#1724
Hard Algorithms Checking existence of edge length limited paths ii
Depth-First Search Union-Find Graph Theory Design Sorting Heap (Priority Queue) Minimum Spanning Tree
51.7% acceptance
Mar 31, 2026
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An undirected graph of n nodes is defined by edgeList, where edgeList[i] = [ui, vi, disi] denotes an edge between nodes ui and vi with distance disi. Note that there may be multiple edges between two nodes, and the graph may not be connected.
Implement the DistanceLimitedPathsExist class:
DistanceLimitedPathsExist(int n, int[][] edgeList) Initializes the class with an undirected graph.
boolean query(int p, int q, int limit) Returns true if there exists a path from p to q such that each edge on the path has a distance strictly less than limit, and otherwise false.
Solution
Rust
Time O(n * m)
Space O(n * m)
struct DistanceLimitedPathsExist {
parent: Vec<Vec<i32>>,
max_weight: Vec<Vec<i32>>,
depth: Vec<i32>,
component: Vec<i32>,
}
/**
* `&self` means the method takes an immutable reference.
* If you need a mutable reference, change it to `&mut self` instead.
*/
impl DistanceLimitedPathsExist {
fn new(n: i32, edge_list: Vec<Vec<i32>>) -> Self {
let n = n as usize;
let log_n = 15;
let mut edges: Vec<(i32, usize, usize)> = edge_list.iter()
.map(|e| (e[2], e[0] as usize, e[1] as usize))
.collect();
edges.sort();
let mut uf: Vec<usize> = (0..n).collect();
let mut rank = vec![0usize; n];
fn find(uf: &mut Vec<usize>, x: usize) -> usize {
if uf[x] != x { uf[x] = find(uf, uf[x]); }
uf[x]
}
let mut adj = vec![vec![]; n];
for &(w, u, v) in &edges {
let ru = find(&mut uf, u);
let rv = find(&mut uf, v);
if ru != rv {
adj[u].push((v, w));
adj[v].push((u, w));
if rank[ru] < rank[rv] { uf[ru] = rv; }
else if rank[ru] > rank[rv] { uf[rv] = ru; }
else { uf[rv] = ru; rank[ru] += 1; }
}
}
let mut component = vec![-1i32; n];
let mut parent_table = vec![vec![-1i32; n]; log_n];
let mut weight_table = vec![vec![0i32; n]; log_n];
let mut depth = vec![0i32; n];
let mut visited = vec![false; n];
let mut comp_id = 0i32;
for start in 0..n {
if visited[start] { continue; }
visited[start] = true;
component[start] = comp_id;
let mut queue = std::collections::VecDeque::new();
queue.push_back(start);
while let Some(u) = queue.pop_front() {
for &(v, w) in &adj[u] {
if !visited[v] {
visited[v] = true;
component[v] = comp_id;
depth[v] = depth[u] + 1;
parent_table[0][v] = u as i32;
weight_table[0][v] = w;
queue.push_back(v);
}
}
}
comp_id += 1;
}
for k in 1..log_n {
for i in 0..n {
let p = parent_table[k - 1][i];
if p != -1 {
parent_table[k][i] = parent_table[k - 1][p as usize];
weight_table[k][i] = weight_table[k - 1][i].max(weight_table[k - 1][p as usize]);
}
}
}
DistanceLimitedPathsExist { parent: parent_table, max_weight: weight_table, depth, component }
}
fn query(&self, p: i32, q: i32, limit: i32) -> bool {
let (mut a, mut b) = (p as usize, q as usize);
if self.component[a] != self.component[b] { return false; }
let log_n = self.parent.len();
let mut max_w = 0i32;
if self.depth[a] < self.depth[b] { std::mem::swap(&mut a, &mut b); }
let diff = self.depth[a] - self.depth[b];
for k in 0..log_n {
if diff & (1 << k) != 0 {
max_w = max_w.max(self.max_weight[k][a]);
a = self.parent[k][a] as usize;
}
}
if a == b { return max_w < limit; }
for k in (0..log_n).rev() {
if self.parent[k][a] != self.parent[k][b] {
max_w = max_w.max(self.max_weight[k][a]);
max_w = max_w.max(self.max_weight[k][b]);
a = self.parent[k][a] as usize;
b = self.parent[k][b] as usize;
}
}
max_w = max_w.max(self.max_weight[0][a]);
max_w = max_w.max(self.max_weight[0][b]);
max_w < limit
}
}
/*
* Your DistanceLimitedPathsExist object will be instantiated and called as such:
* let obj = DistanceLimitedPathsExist::new(n, edgeList);
* let ret_1: bool = obj.query(p, q, limit);
*/