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 C# (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;


public class Program
{
	const int MAX = 100;
	const int INFINITY = (1 << 21);
	const int WHITE = 0;
	const int GRAY = 1;
	const int BLACK = 2;

	static int[,] M;

	public static void Main()
	{
		// ??°???????????????
		int n = int.Parse(Console.ReadLine());
		M = new int[n, n];

		for (int i = 0; i < n; ++i)
			for (int j = 0; j < n; ++j)
				M [i, j] = INFINITY;

		// ?????????????????????
		string readLine = null;
		for (int i = 0; i < n; ++i) {
			
			readLine = Console.ReadLine ();
			string[] splitedNums = readLine.Split (' ');
			int u = int.Parse (splitedNums [0]);
			int k = int.Parse (splitedNums[1]);

			// ??£??\????????¨?????????????????????
			for (int j = 0; j < k; ++j) {

				int v = int.Parse (splitedNums[2 + j * 2]);
				int c = int.Parse (splitedNums[2 + j * 2 + 1]);

				M [u,v] = c;

			}

		}


		// ??????????????¢?´¢
		dijkstra (n);
	}


	//
	// dijkstra - ????????????????????????????????????????????¢?´¢
	//
	//
	static void dijkstra (int n) {

		int minv;
		int[] d = new int[MAX];
		int[] color = new int[MAX];

		for (int i = 0; i < MAX; ++i) {
			d [i] = INFINITY;
			color [i] = WHITE;
		}

		d [0] = 0;
		color [0] = GRAY;
		while (true) {

			minv = INFINITY;
			int u = -1;
			for (int i = 0; i < n; ++i) {
				if (minv > d[i] && color[i] != BLACK) {
					u = i;
					minv = d [i];
				}
			}

			if (u == -1)
				break;

			color [u] = BLACK;
			for (int v = 0; v < n; ++v) {
				if (color [v] != BLACK && M [u,v] != INFINITY) {
					if (d [v] > d [u] + M [u,v]) {
						d [v] = d [u] + M [u, v];
						color [v] = GRAY;
					}
				}
			}
		}

		for (int i = 0; i < n; ++i) {
			Console.WriteLine (string.Format ("d[{0}] = {1}", i, d [i] == INFINITY ? -1 : d[i]));
		}
	}


		
}