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)

use std::io::*;
use std::vec::*;
use std::collections::BinaryHeap;

fn dijkstra(graph: &Vec<Vec<(usize, i64)>>, start: usize) -> Vec<i64> {
    let mut dist = vec![-(1 << 62); graph.len()];
    let mut heap = BinaryHeap::new();
    dist[start] = 0;
    heap.push((0, start));
    while let Some((acc, pos)) = heap.pop() {
        if dist[pos] > acc { continue; }
        for &(dst, cost) in &graph[pos] {
            if acc + cost > dist[dst] {
                dist[dst] = acc + cost;
                heap.push((acc + cost, dst));
            }
        }
    }
    return dist;
}

fn main(){
    let mut input = String::new();
    let _ = stdin().read_line(&mut input);

    let nums: Vec<i32> = input.split_whitespace().map(|e| e.parse().unwrap()).collect();
    let v = nums[0] as usize;
    let e = nums[1];
    let r = nums[2];

    let mut graph = vec![vec![]; v];

    for _ in 0..e {
        let mut input = String::new();
        let _ = stdin().read_line(&mut input);
        let edge: Vec<i64> = input.split_whitespace().map(|e| e.parse().unwrap()).collect();
        let s = edge[0] as usize;
        let t = edge[1] as usize;
        let d = edge[2];
        graph[s].push((t, -d));
    }

    for d in dijkstra(&graph, r as usize) {
        if d <= -(1 << 62) {
            println!("INF");
        } else {
            println!("{}", -d);
        }
    }
}