![\"example](\"https://assets.leetcode.com/uploads/2021/09/22/quiet-place-example1.png\")
There is a network of n servers, labeled from 0 to n - 1. You are given a 2D integer array edges, where edges[i] = [ui, vi] indicates there is a message channel between servers ui and vi, and they can pass any number of messages to each other directly in one second. You are also given a 0-indexed integer array patience of length n.
All servers are connected, i.e., a message can be passed from one server to any other server(s) directly or indirectly through the message channels.
\n\nThe server labeled 0 is the master server. The rest are data servers. Each data server needs to send its message to the master server for processing and wait for a reply. Messages move between servers optimally, so every message takes the least amount of time to arrive at the master server. The master server will process all newly arrived messages instantly and send a reply to the originating server via the reversed path the message had gone through.
At the beginning of second 0, each data server sends its message to be processed. Starting from second 1, at the beginning of every second, each data server will check if it has received a reply to the message it sent (including any newly arrived replies) from the master server:
i will resend the message every patience[i] second(s), i.e., the data server i will resend the message if patience[i] second(s) have elapsed since the last time the message was sent from this server.The network becomes idle when there are no messages passing between servers or arriving at servers.
\n\nReturn the earliest second starting from which the network becomes idle.
\n\n\n
Example 1:
\n\n\nInput: edges = [[0,1],[1,2]], patience = [0,2,1]\nOutput: 8\nExplanation:\nAt (the beginning of) second 0,\n- Data server 1 sends its message (denoted 1A) to the master server.\n- Data server 2 sends its message (denoted 2A) to the master server.\n\nAt second 1,\n- Message 1A arrives at the master server. Master server processes message 1A instantly and sends a reply 1A back.\n- Server 1 has not received any reply. 1 second (1 < patience[1] = 2) elapsed since this server has sent the message, therefore it does not resend the message.\n- Server 2 has not received any reply. 1 second (1 == patience[2] = 1) elapsed since this server has sent the message, therefore it resends the message (denoted 2B).\n\nAt second 2,\n- The reply 1A arrives at server 1. No more resending will occur from server 1.\n- Message 2A arrives at the master server. Master server processes message 2A instantly and sends a reply 2A back.\n- Server 2 resends the message (denoted 2C).\n...\nAt second 4,\n- The reply 2A arrives at server 2. No more resending will occur from server 2.\n...\nAt second 7, reply 2D arrives at server 2.\n\nStarting from the beginning of the second 8, there are no messages passing between servers or arriving at servers.\nThis is the time when the network becomes idle.\n\n\n
Example 2:
\n![\"example](\"https://assets.leetcode.com/uploads/2021/09/04/network_a_quiet_place_2.png\")
\n\nInput: edges = [[0,1],[0,2],[1,2]], patience = [0,10,10]\nOutput: 3\nExplanation: Data servers 1 and 2 receive a reply back at the beginning of second 2.\nFrom the beginning of the second 3, the network becomes idle.\n\n\n
\n
Constraints:
\n\nn == patience.length2 <= n <= 105patience[0] == 01 <= patience[i] <= 105 for 1 <= i < n1 <= edges.length <= min(105, n * (n - 1) / 2)edges[i].length == 20 <= ui, vi < nui != vi给你一个有 n 个服务器的计算机网络，服务器编号为 0 到 n - 1 。同时给你一个二维整数数组 edges ，其中 edges[i] = [ui, vi] 表示服务器 ui 和 vi 之间有一条信息线路，在 一秒 内它们之间可以传输 任意 数目的信息。再给你一个长度为 n 且下标从 0 开始的整数数组 patience 。
题目保证所有服务器都是 相通 的，也就是说一个信息从任意服务器出发，都可以通过这些信息线路直接或间接地到达任何其他服务器。
\n\n编号为 0 的服务器是 主 服务器，其他服务器为 数据 服务器。每个数据服务器都要向主服务器发送信息，并等待回复。信息在服务器之间按 最优 线路传输，也就是说每个信息都会以 最少时间 到达主服务器。主服务器会处理 所有 新到达的信息并 立即 按照每条信息来时的路线 反方向 发送回复信息。
在 0 秒的开始，所有数据服务器都会发送各自需要处理的信息。从第 1 秒开始，每 一秒最 开始 时，每个数据服务器都会检查它是否收到了主服务器的回复信息（包括新发出信息的回复信息）：
i 每 patience[i] 秒都会重发一条信息，也就是说，数据服务器 i 在上一次发送信息给主服务器后的 patience[i] 秒 后 会重发一条信息给主服务器。当没有任何信息在线路上传输或者到达某服务器时，该计算机网络变为 空闲 状态。
\n\n请返回计算机网络变为 空闲 状态的 最早秒数 。
\n\n\n\n
示例 1：
\n\n
输入：edges = [[0,1],[1,2]], patience = [0,2,1]\n输出：8\n解释：\n0 秒最开始时，\n- 数据服务器 1 给主服务器发出信息（用 1A 表示）。\n- 数据服务器 2 给主服务器发出信息（用 2A 表示）。\n\n1 秒时，\n- 信息 1A 到达主服务器，主服务器立刻处理信息 1A 并发出 1A 的回复信息。\n- 数据服务器 1 还没收到任何回复。距离上次发出信息过去了 1 秒（1 < patience[1] = 2），所以不会重发信息。\n- 数据服务器 2 还没收到任何回复。距离上次发出信息过去了 1 秒（1 == patience[2] = 1），所以它重发一条信息（用 2B 表示）。\n\n2 秒时，\n- 回复信息 1A 到达服务器 1 ，服务器 1 不会再重发信息。\n- 信息 2A 到达主服务器，主服务器立刻处理信息 2A 并发出 2A 的回复信息。\n- 服务器 2 重发一条信息（用 2C 表示）。\n...\n4 秒时，\n- 回复信息 2A 到达服务器 2 ，服务器 2 不会再重发信息。\n...\n7 秒时，回复信息 2D 到达服务器 2 。\n\n从第 8 秒开始，不再有任何信息在服务器之间传输，也不再有信息到达服务器。\n所以第 8 秒是网络变空闲的最早时刻。\n\n\n
示例 2：
\n\n
输入：edges = [[0,1],[0,2],[1,2]], patience = [0,10,10]\n输出：3\n解释：数据服务器 1 和 2 第 2 秒初收到回复信息。\n从第 3 秒开始，网络变空闲。\n\n\n
\n\n
提示：
\n\nn == patience.length2 <= n <= 105patience[0] == 01 <= i < n ，满足 1 <= patience[i] <= 1051 <= edges.length <= min(105, n * (n - 1) / 2)edges[i].length == 20 <= ui, vi < nui != vi\\u7248\\u672c\\uff1a \\u7f16\\u8bd1\\u65f6\\uff0c\\u5c06\\u4f1a\\u91c7\\u7528 \\u4e3a\\u4e86\\u4f7f\\u7528\\u65b9\\u4fbf\\uff0c\\u5927\\u90e8\\u5206\\u6807\\u51c6\\u5e93\\u7684\\u5934\\u6587\\u4ef6\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8\\u5bfc\\u5165\\u3002<\\/p>\"],\"java\":[\"Java\",\" \\u7248\\u672c\\uff1a \\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u6807\\u51c6\\u5e93\\u7684\\u5934\\u6587\\u4ef6\\u5df2\\u88ab\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n \\u5305\\u542b Pair \\u7c7b: https:\\/\\/docs.oracle.com\\/javase\\/8\\/javafx\\/api\\/javafx\\/util\\/Pair.html <\\/p>\"],\"python\":[\"Python\",\" \\u7248\\u672c\\uff1a \\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u5e38\\u7528\\u5e93\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8 \\u5bfc\\u5165\\uff0c\\u5982\\uff1aarray<\\/a>, bisect<\\/a>, collections<\\/a>\\u3002\\u5982\\u679c\\u60a8\\u9700\\u8981\\u4f7f\\u7528\\u5176\\u4ed6\\u5e93\\u51fd\\u6570\\uff0c\\u8bf7\\u81ea\\u884c\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n \\u6ce8\\u610f Python 2.7 \\u5c06\\u57282020\\u5e74\\u540e\\u4e0d\\u518d\\u7ef4\\u62a4<\\/a>\\u3002 \\u5982\\u60f3\\u4f7f\\u7528\\u6700\\u65b0\\u7248\\u7684Python\\uff0c\\u8bf7\\u9009\\u62e9Python 3\\u3002<\\/p>\"],\"c\":[\"C\",\" \\u7248\\u672c\\uff1a \\u7f16\\u8bd1\\u65f6\\uff0c\\u5c06\\u4f1a\\u91c7\\u7528 \\u4e3a\\u4e86\\u4f7f\\u7528\\u65b9\\u4fbf\\uff0c\\u5927\\u90e8\\u5206\\u6807\\u51c6\\u5e93\\u7684\\u5934\\u6587\\u4ef6\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n \\u5982\\u60f3\\u4f7f\\u7528\\u54c8\\u5e0c\\u8868\\u8fd0\\u7b97, \\u60a8\\u53ef\\u4ee5\\u4f7f\\u7528 uthash<\\/a>\\u3002 \\\"uthash.h\\\"\\u5df2\\u7ecf\\u9ed8\\u8ba4\\u88ab\\u5bfc\\u5165\\u3002\\u8bf7\\u770b\\u5982\\u4e0b\\u793a\\u4f8b:<\\/p>\\r\\n\\r\\n 1. 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\\u6a21\\u5757\\u4e2d\\u63d0\\u4f9b\\uff1ahttps:\\/\\/www.rubydoc.info\\/github\\/kanwei\\/algorithms\\/Algorithms<\\/p>\"],\"swift\":[\"Swift\",\" \\u7248\\u672c\\uff1a \\u6211\\u4eec\\u901a\\u5e38\\u4fdd\\u8bc1\\u66f4\\u65b0\\u5230 Apple\\u653e\\u51fa\\u7684\\u6700\\u65b0\\u7248Swift<\\/a>\\u3002\\u5982\\u679c\\u60a8\\u53d1\\u73b0Swift\\u4e0d\\u662f\\u6700\\u65b0\\u7248\\u7684\\uff0c\\u8bf7\\u8054\\u7cfb\\u6211\\u4eec\\uff01\\u6211\\u4eec\\u5c06\\u5c3d\\u5feb\\u66f4\\u65b0\\u3002<\\/p>\"],\"golang\":[\"Go\",\" \\u7248\\u672c\\uff1a \\u652f\\u6301 https:\\/\\/godoc.org\\/github.com\\/emirpasic\\/gods@v1.18.1<\\/a> \\u7b2c\\u4e09\\u65b9\\u5e93\\u3002<\\/p>\"],\"python3\":[\"Python3\",\" \\u7248\\u672c\\uff1a \\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u5e38\\u7528\\u5e93\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8 \\u5bfc\\u5165\\uff0c\\u5982array<\\/a>, bisect<\\/a>, collections<\\/a>\\u3002 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