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)

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)*}
    };
}

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)*}
    };
}

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<_>>()
    };

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

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

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

use std::collections::BinaryHeap;

struct Graph {
    edges: Vec<Vec<(usize, i64)>>, // adjacent list
    n: usize
}

impl Graph {
    fn new(n: usize) -> Self {
        Graph {
            edges: vec![Vec::new(); n],
            n: n
        }
    }

    fn add_costs(&mut self, from: usize, to: usize, cost: i64, directed: bool) {
        if directed {
            self.edges[from].push((to, cost));
        } else {
            self.edges[from].push((to, cost));
            self.edges[to].push((from, cost));
        }

    }

    fn dijkstra_search(&self, start: usize) -> (Vec<i64>, Vec<usize>) {
        //const INF: i64 = 1 << 61;
        let mut dist: Vec<i64> = vec![INF; self.n]; // Dijkstraなのでi64ではなくusizeの方がいいかも
        let mut visited: Vec<bool> = vec![false; self.n];
        let mut prev: Vec<usize> = vec![INF as usize; self.n]; //nodeを格納するのにusizeでないの気持ち悪い
        dist[start] = 0;
        let mut que: BinaryHeap<(i64, usize)> = BinaryHeap::new();
        que.push((0, start));
        while let Some((_, from)) = que.pop() {
            if visited[from] {
                continue
            }
            visited[from] = true;
            for edge in &self.edges[from] {
                let (to, cost) = *edge;
                if visited[to] {
                    continue
                }
                if dist[to] > dist[from] + cost {
                    dist[to] = dist[from] + cost;
                    prev[to] = from;
                    que.push((-dist[to], to));
                }
            }
        }
        return (dist, prev)
    }

    fn dijkstra_shortest_path(&self, start: usize, goal: usize) -> Vec<usize> {
        //const INF: usize = 1 << 61;
        let (_, prev) = self.dijkstra_search(start);
        let mut shortest_path: Vec<usize> = vec![];
        let mut node = goal;
        while node != INF as usize {
            shortest_path.push(node);
            node = prev[node];
        }
        shortest_path.reverse();
        return shortest_path
    }
}
const INF: i64 = 1 << 61;

fn main() {
    input! {
    v: usize, e: usize, r:usize,
    std: [(usize, usize, i64); e],
    }
    let mut graph = Graph::new(v);
    for i in 0..e {
        let s = std[i].0;
        let t = std[i].1;
        let d = std[i].2;
        graph.add_costs(s, t, d, true);
    }

    let cost = graph.dijkstra_search(r);
    for i in 0..v {
        let ans = cost.0[i];
        if ans == INF {
            println!("{}", "INF");
        } else {
            println!("{}", ans);
        }
    }
}