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)

#![allow(unused_imports)]
#![allow(dead_code)]

use std::thread;
use std::io::{ self, Read };
use std::fmt;
use std::iter::Iterator;
use std::cmp::*;
use std::collections::*;
use std::str::*;
use std::mem::*;
use std::cell::*;

struct Input {
    stdin: io::Stdin,
    buf: VecDeque<String>
}

impl Input {
    fn new() -> Input {
        Input { 
            stdin: io::stdin(),
            buf: VecDeque::new()
        }
    }

    fn read<T: FromStr>(&mut self) -> T 
    where <T as FromStr>::Err: fmt::Debug {
        self.next().unwrap().parse::<T>().unwrap()
    }

    fn read_2<T: FromStr, U: FromStr>(&mut self) -> (T, U)
    where <T as FromStr>::Err: fmt::Debug,
          <U as FromStr>::Err: fmt::Debug {
        (self.read(), self.read())
    }

    fn read_3<T: FromStr, U: FromStr, V: FromStr>(&mut self) -> (T, U, V)
    where <T as FromStr>::Err: fmt::Debug,
          <U as FromStr>::Err: fmt::Debug,
          <V as FromStr>::Err: fmt::Debug {
        (self.read(), self.read(), self.read())
    }

    fn read_bytes(&mut self) -> Vec<u8> {
        self.next().unwrap().into_bytes()
    }

    fn read_n<T: FromStr>(&mut self, n: usize) -> Vec<T>
    where <T as FromStr>::Err: fmt::Debug {
        let mut v = Vec::new();
        for _ in 0..n { v.push(self.read::<T>()); }
        v
    }
}

impl Iterator for Input {
    type Item = String;
    fn next(&mut self) -> Option<String> {
        while self.buf.is_empty() {
            let mut s = String::new();
            let _res = self.stdin.read_line(&mut s);
            self.buf.extend(s.split_whitespace().map(|s| s.to_owned()));
        }
        self.buf.pop_front()
    }
}

fn dijkstra<U: AsRef<[(usize, i64)]>>(g: &[U], s: usize) -> Vec<i64> {
    let n = g.len();
    let mut d = vec![i64::max_value(); n];
    let mut q = BinaryHeap::<(i64, usize)>::new();
    q.push((0, s));
    d[s] = 0;
    while let Some((ic, u)) = q.pop() {
        let c = -ic;
        if c <= d[u] {
            for &(v, w) in g[u].as_ref() {
                if c + w < d[v] {
                    d[v] = c + w;
                    q.push((-d[v], v));
                }
            }
        }
    }
    d
}

fn run() {
    let mut ip = Input::new();
    let (n, m, r) = ip.read_3();
    let mut g = vec![vec![]; n];
    for _ in 0..m {
        let (u, v, w): (usize, usize, i64) = ip.read_3();
        g[u].push((v, w));
    }
    let d = dijkstra(&g, r);
    for x in d {
        if x < i64::max_value() { println!("{}", x); }
        else { println!("INF"); }
    }
}

fn main() {
    let _ = thread::Builder::new()
        .stack_size(50 * 1024 * 1024)
        .spawn(run).unwrap()
        .join();
}