Checking Existence of Edge Length Limited Paths
<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>

<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>

<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>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1600-1699/1697.Checking%20Existence%20of%20Edge%20Length%20Limited%20Paths/images/h.png" style="width: 267px; height: 262px;" />
<pre>
<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]]
<strong>Output:</strong> [false,true]
<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.
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.
For the second query, there is a path (0 -&gt; 1 -&gt; 2) of two edges with distances less than 5, thus we return true for this query.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1600-1699/1697.Checking%20Existence%20of%20Edge%20Length%20Limited%20Paths/images/q.png" style="width: 390px; height: 358px;" />
<pre>
<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]]
<strong>Output:</strong> [true,false]
<strong>Explanation:</strong> The above figure shows the given graph.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= edgeList.length, queries.length &lt;= 10<sup>5</sup></code></li>
	<li><code>edgeList[i].length == 3</code></li>
	<li><code>queries[j].length == 3</code></li>
	<li><code>0 &lt;= u<sub>i</sub>, v<sub>i</sub>, p<sub>j</sub>, q<sub>j</sub> &lt;= n - 1</code></li>
	<li><code>u<sub>i</sub> != v<sub>i</sub></code></li>
	<li><code>p<sub>j</sub> != q<sub>j</sub></code></li>
	<li><code>1 &lt;= dis<sub>i</sub>, limit<sub>j</sub> &lt;= 10<sup>9</sup></code></li>
	<li>There may be <strong>multiple</strong> edges between two nodes.</li>
</ul>
Union Find; Graph; Array; Two Pointers; Sorting
impl Solution {
    #[allow(dead_code)]
    pub fn distance_limited_paths_exist(
        n: i32,
        edge_list: Vec<Vec<i32>>,
        queries: Vec<Vec<i32>>,
    ) -> Vec<bool> {
        let mut disjoint_set: Vec<usize> = vec![0; n as usize];
        let mut ans_vec: Vec<bool> = vec![false; queries.len()];
        let mut q_vec: Vec<usize> = vec![0; queries.len()];

        // Initialize the set
        for i in 0..n {
            disjoint_set[i as usize] = i as usize;
        }

        // Initialize the q_vec
        for i in 0..queries.len() {
            q_vec[i] = i;
        }

        // Sort the q_vec based on the query limit, from the lowest to highest
        q_vec.sort_by(|i, j| queries[*i][2].cmp(&queries[*j][2]));

        // Sort the edge_list based on the edge weight, from the lowest to highest
        let mut edge_list = edge_list.clone();
        edge_list.sort_by(|i, j| i[2].cmp(&j[2]));

        let mut edge_idx: usize = 0;
        for q_idx in &q_vec {
            let s = queries[*q_idx][0] as usize;
            let d = queries[*q_idx][1] as usize;
            let limit = queries[*q_idx][2];
            // Construct the disjoint set
            while edge_idx < edge_list.len() && edge_list[edge_idx][2] < limit {
                Solution::union(
                    edge_list[edge_idx][0] as usize,
                    edge_list[edge_idx][1] as usize,
                    &mut disjoint_set,
                );
                edge_idx += 1;
            }
            // If the parents of s & d are the same, this query should be `true`
            // Otherwise, the current query is `false`
            ans_vec[*q_idx] = Solution::check_valid(s, d, &mut disjoint_set);
        }

        ans_vec
    }

    #[allow(dead_code)]
    pub fn find(x: usize, d_set: &mut Vec<usize>) -> usize {
        if d_set[x] != x {
            d_set[x] = Solution::find(d_set[x], d_set);
        }
        return d_set[x];
    }

    #[allow(dead_code)]
    pub fn union(s: usize, d: usize, d_set: &mut Vec<usize>) {
        let p_s = Solution::find(s, d_set);
        let p_d = Solution::find(d, d_set);
        d_set[p_s] = p_d;
    }

    #[allow(dead_code)]
    pub fn check_valid(s: usize, d: usize, d_set: &mut Vec<usize>) -> bool {
        let p_s = Solution::find(s, d_set);
        let p_d = Solution::find(d, d_set);
        p_s == p_d
    }
}
