Problem:
Single Source Shortest Path

For a given weighted graph G(V, E) and a source r, find the source shortest path to each vertex from the source (SSSP: Single Source Shortest Path).

Input

An edge-weighted graph G (V, E) and the source r.

|V| |E| r
s0 t0 d0
s1 t1 d1
:
s|E|-1 t|E|-1 d|E|-1

|V| is the number of vertices and |E| is the number of edges in G. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively. r is the source of the graph.

si and ti represent source and target vertices of i-th edge (directed) and di represents the cost of the i-th edge.

Output

Print the costs of SSSP in the following format.

c0
c1
:
c|V|-1

The output consists of |V| lines. Print the cost of the shortest path from the source r to each vertex 0, 1, ... |V|-1 in order. If there is no path from the source to a vertex, print INF.

Constraints

1 ≤ |V| ≤ 100000

0 ≤ di ≤ 10000

0 ≤ |E| ≤ 500000

There are no parallel edges

There are no self-loops

Sample Input 1

4 5 0
0 1 1
0 2 4
1 2 2
2 3 1
1 3 5

Sample Output 1

0
1
3
4

Sample Input 2

4 6 1
0 1 1
0 2 4
2 0 1
1 2 2
3 1 1
3 2 5

Sample Output 2

3
0
2
INF

Solution in Rust (judge verdict: Accepted)

use std::cmp::*;
use std::collections::HashMap;
use std::io::*;
use std::str::FromStr;
use std::string::String;

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();

    token.parse().ok().expect("failed to parse token")
}

#[derive(Eq, PartialEq, Clone, Debug)]
pub struct Rev<T>(pub T);

impl<T: PartialOrd> PartialOrd for Rev<T> {
    fn partial_cmp(&self, other: &Rev<T>) -> Option<std::cmp::Ordering> {
        other.0.partial_cmp(&self.0)
    }
}

impl<T: Ord> Ord for Rev<T> {
    fn cmp(&self, other: &Rev<T>) -> std::cmp::Ordering {
        other.0.cmp(&self.0)
    }
}

use std::collections::BinaryHeap;

#[derive(Clone)]
struct Edge {
    to: usize,
    cost: i32,
}

fn dijkstra(graph: &Vec<Vec<Edge>>, start: usize) -> Vec<i32> {
    let n = graph.len();
    let mut distance: Vec<i32> = vec![1_000_000_000; n];
    let mut visited: Vec<bool> = vec![false; n];
    let mut heap: BinaryHeap<Rev<(i32, usize)>> = BinaryHeap::new();
    heap.push(Rev((0, start))); //(cost, from)

    while !heap.is_empty() {
        let Rev((cost, from)) = heap.pop().unwrap();
        if visited[from] == true {
            continue;
        }
        visited[from] = true;
        distance[from] = cost;

        for e in &graph[from] {
            if distance[e.to] <= cost + e.cost {
                continue;
            }

            heap.push(Rev((cost + e.cost, e.to)));
        }
    }

    return distance;
}

fn main() {
    let (v, e, r): (usize, usize, usize) = (read(), read(), read());
    let mut graph: Vec<Vec<Edge>> = vec![Vec::new(); v];

    for _ in 0..e {
        let (s, t, d): (usize, usize, i32) = (read(), read(), read());
        graph[s].push(Edge { to: t, cost: d });
    }

    for ans in dijkstra(&graph, r) {
        if ans == 1_000_000_000 {
            println!("INF");
        } else {
            println!("{}", ans);
        }
    }
}