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::fmt::Debug;
use std::io::{stdin, Read};
use std::string::*;

#[derive(Eq, PartialEq, Clone, Debug)]
pub struct Rev<T>(pub T);

impl<T: PartialOrd> PartialOrd for Rev<T> {
    fn partial_cmp(&self, other: &Rev<T>) -> Option<std::cmp::Ordering> {
        other.0.partial_cmp(&self.0)
    }
}

impl<T: Ord> Ord for Rev<T> {
    fn cmp(&self, other: &Rev<T>) -> std::cmp::Ordering {
        other.0.cmp(&self.0)
    }
}

macro_rules! read {
    (($($t:tt),*)) => {
        ( $(read!($t)),* )
    };
    ([[$t:tt; $len1:expr]; $len2:expr]) => {
        (0..$len2).map(|_| read!([$t; $len1])).collect::<Vec<_>>()
    };

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

    (chars) => {
        read!(String).chars().collect::<Vec<char>>()
    };

    (usize1) => {
        read!(usize) - 1
    };

    ($t:ty) => {{
        let stdin = stdin();
        let stdin = stdin.lock();
        let token: String = stdin
            .bytes()
            .map(|c| c.unwrap() as char)
            .skip_while(|c| c.is_whitespace())
            .take_while(|c| !c.is_whitespace())
            .collect();

        token.parse::<$t>().unwrap()
    }};
}

macro_rules! input {
    (mut $name:ident: $t:tt, $($r:tt)*) => {
        let mut $name = read!($t);
        input!($($r)*);
    };

    (mut $name:ident: $t:tt) => {
        let mut $name = read!($t);
    };

    ($name:ident: $t:tt, $($r:tt)*) => {
        let $name = read!($t);
        input!($($r)*);
    };

    ($name:ident: $t:tt) => {
        let $name = read!($t);
    };
}

struct Combination {
    MOD: i64,
    fac: Vec<i64>,
    fac_inv: Vec<i64>,
}

impl Combination {
    pub fn new(n: i64) -> Self {
        let MOD: i64 = 1_000_000_007;
        let mut fac: Vec<i64> = vec![0; n as usize + 1];
        let mut fac_inv: Vec<i64> = vec![0; n as usize + 1];

        let get_inverse = |mut n: i64| -> i64 {
            let (mut res, mut p) = (1, MOD - 2);

            while p != 0 {
                if p & 1 == 1 {
                    res = (res * n) % MOD;
                }
                n = (n * n) % MOD;
                p >>= 1;
            }

            return res;
        };

        fac[0] = 1;

        for i in 1..n + 1 {
            fac[i as usize] = (fac[i as usize - 1] * i) % MOD;
        }

        for i in 0..n + 1 {
            fac_inv[i as usize] = get_inverse(fac[i as usize]);
        }

        Combination {
            MOD: MOD,
            fac: fac,
            fac_inv: fac_inv,
        }
    }

    fn nCr(&self, n: i64, r: i64) -> i64 {
        if n < r {
            return 0;
        }

        let a: i64 = self.fac[n as usize];
        let b: i64 = self.fac_inv[(n - r) as usize];
        let c: i64 = self.fac_inv[r as usize];
        let bc: i64 = (b * c) % self.MOD;

        return (a * bc) % self.MOD;
    }

    fn nPr(&self, n: i64, r: i64) -> i64 {
        if n < r {
            return 0;
        }

        let a: i64 = self.fac[n as usize];
        let b: i64 = self.fac_inv[(n - r) as usize];

        return (a * b) % self.MOD;
    }

    fn nHr(&self, n: i64, r: i64) -> i64 {
        if n == 0 && r == 0 {
            return 1;
        }

        return self.nCr(n + r - 1, r);
    }
}

pub trait SliceExt<T>: Iterator + Sized {
    fn vec(self) -> Vec<Self::Item> {
        self.collect()
    }
}

#[derive(Copy, Clone, Eq, PartialEq)]
struct Edge {
    to: usize,
    cost: i64,
}

fn dijkstra(graph: &Vec<Vec<Edge>>, s: usize) -> Vec<i64> {
        use std::collections::BinaryHeap;
        let mut dist = vec![1e18 as i64; graph.len()];
        let mut heap = BinaryHeap::new();
        dist[s] = 0;
        heap.push((0, s));
        while let Some((cost, v)) = heap.pop() {
            if dist[v] < cost {
                continue;
            }

            for e in &graph[v] {
                if dist[e.to] <= dist[v] + e.cost {
                    continue;
                }
                dist[e.to] = dist[v] + e.cost;
                heap.push((0, e.to));
            }
        }
        return dist;
    }


fn main() {
    input!(V: usize, E: usize, r: usize);
    let mut g = vec![Vec::new(); V];
    for _ in 0..E {
        input!(s: usize, t: usize, d: i64);
        g[s].push(Edge{to: t, cost: d});
    }

    let mut res = dijkstra(&g, r);
    for a in res {
        println!("{}", if a == 1e18 as i64 { "INF".to_string() } else { a.to_string() });
    }
}