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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashSet;

public class Main {
	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		int n = Integer.parseInt(br.readLine());
		
		int[][] a = new int[n][n];
		String[] str; 
		for(int i = 0; i < n; ++i){
			for(int j = 0; j < n; ++j){
				a[i][j] = Integer.MAX_VALUE;
			}
			str = br.readLine().split(" ");
			int u = Integer.parseInt(str[0]);
			int k = Integer.parseInt(str[1]);
			for(int j = 0; j < k; ++j) {
				int v1 = Integer.parseInt(str[2 + j * 2    ]);
				int c1 = Integer.parseInt(str[2 + j * 2 + 1]);
				a[u][v1] = c1;
			}
		}

		int[] d = new int[n];
		HashSet<Integer> t = new HashSet<Integer>(n);
		for(int i = 0; i < n; i++){
			d[i] = a[0][i];
			t.add(i);
		}
		
		int[] p = new int[n];
		int u = 0;
		p[u] = 0; // first node
		d[p[u]] = 0; // cost
		while(!t.isEmpty()){
			t.remove(p[u]);
			int min = Integer.MAX_VALUE;
			for(int node : t){
				
				if(d[p[u]] + a[p[u]][node] > 0 && d[p[u]] + a[p[u]][node] < d[node]){
					d[node] = d[p[u]] + a[p[u]][node];
				}
				if(d[node] < min){
					min = d[node];
					p[u+1] = node;
				}
			}
			u += 1;
		}
		
		StringBuffer sb = new StringBuffer();
		for(int i = 0; i < n; i++){
			sb.append(i + " " + d[i] + "\n");
		}
		System.out.print(sb);
	}

}