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::fmt::Debug;
use std::io::{stdin, Read};
use std::str::FromStr;

//mod lib;

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();

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

static MOD: i64 = 1_000_000_007;

fn read_vec1<T: FromStr>(n: usize) -> Vec<T> {
    return (0..n).map(|_| read()).collect();
}

fn read_vec2<T: FromStr>(n: usize, m: usize) -> Vec<Vec<T>> {
    return (0..n).map(|_| read_vec1(m)).collect();
}

#[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<Ordering> {
        other.0.partial_cmp(&self.0)
    }
}

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

fn add_by_mod(a: &i64, b: &i64) -> i64 {
    return (a % MOD + b % MOD) % MOD;
}

#[derive(Clone, Copy, Debug)]
pub struct Edge {
    cost: u64,
    from: usize,
    to: usize,
}

pub fn dijkstra(graph: &Vec<Vec<Edge>>, s: &usize) -> Vec<u64> {
    use std::collections::BinaryHeap;
    let inf = 1e18 as u64;
    let mut dp = vec![inf; graph.len()];
    let mut used = vec![false; graph.len()];
    let mut que: BinaryHeap<Rev<(u64, usize)>> = BinaryHeap::new();
    que.push(Rev((0, *s)));

    while que.len() > 0 {
        let Rev((now_cost, now_v)) = que.pop().unwrap();
        if used[now_v] {
            continue;
        }
        used[now_v] = true;
        dp[now_v] = now_cost;
        for e in graph[now_v].iter() {
            if e.cost + now_cost > dp[e.to] {
                continue;
            }
            que.push(Rev((e.cost + now_cost, e.to)));
        }
    }

    return dp;
}

fn main() {
    let (v, e, r): (usize, usize, usize) = (read(), read(), read());
    let mut graph = vec![Vec::new(); v];
    for _ in 0..e {
        let (s, t, d): (usize, usize, u64) = (read(), read(), read());
        graph[s].push(Edge {
            cost: d,
            from: s,
            to: t,
        });
    }

    let dist = dijkstra(&graph, &r);
    for d in dist.iter() {
        if *d == 1e18 as u64 {
            println!("{}", "INF");
        } else {
            println!("{}", *d);
        }
    }
}