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 in=new Scanner(System.in);
		int n=in.nextInt();
		List<List<Node>> ls=new ArrayList<>();
		
		for(int i=0;i<n;i++)ls.add(new ArrayList<Node>());
		for(int i=0;i<n;i++) {
			int u=Integer.parseInt(in.next()),k=Integer.parseInt(in.next());
			for(int j=0;j<k;j++) {
				int v=Integer.parseInt(in.next()),
						c=Integer.parseInt(in.next());
				ls.get(u).add(new Node(v,c));
			}
		}
		
		int visit[]=new int[n],parent[]=new int[n],d[]=new int[n];
		for(int i=0;i<n;i++) {
			parent[i]=-1; d[i]=Integer.MAX_VALUE;
		}
		d[0]=0;

		while(true) {
			int u=-1,min=Integer.MAX_VALUE;

			for(int i=0;i<n;i++) {
				if(visit[i]<2 && d[i]<min) {
					min=d[i];
					u=i;
				}
			}

			if(u==-1)break;
			visit[u]=2;

			for(int i=0;i<ls.get(u).size();i++) {
				Node v=ls.get(u).get(i);
				if(visit[v.v]<2 && d[u]+v.c<d[v.v]) {
					d[v.v]=d[u]+v.c;
					parent[v.v]=u;
					visit[v.v]=1;
				}
			}
		}
		
		for(int i=0;i<n;i++)System.out.println(i+" "+d[i]);
	}

}

class Node{
	int v,c;
	Node(int a,int b){
		v=a;
		c=b;
	}
}