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)

// input macro
// ref: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let mut s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};

    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };

    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };

    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };

    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };

    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

use std::collections::BinaryHeap;

struct Dijkstra {
    pub edges: Vec<Vec<(usize, i64)>>,
    pub start: usize,
}

impl Dijkstra {
    fn get_shortest_path(&self) -> Vec<i64> {
        let node_num = self.edges.len();
        assert!(self.start < node_num, "invalid start node");

        let mut pque: BinaryHeap<(i64, usize)> = BinaryHeap::new();
        let mut distance = vec![std::i64::MAX; node_num];

        pque.push((0, self.start));
        distance[self.start] = 0;

        while !pque.is_empty() {
            let (min_distance, idx) = pque.pop().unwrap();
            if distance[idx] < -min_distance { continue; }
            for i in 0..self.edges[idx].len() {
                let (to, cost) = self.edges[idx][i];
                let new_cost = distance[idx] + cost;
                if distance[to] > new_cost {
                    distance[to] = new_cost;
                    pque.push((-new_cost, to));
                }
            }
        }

        distance
    }
}

#[allow(unused_mut)]
fn main() {
    input!(
        v: usize,
        e: usize,
        r: usize,
        std: [(usize, usize, i64); e],
    );
    let mut dj = Dijkstra {
        edges: vec![Vec::new(); v],
        start: r,
    };

    for &(s,t,d) in std.iter() {
        dj.edges[s].push((t, d));
    }

    let distance = dj.get_shortest_path();
    for (_, d) in distance.iter().enumerate() {
        if *d == std::i64::MAX {
            println!("INF");
        }
        else {
            println!("{}", d);
        }
    }
}