Problem:
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Single Source Shortest Path II

For a given weighted graph $G = (V, E)$, find the shortest path from a source to each vertex. For each vertex $u$, print the total weight of edges on the shortest path from vertex $0$ to $u$.

Input

In the first line, an integer $n$ denoting the number of vertices in $G$ is given. In the following $n$ lines, adjacency lists for each vertex $u$ are respectively given in the following format:

$u$ $k$ $v_1$ $c_1$ $v_2$ $c_2$ ... $v_k$ $c_k$

Vertices in $G$ are named with IDs $0, 1, ..., n-1$. $u$ is ID of the target vertex and $k$ denotes its degree. $v_i (i = 1, 2, ... k)$ denote IDs of vertices adjacent to $u$ and $c_i$ denotes the weight of a directed edge connecting $u$ and $v_i$ (from $u$ to $v_i$).

Output

For each vertex, print its ID and the distance separated by a space character in a line respectively. Print in order of vertex IDs.

Constraints

$1 \leq n \leq 10,000$

$0 \leq c_i \leq 100,000$

$|E| < 500,000$

All vertices are reachable from vertex $0$

Sample Input 1

5
0 3 2 3 3 1 1 2
1 2 0 2 3 4
2 3 0 3 3 1 4 1
3 4 2 1 0 1 1 4 4 3
4 2 2 1 3 3

Sample Output 1

0 0
1 2
2 2
3 1
4 3

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in Rust (judge verdict: Accepted)

use std::io::*;
use std::str::FromStr;
use std::collections::BinaryHeap;

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

type Graph = Vec<Vec<(usize,usize)>>;

fn dijkstra(s:usize,g:Graph){
    let mut d = vec![isize::max_value();g.len()];
    let mut bh = BinaryHeap::new();
    // white=-1, gray=0, black=1 whiteで初期化
    let mut color:Vec<isize> = vec![-1;g.len()];

    d[s] = 0;
    //(距離,頂点)
    bh.push((0,s));
    color[s] = 0;

    while !bh.is_empty() {
        let f = bh.pop().unwrap();
        //最小距離の隣接頂点
        let u = f.1;
        color[u] = 1;
        //最小距離でなければ無視
        if d[u] < f.0 * (-1) {
            continue;
        }

        //v(頂点,距離)
        for v in g[u].iter() {
            //未確定頂点か判定
            if color[v.0] != 1 {
                if d[v.0] > d[u] + v.1 as isize {
                    d[v.0] = d[u] + v.1 as isize;
                    bh.push( (d[v.0] * (-1), v.0) );
                    color[v.0] = 0;
                }
            }
        }
    }

    for (i,e) in d.iter().enumerate(){
        println!("{} {}",i,e);
    }
}

fn main() {
    
    let n: usize = read();
    let mut G: Graph = vec![Vec::new(); n];
    for _i in 0..n {
        let u: usize = read();
        let k: usize = read();
        for _j in 0..k {
            let v: usize = read();
            let c: usize = read();
            G[u].push((v,c));
        }
    }

    dijkstra(0,G);    
    
}