0c\u6700\u540e\u4e00\u4e2a\u5355\u8bcd\u4e3a j\uff0c\u5219\u5c1d\u8bd5\u6240\u6709\u672a\u88ab\u4f7f\u7528\u7684\u5355\u8bcd k\uff08\u5373 i \u7684\u7b2c k \u4f4d\u4e3a0\uff09\u3002<\/p>\n\n\n\n

\u82e5 k \u7684\u9996\u5b57\u6bcd\u7b49\u4e8e j \u7684\u5c3e\u5b57\u6bcd\uff0c\u5219\u66f4\u65b0\u72b6\u6001 i | (1 << k) \u7684\u503c\u4e3a dp[i][j]+len(k)\u3002<\/p>\n\n\n\n

\u200b\u200b\u8def\u5f84\u56de\u6eaf\u200b\u200b<\/p>\n\n\n\n

\u8bb0\u5f55\u6bcf\u4e2a\u72b6\u6001\u7684\u524d\u9a71\u8282\u70b9\uff08\u5373\u4e0a\u4e00\u4e2a\u5355\u8bcd\uff09\uff0c\u6700\u7ec8\u4ece\u6700\u5927\u957f\u5ea6\u7684\u72b6\u6001\u56de\u6eaf\u8def\u5f84\u3002<\/p>\n\n\n\n

\u9884\u5904\u7406\u5173\u952e\u70b9<\/p>\n\n\n\n

\u200b\u200b\u8fde\u63a5\u5173\u7cfb\u77e9\u9635\u200b\u200b\uff1a\u9884\u5904\u7406\u6240\u6709\u5355\u8bcd\u5bf9\u7684\u8fde\u63a5\u53ef\u80fd\u6027\uff08\u5373 word[j] \u7684\u5c3e\u5b57\u6bcd\u662f\u5426\u7b49\u4e8e word[k] \u7684\u9996\u5b57\u6bcd\uff09\u3002<\/p>\n\n\n\n

\u200b\u200b\u4e8c\u8fdb\u5236\u64cd\u4f5c\u200b\u200b\uff1a\u5229\u7528\u4f4d\u8fd0\u7b97\u9ad8\u6548\u5224\u65ad\u5355\u8bcd\u662f\u5426\u88ab\u4f7f\u7528 i&(1<<k)\uff08\u4f8b\u5982 \u5224\u65ad\u7b2c k \u4e2a\u5355\u8bcd\u662f\u5426\u88ab\u4f7f\u7528\uff09\u3002<\/p>\n\n\n\n

\u4ee3\u7801\u5b9e\u73b0<\/h3>\n\n\n
\npackage main\n\nimport (\n    "fmt"\n    "slices"\n)\n\nfunc main() {\n    \/\/ \u5b9a\u4e49\u4e00\u4e2a\u5b57\u7b26\u4e32\u5207\u7247\uff0c\u5305\u542b\u591a\u4e2a\u5355\u8bcd\n    words := []string{"word", "dd", "da", "dc", "dword", "d"}\n    \/\/ \u8c03\u7528 WordSolitaire \u51fd\u6570\u89e3\u51b3\u5355\u8bcd\u63a5\u9f99\u95ee\u9898\uff0c\u5e76\u5c06\u7ed3\u679c\u5b58\u50a8\u5728 res \u4e2d\n    res := WordSolitaire(words)\n    \/\/ \u6253\u5370\u6700\u7ec8\u7684\u6700\u957f\u63a5\u9f99\u5e8f\u5217\n    fmt.Println(res)\n}\n\n\/\/ WordSolitaire \u51fd\u6570\u7528\u4e8e\u89e3\u51b3\u5355\u8bcd\u63a5\u9f99\u95ee\u9898\uff0c\u627e\u51fa\u7ed9\u5b9a\u5355\u8bcd\u5217\u8868\u4e2d\u80fd\u5f62\u6210\u7684\u6700\u957f\u63a5\u9f99\u5e8f\u5217\nfunc WordSolitaire(words []string) []string {\n    \/\/ n \u4e3a\u5355\u8bcd\u5217\u8868\u7684\u957f\u5ea6\uff0cstateMax \u8868\u793a\u6240\u6709\u53ef\u80fd\u7684\u72b6\u6001\u6570\u91cf\uff0c\u4f7f\u7528\u4f4d\u8fd0\u7b97 1 << len(words) \u5f97\u5230\n    n, stateMax := len(words), 1<<len(words)\n    \/\/ dp \u6570\u7ec4\u7528\u4e8e\u8bb0\u5f55\u4ee5\u6bcf\u4e2a\u5355\u8bcd\u7ed3\u5c3e\uff0c\u5728\u6bcf\u79cd\u72b6\u6001\u4e0b\u7684\u6700\u957f\u63a5\u9f99\u5e8f\u5217\u957f\u5ea6\n    dp := make([][]int, n)\n    \/\/ pre \u6570\u7ec4\u7528\u4e8e\u8bb0\u5f55\u5728\u6bcf\u79cd\u72b6\u6001\u4e0b\uff0c\u5f53\u524d\u5355\u8bcd\u7684\u524d\u4e00\u4e2a\u5355\u8bcd\u7684\u7d22\u5f15\uff0c\u7528\u4e8e\u56de\u6eaf\u8def\u5f84\n    pre := make([][]int, n)\n    \/\/ \u521d\u59cb\u5316 dp \u548c pre \u6570\u7ec4\n    for i := range dp {\n        dp[i] = make([]int, stateMax)\n        pre[i] = make([]int, stateMax)\n    }\n\n    \/\/ back \u51fd\u6570\u7528\u4e8e\u83b7\u53d6\u5b57\u7b26\u4e32\u7684\u6700\u540e\u4e00\u4e2a\u5b57\u7b26\u7684 ASCII \u7801\u503c\n    back := func(s string) int { return int(s[len(s)-1]) }\n    \/\/ front \u51fd\u6570\u7528\u4e8e\u83b7\u53d6\u5b57\u7b26\u4e32\u7684\u7b2c\u4e00\u4e2a\u5b57\u7b26\u7684 ASCII \u7801\u503c\n    front := func(s string) int { return int(s[0]) }\n\n    \/\/ index \u7528\u4e8e\u8bb0\u5f55\u6700\u957f\u63a5\u9f99\u5e8f\u5217\u7684\u6700\u540e\u4e00\u4e2a\u5355\u8bcd\u7684\u7d22\u5f15\n    \/\/ state \u7528\u4e8e\u8bb0\u5f55\u6700\u957f\u63a5\u9f99\u5e8f\u5217\u5bf9\u5e94\u7684\u72b6\u6001\n    \/\/ size \u7528\u4e8e\u8bb0\u5f55\u6700\u957f\u63a5\u9f99\u5e8f\u5217\u7684\u957f\u5ea6\n    var index, state, size int\n\n    \/\/ \u521d\u59cb\u5316\u6bcf\u4e2a\u5355\u8bcd\u5355\u72ec\u4f5c\u4e3a\u4e00\u4e2a\u63a5\u9f99\u5e8f\u5217\u7684\u60c5\u51b5\n    for i, word := range words {\n        \/\/ \u72b6\u6001 1 << i \u8868\u793a\u53ea\u6709\u7b2c i \u4e2a\u5355\u8bcd\u88ab\u4f7f\u7528\n        dp[i][1<<i] = len(word)\n        \/\/ \u5982\u679c\u5f53\u524d\u63a5\u9f99\u5e8f\u5217\u957f\u5ea6\u5927\u4e8e\u4e4b\u524d\u8bb0\u5f55\u7684\u6700\u957f\u957f\u5ea6\n        if size < dp[i][1<<i] {\n            \/\/ \u66f4\u65b0\u6700\u957f\u957f\u5ea6\n            size = dp[i][1<<i]\n            \/\/ \u66f4\u65b0\u6700\u957f\u63a5\u9f99\u5e8f\u5217\u7684\u6700\u540e\u4e00\u4e2a\u5355\u8bcd\u7684\u7d22\u5f15\n            index = i\n            \/\/ \u66f4\u65b0\u6700\u957f\u63a5\u9f99\u5e8f\u5217\u5bf9\u5e94\u7684\u72b6\u6001\n            state = 1 << i\n        }\n    }\n\n    \/\/ \u904d\u5386\u6240\u6709\u53ef\u80fd\u7684\u72b6\u6001\n    for k := 0; k < stateMax; k++ {\n        \/\/ \u904d\u5386\u6bcf\u4e2a\u5355\u8bcd\n        for i := range words {\n            \/\/ \u5982\u679c\u5f53\u524d\u72b6\u6001\u4e0b\u7b2c i \u4e2a\u5355\u8bcd\u672a\u88ab\u4f7f\u7528\uff0c\u5219\u8df3\u8fc7\n            if k&(1<<i) == 0 {\n                continue\n            }\n            \/\/ \u518d\u6b21\u904d\u5386\u6bcf\u4e2a\u5355\u8bcd\n            for j := range words {\n                \/\/ \u5982\u679c\u5f53\u524d\u72b6\u6001\u4e0b\u7b2c j \u4e2a\u5355\u8bcd\u5df2\u7ecf\u88ab\u4f7f\u7528\uff0c\u6216\u8005\u7b2c i \u4e2a\u5355\u8bcd\u7684\u6700\u540e\u4e00\u4e2a\u5b57\u7b26\u548c\u7b2c j \u4e2a\u5355\u8bcd\u7684\u7b2c\u4e00\u4e2a\u5b57\u7b26\u4e0d\u76f8\u540c\uff0c\u5219\u8df3\u8fc7\n                if k&(1<<j) != 0 || back(words[i]) != front(words[j]) {\n                    continue\n                }\n                \/\/ \u8ba1\u7b97\u65b0\u7684\u72b6\u6001\uff0c\u5c06\u7b2c j \u4e2a\u5355\u8bcd\u52a0\u5165\u5f53\u524d\u72b6\u6001\n                newState := k | (1 << j)\n                \/\/ \u5982\u679c\u4ee5\u7b2c j \u4e2a\u5355\u8bcd\u7ed3\u5c3e\uff0c\u5728\u65b0\u72b6\u6001\u4e0b\u7684\u63a5\u9f99\u5e8f\u5217\u957f\u5ea6\u5c0f\u4e8e\u4ee5\u7b2c i \u4e2a\u5355\u8bcd\u7ed3\u5c3e\uff0c\u5728\u5f53\u524d\u72b6\u6001\u4e0b\u7684\u63a5\u9f99\u5e8f\u5217\u957f\u5ea6\u52a0\u4e0a\u7b2c j \u4e2a\u5355\u8bcd\u7684\u957f\u5ea6\n                if dp[j][newState] < dp[i][k]+len(words[j]) {\n                    \/\/ \u66f4\u65b0\u4ee5\u7b2c j \u4e2a\u5355\u8bcd\u7ed3\u5c3e\uff0c\u5728\u65b0\u72b6\u6001\u4e0b\u7684\u63a5\u9f99\u5e8f\u5217\u957f\u5ea6\n                    dp[j][newState] = dp[i][k] + len(words[j])\n                    \/\/ \u8bb0\u5f55\u7b2c j \u4e2a\u5355\u8bcd\u5728\u65b0\u72b6\u6001\u4e0b\u7684\u524d\u4e00\u4e2a\u5355\u8bcd\u7684\u7d22\u5f15\u4e3a i\n                    pre[j][newState] = i\n                }\n                \/\/ \u5982\u679c\u65b0\u72b6\u6001\u4e0b\u7684\u63a5\u9f99\u5e8f\u5217\u957f\u5ea6\u5927\u4e8e\u4e4b\u524d\u8bb0\u5f55\u7684\u6700\u957f\u957f\u5ea6\n                if size < dp[j][newState] {\n                    \/\/ \u66f4\u65b0\u6700\u957f\u957f\u5ea6\n                    size = dp[j][newState]\n                    \/\/ \u66f4\u65b0\u6700\u957f\u63a5\u9f99\u5e8f\u5217\u7684\u6700\u540e\u4e00\u4e2a\u5355\u8bcd\u7684\u7d22\u5f15\n                    index = j\n                    \/\/ \u66f4\u65b0\u6700\u957f\u63a5\u9f99\u5e8f\u5217\u5bf9\u5e94\u7684\u72b6\u6001\n                    state = newState\n                }\n            }\n        }\n    }\n\n    \/\/ \u7528\u4e8e\u5b58\u50a8\u6700\u7ec8\u7684\u6700\u957f\u63a5\u9f99\u5e8f\u5217\n    res := make([]string, 0, n)\n    \/\/ \u56de\u6eaf\u8def\u5f84\uff0c\u6784\u5efa\u6700\u957f\u63a5\u9f99\u5e8f\u5217\n    for i := 0; i < n; i++ {\n        \/\/ \u5c06\u5f53\u524d\u5355\u8bcd\u52a0\u5165\u7ed3\u679c\u5217\u8868\n        res = append(res, words[index])\n        \/\/ \u66f4\u65b0\u5f53\u524d\u5355\u8bcd\u7684\u7d22\u5f15\u4e3a\u524d\u4e00\u4e2a\u5355\u8bcd\u7684\u7d22\u5f15\n        index = pre[index][state]\n        \/\/ \u4ece\u72b6\u6001\u4e2d\u79fb\u9664\u5f53\u524d\u5355\u8bcd\n        state = state ^ (1 << index)\n        \/\/ \u5982\u679c\u6240\u6709\u5355\u8bcd\u90fd\u5df2\u7ecf\u5904\u7406\u5b8c\u6bd5\uff0c\u5219\u9000\u51fa\u5faa\u73af\n        if state == 0 {\n            break\n        }\n    }\n    \/\/ \u7531\u4e8e\u56de\u6eaf\u5f97\u5230\u7684\u7ed3\u679c\u662f\u9006\u5e8f\u7684\uff0c\u6240\u4ee5\u9700\u8981\u53cd\u8f6c\u7ed3\u679c\u5217\u8868\n    slices.Reverse(res)\n    return res\n}\n\n\n<\/pre><\/div>\n\n\n
\u590d\u6742\u5ea6\u5206\u6790<\/strong><\/h4>\n\n\n\n
\"\"<\/figure>\n\n\n\n
<\/p>\n\n\n\n
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