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 scan = new Scanner(System.in);
		int n = scan.nextInt();
		int g[][] = new int[114][114];
		for (int i=0; i<114; i++) for (int j=0; j<114; j++) {
			if (i==j) g[i][j] = 0;
			else g[i][j] = 123456789;
		}
		
		for (int i=0; i<n; i++) {
			int v = scan.nextInt();
			int k = scan.nextInt();
			for (int j=0; j<k; j++) {
				int to = scan.nextInt(); int cost = scan.nextInt();
				g[v][to] = cost;
			}
		}
		
		for (int k=0; k<n; k++) {
			for (int i=0; i<n; i++) {
				for (int j=0; j<n; j++) {
					g[i][j] = Math.min(g[i][j], g[i][k]+g[k][j]);
				}
			}
		}
		
		int ans = 0;
		for (int i=0; i<n; i++) {
			System.out.println(i+" "+g[0][i]);
		}
	}
}