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);
		
		//頂点の数
		int n = sc.nextInt();
		//定数（∞として扱う）
		final int inf = Integer.MAX_VALUE;
		//u:頂点の番号　k:出字数 v:隣接する頂点の番号 c:隣接する頂点への辺の重み
		int u, k, v, c;
		int min;
		//全て定数で初期化
		int[] d = new int[n];
		Arrays.fill(d, inf);
		//頂点を訪問したかを示す
		int[] visit = new int[n];
		int white = 0, gray = 1, black = 2;
		
		int[][] M = new int[n][n];
		for(int i=0; i<n; i++) { for(int j=0; j<n; j++) { M[i][j] = inf; } }
		
		for(int i=0; i<n; i++) {
			u = sc.nextInt();
			k = sc.nextInt();
			//出字数分だけ
			for(int j=0; j<k; j++) {
				v = sc.nextInt();
				c = sc.nextInt();
				M[u][v] = c;
			}
		}
		
		d[0] = 0;
		visit[0] = gray;
		while( true ) {
			min = inf;
			int indexU = -1;
			for(int i=0; i<n; i++) {
				if(min > d[i] && visit[i] != black) {
					indexU = i;
					min = d[i];
				}
			}
			if(indexU == -1) break;
			visit[indexU] = black; //訪問済みに変更
			for(v=0; v<n; v++) {
				if(visit[v]!=black && M[indexU][v]!=inf) {
					if(d[v] > d[indexU] + M[indexU][v]) {
						d[v] = d[indexU] + M[indexU][v];
						visit[v] = gray;
					}
				}
			}
		}
		
		for(int i=0; i<n; i++) {
			if(d[i] == inf) { System.out.println(i+" "+-1); }
			else { System.out.println(i+" "+d[i]); }
		}
	}
}