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)

//usage
//input! {
//  h: i32;
//  v: [i32; n]
//  x: [[i32; n]; m]
//  f: chars <- Vec<char>
//}
use std::collections::BinaryHeap;

#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};

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

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

#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };

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

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

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

    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };

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

    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}
const INF: i64 = std::i64::MAX;

#[derive(Debug)]
struct Graph {
    node: usize,
    directed: bool,
    graph: Vec<Vec<(usize, i64)>>,
}

impl Graph {
    fn new(n: usize, flag: bool) -> Graph {
        Graph { node: n, directed: flag, graph: vec![vec![]; n] }
    }

    fn add_edge(&mut self, start_node: usize, end_node: usize, cost: i64) -> () {
        self.graph[start_node].push((end_node, cost));
        if !self.directed { self.graph[end_node].push((start_node, cost)); }
    }
    fn dijkstra(&self, start_node: usize) -> Vec<i64> {
        let mut dist = vec![INF; self.node];
        dist[start_node] = 0;

        let mut queue: BinaryHeap<(i64, usize)> = BinaryHeap::new();
        queue.push((0, start_node));

        while !queue.is_empty() {
            let (min_dist, idx) = queue.pop().unwrap();
            if dist[idx] < -min_dist {
                continue;
            }
            for &(to, weight) in &self.graph[idx] {
                let cost_cand = dist[idx] + weight;
                if dist[to] > cost_cand {
                    dist[to] = cost_cand;
                    queue.push((-cost_cand, to));
                }
            }
        }
        dist
    }
}

fn main() {
    input! {
        v: usize, e: usize, r: usize,
        g: [(usize, usize, i64); e]
    }

    let mut graph = Graph::new(v, true);
    for &(x, y, z) in &g {
        graph.add_edge(x, y, z);
    }

    let cost = graph.dijkstra(r);
    for x in cost {
        println!("{}", if x == INF {"INF".to_owned()} else {x.to_string()});
    }
}