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)

#[derive(PartialEq, Eq)]
pub struct Reverse<T>(pub T);

impl<T: PartialOrd> PartialOrd for Reverse<T> {
    #[inline]
    fn partial_cmp(&self, other: &Reverse<T>) -> Option<Ordering> {
        other.0.partial_cmp(&self.0)
    }

    #[inline]
    fn lt(&self, other: &Self) -> bool {
        other.0 < self.0
    }
    #[inline]
    fn le(&self, other: &Self) -> bool {
        other.0 <= self.0
    }
    #[inline]
    fn gt(&self, other: &Self) -> bool {
        other.0 > self.0
    }
    #[inline]
    fn ge(&self, other: &Self) -> bool {
        other.0 >= self.0
    }
}

impl<T: Ord> Ord for Reverse<T> {
    #[inline]
    fn cmp(&self, other: &Reverse<T>) -> Ordering {
        other.0.cmp(&self.0)
    }
}

#[derive(Debug, Clone, Copy)]
struct Edge {
    cost: usize,
    node: usize,
}

#[derive(Debug, Clone, Copy)]
struct State {
    dist: usize,
    position: usize,
}

fn shortest_path(adjl: &Vec<Vec<Edge>>, start: usize) -> Vec<usize> {
    let mut dist = vec![INF; adjl.len()];
    let mut que: BinaryHeap<(Reverse<usize>, usize)> = BinaryHeap::new();
    que.push((Reverse(0), start));
    while let Some((Reverse(c), node)) = que.pop() {
        if dist[node] < c {
            continue;
        }
        dist[node] = c;
        for next in &adjl[node] {
            if c + next.cost < dist[next.node] {
                que.push((Reverse(c + next.cost), next.node));
            }
        }
    }
    dist
}

fn solve() {
    let (v, e, start): (usize, usize, usize) = (read::<usize>(), read::<usize>(), read::<usize>());
    let mut adjl = vec![vec![]; v];
    for _ in 0..e {
        let (s, t, cost): (usize, usize, usize) =
            (read::<usize>(), read::<usize>(), read::<usize>());
        adjl[s].push(Edge { cost, node: t });
    }
    // println!("{:?}", adjl);
    for d in shortest_path(&adjl, start) {
        if d == INF {
            println!("INF");
        } else {
            println!("{}", d);
        }
    }
}

fn main() {
    let stack_size = 104_857_600;
    let thd = std::thread::Builder::new().stack_size(stack_size);
    thd.spawn(|| solve()).unwrap().join().unwrap();
}

// =========
#[allow(unused_imports)]
use std::cmp::{max, min, Ord, Ordering, PartialOrd};
#[allow(unused_imports)]
use std::collections::{BinaryHeap, HashMap, HashSet};
#[allow(unused_imports)]
use std::process::exit;

#[allow(dead_code)]
const MOD: usize = 1000000007;
const INF: usize = std::usize::MAX;

fn read<T: std::str::FromStr>() -> T {
    use std::io::Read;
    let stdin = std::io::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")
}

// =========