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72 lines
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72 lines
4.9 KiB
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<p>There is a network of <code>n</code> servers, labeled from <code>0</code> to <code>n - 1</code>. You are given a 2D integer array <code>edges</code>, where <code>edges[i] = [u<sub>i</sub>, v<sub>i</sub>]</code> indicates there is a message channel between servers <code>u<sub>i</sub></code> and <code>v<sub>i</sub></code>, and they can pass <strong>any</strong> number of messages to <strong>each other</strong> directly in <strong>one</strong> second. You are also given a <strong>0-indexed</strong> integer array <code>patience</code> of length <code>n</code>.</p>
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<p>All servers are <strong>connected</strong>, i.e., a message can be passed from one server to any other server(s) directly or indirectly through the message channels.</p>
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<p>The server labeled <code>0</code> is the <strong>master</strong> server. The rest are <strong>data</strong> servers. Each data server needs to send its message to the master server for processing and wait for a reply. Messages move between servers <strong>optimally</strong>, so every message takes the <strong>least amount of time</strong> to arrive at the master server. The master server will process all newly arrived messages <strong>instantly</strong> and send a reply to the originating server via the <strong>reversed path</strong> the message had gone through.</p>
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<p>At the beginning of second <code>0</code>, each data server sends its message to be processed. Starting from second <code>1</code>, at the <strong>beginning</strong> of <strong>every</strong> 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:</p>
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<ul>
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<li>If it has not, it will <strong>resend</strong> the message periodically. The data server <code>i</code> will resend the message every <code>patience[i]</code> second(s), i.e., the data server <code>i</code> will resend the message if <code>patience[i]</code> second(s) have <strong>elapsed</strong> since the <strong>last</strong> time the message was sent from this server.</li>
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<li>Otherwise, <strong>no more resending</strong> will occur from this server.</li>
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</ul>
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<p>The network becomes <strong>idle</strong> when there are <strong>no</strong> messages passing between servers or arriving at servers.</p>
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<p>Return <em>the <strong>earliest second</strong> starting from which the network becomes <strong>idle</strong></em>.</p>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<img alt="example 1" src="https://assets.leetcode.com/uploads/2021/09/22/quiet-place-example1.png" style="width: 750px; height: 384px;" />
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<pre>
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<strong>Input:</strong> edges = [[0,1],[1,2]], patience = [0,2,1]
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<strong>Output:</strong> 8
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<strong>Explanation:</strong>
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At (the beginning of) second 0,
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- Data server 1 sends its message (denoted 1A) to the master server.
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- Data server 2 sends its message (denoted 2A) to the master server.
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At second 1,
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- Message 1A arrives at the master server. Master server processes message 1A instantly and sends a reply 1A back.
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- 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.
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- 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).
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At second 2,
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- The reply 1A arrives at server 1. No more resending will occur from server 1.
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- Message 2A arrives at the master server. Master server processes message 2A instantly and sends a reply 2A back.
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- Server 2 resends the message (denoted 2C).
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...
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At second 4,
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- The reply 2A arrives at server 2. No more resending will occur from server 2.
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...
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At second 7, reply 2D arrives at server 2.
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Starting from the beginning of the second 8, there are no messages passing between servers or arriving at servers.
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This is the time when the network becomes idle.
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</pre>
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<p><strong>Example 2:</strong></p>
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<img alt="example 2" src="https://assets.leetcode.com/uploads/2021/09/04/network_a_quiet_place_2.png" style="width: 100px; height: 85px;" />
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<pre>
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<strong>Input:</strong> edges = [[0,1],[0,2],[1,2]], patience = [0,10,10]
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<strong>Output:</strong> 3
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<strong>Explanation:</strong> Data servers 1 and 2 receive a reply back at the beginning of second 2.
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From the beginning of the second 3, the network becomes idle.
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>n == patience.length</code></li>
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<li><code>2 <= n <= 10<sup>5</sup></code></li>
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<li><code>patience[0] == 0</code></li>
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<li><code>1 <= patience[i] <= 10<sup>5</sup></code> for <code>1 <= i < n</code></li>
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<li><code>1 <= edges.length <= min(10<sup>5</sup>, n * (n - 1) / 2)</code></li>
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<li><code>edges[i].length == 2</code></li>
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<li><code>0 <= u<sub>i</sub>, v<sub>i</sub> < n</code></li>
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<li><code>u<sub>i</sub> != v<sub>i</sub></code></li>
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<li>There are no duplicate edges.</li>
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<li>Each server can directly or indirectly reach another server.</li>
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</ul>
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