Problem:
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Single Source Shortest Path

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

$1 \leq n \leq 100$

$0 \leq c_i \leq 100,000$

$|E| \leq 10,000$

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 JAVA (judge verdict: Accepted)

import java.util.*;

public class Main {
	public static void main (String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		ArrayList<HashMap<Integer, Integer>> graph = new ArrayList<>();
		for (int i = 0; i < n; i++) {
		    graph.add(new HashMap<>());
		}
		for (int i = 0; i < n; i++) {
		    int from = sc.nextInt();
		    int count = sc.nextInt();
		    for (int j = 0; j < count; j++) {
		        graph.get(from).put(sc.nextInt(), sc.nextInt());
		    }
		}
		int[] costs = new int[n];
		Arrays.fill(costs, Integer.MAX_VALUE);
		PriorityQueue<Path> queue = new PriorityQueue<>();
		queue.add(new Path(0, 0));
		while (queue.size() > 0) {
		    Path p = queue.poll();
		    if (costs[p.idx] <= p.value) {
		        continue;
		    }
		    costs[p.idx] = p.value;
		    for (Map.Entry<Integer, Integer> entry : graph.get(p.idx).entrySet()) {
		        queue.add(new Path(entry.getKey(), entry.getValue() + p.value));
		    }
		}
		StringBuilder sb = new StringBuilder();
		for (int i = 0; i < n; i++) {
		    sb.append(i).append(" ").append(costs[i]).append("\n");
		}
		System.out.print(sb);
	}
	
	static class Path implements Comparable<Path> {
	    int idx;
	    int value;
	    
	    public Path(int idx, int value) {
	        this.idx = idx;
	        this.value = value;
	    }
	    
	    public int compareTo(Path another) {
	        return value - another.value;
	    }
	}
}