{"id":10301,"date":"2025-04-09T22:25:42","date_gmt":"2025-04-10T05:25:42","guid":{"rendered":"https:\/\/zxi.mytechroad.com\/blog\/?p=10301"},"modified":"2025-04-10T07:21:28","modified_gmt":"2025-04-10T14:21:28","slug":"leetcode-646-maximum-length-of-pair-chain","status":"publish","type":"post","link":"https:\/\/zxi.mytechroad.com\/blog\/dynamic-programming\/leetcode-646-maximum-length-of-pair-chain\/","title":{"rendered":"\u82b1\u82b1\u9171 LeetCode 646. Maximum Length of Pair Chain"},"content":{"rendered":"\n

\u8fd9\u9898\u6211\u9009DP\uff0c\u56e0\u4e3a\u4e0d\u9700\u8981\u8bc1\u660e\uff0c\u76f4\u63a5\u5e72\u5c31\u884c\u4e86\u3002<\/p>\n\n\n\n

\u65b9\u6cd51: DP<\/p>\n\n\n\n

\u9996\u5148\u8fd8\u662f\u9700\u8981\u5bf9pairs\u7684right\u8fdb\u884c\u6392\u5e8f\u3002\u4e00\u65b9\u9762\u662f\u4e3a\u4e86\u65b9\u4fbfchaining\uff0c\u53e6\u4e00\u65b9\u9762\u662f\u53ef\u4ee5\u53bb\u91cd\u3002<\/p>\n\n\n\n

\u7136\u540e\u5b9a\u4e49 dp[i] := \u4ee5pairs[i]\u4f5c\u4e3a\u7ed3\u5c3e\uff0c\u6700\u957f\u7684\u5e8f\u5217\u7684\u957f\u5ea6\u3002

\u72b6\u6001\u8f6c\u79fb\uff1adp[i] = max(dp[j] + 1) where pairs[i].left > pairs[j].right and 0 < j < i.<\/p>\n\n\n\n

\u89e3\u91ca\uff1a\u5bf9\u4e8epairs[i]\uff0c\u627e\u4e00\u4e2a\u6700\u4f18\u7684pairs[j]\uff0c\u6ee1\u8db3pairs[i].left > pairs[j].right\uff0c\u8fd9\u6837\u6211\u5c31\u53ef\u4ee5\u628apairs[i]\u8ffd\u52a0\u5230\u4ee5pairs[j]\u7ed3\u5c3e\u7684\u6700\u957f\u5e8f\u5217\u540e\u9762\u4e86\uff0c\u957f\u5ea6+1\u3002<\/p>\n\n\n\n

\u8fb9\u68c0\u6761\u4ef6\uff1adp[0:n] = 1\uff0c\u6bcf\u4e2apair\u4ee5\u81ea\u5df1\u4f5c\u4e3a\u5e8f\u5217\u7684\u6700\u540e\u5143\u7d20\uff0c\u957f\u5ea6\u4e3a1\u3002<\/p>\n\n\n\n

\u65f6\u95f4\u590d\u6742\u5ea6\uff1aO(n2<\/sup>)
\u7a7a\u95f4\u590d\u6742\u5ea6\uff1aO(n)<\/p>\n\n\n\n

\nclass Solution {\npublic:\n  int findLongestChain(vector>& pairs) {\n    sort(begin(pairs), end(pairs), [](const auto& p1, const auto& p2){\n      return p1[1] < p2[1];\n    });\n\n    const int n = pairs.size();\n\n    vector dp(n, 1);\n    for (int i = 0; i < n; ++i)\n      for (int j = 0; j < i; ++j)\n        if (pairs[i][0] > pairs[j][1])\n          dp[i] = max(dp[i], dp[j] + 1);\n\n    return *max_element(begin(dp), end(dp));\n  }\n};\n\n<\/pre>\n\n\n\n
\u65b9\u6cd52: \u8d2a\u5fc3<\/p>\n\n\n\n
\u548cDP\u4e00\u6837\uff0c\u5bf9\u6570\u636e\u8fdb\u884c\u6392\u5e8f\u3002<\/p>\n\n\n\n
\u6bcf\u5f53\u6211\u770b\u5230 cur.left > prev.right\uff0c\u90a3\u4e48\u5c31\u76f4\u63a5\u628acur\u63a5\u5728prev\u540e\u9762\u3002\u6211\u4eec\u9700\u8981\u8bc1\u660e\u8fd9\u4e48\u505a\u662f\u6700\u4f18\u7684\uff0c\u800c\u4e0d\u662f\u8df3\u8fc7\u5b83\u9009\u540e\u9762\u7684\u5143\u7d20\u3002

Case 0: cur\u5df2\u7ecf\u662f\u6700\u540e\u4e00\u4e2a\u5143\u7d20\u4e86\uff0c\u8df3\u8fc7\u5c31\u4e0d\u662f\u6700\u4f18\u89e3\u4e86\u3002

\u5047\u8bbecur\u540e\u9762\u6709next, \u56e0\u4e3a\u5df2\u7ecf\u6392\u5e8f\u8fc7\u4e86\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u77e5 next.right >= cur.right\u3002

Case 1: next.right == cur.right\u3002\u8fd9\u65f6\u5019\u9009cur\u548c\u9009next\u5bf9\u540e\u9762\u7684\u51b3\u7b56\u6765\u8bf4\u662f\u4e00\u6837\u7684\uff0c\u4f46\u7531\u4e8eCase 0\u7684\u5b58\u5728\uff0c\u6211\u5fc5\u987b\u9009cur\u3002

Case 2: next.right > cur.right\u3002\u4e0d\u7ba1left\u7684\u60c5\u51b5\u600e\u4e48\u6837\uff0c\u7531\u4e8eright\u66f4\u5c0f\uff0c\u8fd9\u65f6\u5019\u9009\u62e9cur\u4e00\u5b9a\u662f\u4f18\u4e8enext\u3002<\/p>\n\n\n\n
\u7efc\u4e0a\u6240\u8ff0\uff0c\u770b\u5230\u6709\u5143\u7d20\u53ef\u4ee5\u8fde\u63a5\u8d77\u6765\u5c31\u8d2a\u5fc3\u7684\u9009\u5b83\u5c31\u5bf9\u4e86\u3002<\/p>\n\n\n\n
\u65f6\u95f4\u590d\u6742\u5ea6\uff1aO(nlogn)
\u7a7a\u95f4\u590d\u6742\u5ea6\uff1aO(1)<\/p>\n\n\n\n
\nclass Solution {\npublic:\n  int findLongestChain(vector>& pairs) {\n    sort(begin(pairs), end(pairs), [](const auto& p1, const auto& p2){\n      return p1[1] < p2[1];\n    });\n\n    int right = INT_MIN;\n    int ans = 0;\n    for (const auto& p : pairs)\n      if (p[0] > right) {\n        right = p[1];\n        ++ans;\n      }\n    return ans;\n  }\n};\n\n<\/pre>\n","protected":false},"excerpt":{"rendered":"
\u8fd9\u9898\u6211\u9009DP\uff0c\u56e0\u4e3a\u4e0d\u9700\u8981\u8bc1\u660e\uff0c\u76f4\u63a5\u5e72\u5c31\u884c\u4e86\u3002 \u65b9\u6cd51: DP \u9996\u5148\u8fd8\u662f\u9700\u8981\u5bf9pairs\u7684right\u8fdb\u884c\u6392\u5e8f\u3002\u4e00\u65b9\u9762\u662f\u4e3a\u4e86\u65b9\u4fbfchaining\uff0c\u53e6\u4e00\u65b9\u9762\u662f\u53ef\u4ee5\u53bb\u91cd\u3002 \u7136\u540e\u5b9a\u4e49 dp[i] := \u4ee5pairs[i]\u4f5c\u4e3a\u7ed3\u5c3e\uff0c\u6700\u957f\u7684\u5e8f\u5217\u7684\u957f\u5ea6\u3002 \u72b6\u6001\u8f6c\u79fb\uff1adp[i] = max(dp[j] + 1) where pairs[i].left > pairs[j].right and 0 < j < i. \u89e3\u91ca\uff1a\u5bf9\u4e8epairs[i]\uff0c\u627e\u4e00\u4e2a\u6700\u4f18\u7684pairs[j]\uff0c\u6ee1\u8db3pairs[i].left >…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[46,51],"tags":[18,88,177,720,493],"class_list":["post-10301","post","type-post","status-publish","format-standard","hentry","category-dynamic-programming","category-greedy","tag-dp","tag-greedy","tag-medium","tag-proof","tag-subset","entry","simple"],"_links":{"self":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/10301","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=10301"}],"version-history":[{"count":3,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/10301\/revisions"}],"predecessor-version":[{"id":10306,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/posts\/10301\/revisions\/10306"}],"wp:attachment":[{"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/media?parent=10301"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/categories?post=10301"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/zxi.mytechroad.com\/blog\/wp-json\/wp\/v2\/tags?post=10301"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}