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: Accepted)

using System;

public class SingleSourceShortestPath
{
	const int MAX = 100;
	const int INFTY = Int32.MaxValue;
	const int WHITE = 0;
	const int GRAY = 1;
	const int BLACK = 2;

	static int vertexNum; // ????????° = V
	static int[,] M = new int[MAX,MAX]; // ????????????????¨????????????£??\??????

	static void dijkstra() {
		int minv;
		int[] d = new int[MAX]; // ?§????s????????????v?????§??????????????????????¨????
		int[] color = new int[MAX]; // ?¨??????¶???????????§??¨???

		// ?????????
		for (int i = 0; i < vertexNum; i++) {
			d[i] = INFTY;
			color[i] = WHITE; 
		}

		// ????????????????????????
		d[0] = 0;
		color[0] = GRAY;

		while (true) {
			minv = INFTY;
			int u = -1;
			for (int i = 0; i < vertexNum; 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 < vertexNum; v++) {
				//???????¨?????????????????????????u??¨v?????????????????????
				if (color[v] != BLACK && M[u,v] != INFTY) {
					if (d[v] > d[u] + M[u,v]) {
						d[v] = d[u] + M[u,v];
						color[v] = GRAY;
					}
				}
			}
		}
		// ????????¨?????????????????????
		for (int i = 0; i < vertexNum; i++) {
			Console.WriteLine ("{0} {1}", i, (d[i] == INFTY ? -1 : d[i]));
		}
	}
	public static void Main(String[] args) {
		// ????????°
		vertexNum = int.Parse(Console.ReadLine ());
		// ??????????????????
		for (int i = 0; i < vertexNum; i++) {
			for (int j = 0; j < vertexNum; j++) {
				M[i,j] = INFTY;
			}
		}

		int k, c, u, v;
		for (int i = 0; i < vertexNum; i++) {
			string[] readLine = Console.ReadLine().Split(' ');
			int s = 0;
			u = int.Parse(readLine[s]);	// ????????????
			s++;
			k = int.Parse(readLine[s]); 	// ????¬???°
			for (int j = 0; j < k; j++) {
				s++;
				v = int.Parse(readLine[s]);	// ??£??\?????????????????????
				s++;
				c = int.Parse(readLine[s]); // u??¨v????????????????????????
				M[u, v] = c;
			}
		}
		dijkstra ();
	}
}