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| 7 | + |
| 8 | +[< Previous](../jump-game-vi "Jump Game VI") |
| 9 | + |
| 10 | +[Next >](../number-of-distinct-substrings-in-a-string "Number of Distinct Substrings in a String") |
| 11 | + |
| 12 | +## [1697. Checking Existence of Edge Length Limited Paths (Hard)](https://leetcode.com/problems/checking-existence-of-edge-length-limited-paths "检查边长度限制的路径是否存在") |
| 13 | + |
| 14 | +<p>An undirected graph of <code>n</code> nodes is defined by <code>edgeList</code>, where <code>edgeList[i] = [u<sub>i</sub>, v<sub>i</sub>, dis<sub>i</sub>]</code> denotes an edge between nodes <code>u<sub>i</sub></code> and <code>v<sub>i</sub></code> with distance <code>dis<sub>i</sub></code>. Note that there may be <strong>multiple</strong> edges between two nodes.</p> |
| 15 | + |
| 16 | +<p>Given an array <code>queries</code>, where <code>queries[j] = [p<sub>j</sub>, q<sub>j</sub>, limit<sub>j</sub>]</code>, your task is to determine for each <code>queries[j]</code> whether there is a path between <code>p<sub>j</sub></code> and <code>q<sub>j</sub></code><sub> </sub>such that each edge on the path has a distance <strong>strictly less than</strong> <code>limit<sub>j</sub></code> .</p> |
| 17 | + |
| 18 | +<p>Return <em>a <strong>boolean array</strong> </em><code>answer</code><em>, where </em><code>answer.length == queries.length</code> <em>and the </em><code>j<sup>th</sup></code> <em>value of </em><code>answer</code> <em>is </em><code>true</code><em> if there is a path for </em><code>queries[j]</code><em> is </em><code>true</code><em>, and </em><code>false</code><em> otherwise</em>.</p> |
| 19 | + |
| 20 | +<p> </p> |
| 21 | +<p><strong>Example 1:</strong></p> |
| 22 | +<img alt="" src="https://assets.leetcode.com/uploads/2020/12/08/h.png" style="width: 267px; height: 262px;" /> |
| 23 | +<pre> |
| 24 | +<strong>Input:</strong> n = 3, edgeList = [[0,1,2],[1,2,4],[2,0,8],[1,0,16]], queries = [[0,1,2],[0,2,5]] |
| 25 | +<strong>Output:</strong> [false,true] |
| 26 | +<strong>Explanation:</strong> The above figure shows the given graph. Note that there are two overlapping edges between 0 and 1 with distances 2 and 16. |
| 27 | +For the first query, between 0 and 1 there is no path where each distance is less than 2, thus we return false for this query. |
| 28 | +For the second query, there is a path (0 -> 1 -> 2) of two edges with distances less than 5, thus we return true for this query. |
| 29 | +</pre> |
| 30 | + |
| 31 | +<p><strong>Example 2:</strong></p> |
| 32 | +<img alt="" src="https://assets.leetcode.com/uploads/2020/12/08/q.png" style="width: 390px; height: 358px;" /> |
| 33 | +<pre> |
| 34 | +<strong>Input:</strong> n = 5, edgeList = [[0,1,10],[1,2,5],[2,3,9],[3,4,13]], queries = [[0,4,14],[1,4,13]] |
| 35 | +<strong>Output:</strong> [true,false] |
| 36 | +<strong>Exaplanation:</strong> The above figure shows the given graph. |
| 37 | +</pre> |
| 38 | + |
| 39 | +<p> </p> |
| 40 | +<p><strong>Constraints:</strong></p> |
| 41 | + |
| 42 | +<ul> |
| 43 | + <li><code>2 <= n <= 10<sup>5</sup></code></li> |
| 44 | + <li><code>1 <= edgeList.length, queries.length <= 10<sup>5</sup></code></li> |
| 45 | + <li><code>edgeList[i].length == 3</code></li> |
| 46 | + <li><code>queries[j].length == 3</code></li> |
| 47 | + <li><code>0 <= u<sub>i</sub>, v<sub>i</sub>, p<sub>j</sub>, q<sub>j</sub> <= n - 1</code></li> |
| 48 | + <li><code>u<sub>i</sub> != v<sub>i</sub></code></li> |
| 49 | + <li><code>p<sub>j</sub> != q<sub>j</sub></code></li> |
| 50 | + <li><code>1 <= dis<sub>i</sub>, limit<sub>j</sub> <= 10<sup>9</sup></code></li> |
| 51 | + <li>There may be <strong>multiple</strong> edges between two nodes.</li> |
| 52 | +</ul> |
| 53 | + |
| 54 | +### Related Topics |
| 55 | + [[Sort](../../tag/sort/README.md)] |
| 56 | + [[Union Find](../../tag/union-find/README.md)] |
| 57 | + |
| 58 | +### Hints |
| 59 | +<details> |
| 60 | +<summary>Hint 1</summary> |
| 61 | +All the queries are given in advance. Is there a way you can reorder the queries to avoid repeated computations? |
| 62 | +</details> |
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