{"id":10292,"date":"2025-04-06T19:11:53","date_gmt":"2025-04-07T02:11:53","guid":{"rendered":"https:\/\/zxi.mytechroad.com\/blog\/?p=10292"},"modified":"2025-04-06T19:28:58","modified_gmt":"2025-04-07T02:28:58","slug":"leetcode-514-freedom-trail","status":"publish","type":"post","link":"https:\/\/zxi.mytechroad.com\/blog\/dynamic-programming\/leetcode-514-freedom-trail\/","title":{"rendered":"\u82b1\u82b1\u9171 LeetCode 514. Freedom Trail"},"content":{"rendered":"\n<p>\u4e00\u773cDP\uff0c\u770b\u6570\u636e\u89c4\u6a21\u6807\u7a0b\u5e94\u8be5\u662fO(100<sup>3<\/sup>)\u3002<\/p>\n\n\n\n<p>\u9636\u6bb5\u80af\u5b9a\u5c31\u662f\u541f\u5531\u5b8c\u4e00\u4e2a\u5b57\u7b26\uff0c\u72b6\u6001\u548c\u54ea\u4e2a\u5b57\u7b26\u572812:00\u70b9\u6709\u5173\u3002<\/p>\n\n\n\n<p>\u6240\u4ee5\u6211\u4eec\u5b9a\u4e49 dp[i][j] := \u541f\u5531\u5b8ckeys[0~i]\u540e\uff0crings[j]\u505c\u572812:00\u70b9\u6240\u9700\u8981\u7684\u6700\u5c11\u6b65\u6570\u3002<\/p>\n\n\n\n<p>\u8f6c\u79fb\u65b9\u7a0b\uff1adp[i][j] = min(dp[i-1][k] + steps(k, j) + 1)  if keys[i] == rings[j] else +inf.<\/p>\n\n\n\n<p>\u7b2ci-1\u5b57\u7b26\u541f\u5531\u5b8cring\u505c\u7559\u5728k\uff0c\u7b2ci\u4e2a\u5b57\u7b26\u541f\u5531\u5b8cring\u505c\u7559\u5728j (rings[j] \u5fc5\u987b\u548c keys[i] \u76f8\u540c)\uff0csteps(k, j)\u8868\u793aring\u4ecek\u8f6c\u5230j\u6240\u9700\u8981\u7684\u6700\u5c11\u6b65\u6570\uff0c\u6700\u540e\u8fd8\u8981+1\uff0c\u8868\u793a\u541f\u5531\u5f53\u524d\u5b57\u7b26\u6240\u9700\u8981\u7684\u989d\u5916\u6b65\u9aa4\u3002<\/p>\n\n\n\n<p>\u8fb9\u754c\u6761\u4ef6\uff1a\u5bf9\u4e8e\u7b2c0\u4e2a\u5b57\u7b26\uff0cring\u4e00\u5f00\u59cb\u505c\u7559\u5728\u7b2c0\u4e2a\u5b57\u7b26\uff0c\u6700\u5c0f\u6b65\u6570\u5c31\u662f1 + steps(0, key[0])\u3002<\/p>\n\n\n\n<p>\u65f6\u95f4\u590d\u6742\u5ea6\uff1aO(mn<sup>2<\/sup>)<br>\u7a7a\u95f4\u590d\u6742\u5ea6\uff1aO(mn) \u53ef\u4ee5\u964d\u7ef4\u5230 O(n)<\/p>\n\n\n\n<pre lang=\"c++\">\nclass Solution {\npublic:\n  int findRotateSteps(string ring, string key) {\n    const int n = ring.size();\n    const int m = key.size();\n    auto steps = [n](int i, int j) {\n      return min(abs(i - j), n - abs(i - j));\n    };\n    \/\/ dp[i][j] min steps to spell key[0~i] and ring[j] is at 12:00.\n    vector<vector<int>> dp(m, vector<int>(n, INT_MAX\/2));\n    for (int i = 0; i < m; ++i)\n      for (int j = 0; j < n; ++j) {\n        if (ring[j] != key[i]) continue;\n        for (int k = 0; k < n; ++k)\n          dp[i][j] = min(dp[i][j], 1 + (i == 0 ? steps(0, j) : (dp[i - 1][k] + steps(j, k))));\n      }\n    return *min_element(begin(dp.back()), end(dp.back()));\n  }\n};\n\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>\u4e00\u773cDP\uff0c\u770b\u6570\u636e\u89c4\u6a21\u6807\u7a0b\u5e94\u8be5\u662fO(1003)\u3002 \u9636\u6bb5\u80af\u5b9a\u5c31\u662f\u541f\u5531\u5b8c\u4e00\u4e2a\u5b57\u7b26\uff0c\u72b6\u6001\u548c\u54ea\u4e2a\u5b57\u7b26\u572812:00\u70b9\u6709\u5173\u3002 \u6240\u4ee5\u6211\u4eec\u5b9a\u4e49 dp[i][j] := \u541f\u5531\u5b8ckeys[0~i]\u540e\uff0crings[j]\u505c\u572812:00\u70b9\u6240\u9700\u8981\u7684\u6700\u5c11\u6b65\u6570\u3002 \u8f6c\u79fb\u65b9\u7a0b\uff1adp[i][j] = min(dp[i-1][k] + steps(k, j) + 1) if keys[i] == rings[j] else +inf. \u7b2ci-1\u5b57\u7b26\u541f\u5531\u5b8cring\u505c\u7559\u5728k\uff0c\u7b2ci\u4e2a\u5b57\u7b26\u541f\u5531\u5b8cring\u505c\u7559\u5728j (rings[j] \u5fc5\u987b\u548c keys[i] \u76f8\u540c)\uff0csteps(k,&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[46],"tags":[18,151,836],"class_list":["post-10292","post","type-post","status-publish","format-standard","hentry","category-dynamic-programming","tag-dp","tag-head","tag-ring","entry","simple"],"_links":{"self":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/10292","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/comments?post=10292"}],"version-history":[{"count":4,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/10292\/revisions"}],"predecessor-version":[{"id":10299,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/10292\/revisions\/10299"}],"wp:attachment":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/media?parent=10292"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/categories?post=10292"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/tags?post=10292"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}