Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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::Read;
use std::collections::BinaryHeap;

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_to_string(&mut buf).unwrap();

    let answer = solve(&buf);

    println!("{}", answer);
}

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

    let n: usize = iterator.next().unwrap().parse().unwrap();
    let mut graph: Vec<Vec<(usize, usize)>> = vec![Vec::new(); n];
    for _ in 0..n {
        let u: usize = iterator.next().unwrap().parse().unwrap();
        let k: usize = iterator.next().unwrap().parse().unwrap();
        for _ in 0..k {
            let v: usize = iterator.next().unwrap().parse().unwrap();
            let c: usize = iterator.next().unwrap().parse().unwrap();
            graph[u].push((v, c));
        }
    }

    // let mut color: Vec<Color> = vec![Color::WHITE; n];
    // let mut d: Vec<usize> = vec![INF; n];
    // d[0] = 0;
    //
    // let mut pq: BinaryHeap<(isize, usize)> = BinaryHeap::new();
    // pq.push((0, 0));
    //
    // while !pq.is_empty() {
    //     let pair = pq.pop().unwrap();
    //     let u = pair.1;
    //
    //     color[u] = Color::BLACK;
    //
    //     if d[u] < (-pair.0) as usize {
    //         continue;
    //     }
    //
    //     for &edge in &graph[u] {
    //         let v = edge.0;
    //         if color[v] == Color::BLACK {
    //             continue;
    //         }
    //         if d[v] > d[u] + edge.1 {
    //             d[v] = d[u] + edge.1;
    //             pq.push((d[v] as isize * -1, v));
    //             color[v] = Color::GRAY;
    //         }
    //     }
    // }

    let mut color: Vec<Color> = vec![Color::WHITE; n];
    let mut d: Vec<usize> = vec![INF; n];
    let mut p: Vec<isize> = vec![-1; n];
    d[0] = 0;

    loop {
        let mut min_cost = INF;
        let mut u = 0;
        for i in 0..n {
            if color[i] != Color::BLACK && d[i] < min_cost {
                min_cost = d[i];
                u = i;
            }
        }

        if min_cost == INF {
            break;
        }

        color[u] = Color::BLACK;

        for &edge in &graph[u] {
            let v = edge.0;
            if color[v] == Color::BLACK {
                continue;
            }
            if d[u] + edge.1 < d[v] {
                d[v] = d[u] + edge.1;
                p[v] = u as isize;
                color[v] = Color::GRAY;
            }
        }
    }

    let mut result = String::new();
    for i in 0..n {
        result.push_str(&format!("{} {}\n", i, d[i]));
    }
    return result.trim().to_string();
}

const INF: usize = 1_000_000_000;

#[derive(Clone, PartialEq)]
enum Color {
    WHITE, GRAY, BLACK,
}