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;
using System.Linq;
using System.Collections.Generic;
using System.Text;



class B
{
    static int[,] G;
    static internal int n;
    const int INFTY = int.MaxValue;
    public static void Main() {
        n = int.Parse(Console.ReadLine());
        G = new int[n, n];
        for(int i = 0; i < n; i++) {
            for(int j=0;j<n; j++) {
                G[i, j] = INFTY;
            }
        }
        for (int i = 0; i < n; i++) {
            int[] input = Array.ConvertAll(Console.ReadLine().Split(' '),int.Parse);
            for(int j = 0; j < input[1]; j++) {
                G[input[0], input[2 + j * 2]] = input[3 + j * 2];
            }
        }
        dijkstra();
    }

    public static void dijkstra() {
        var d = Enumerable.Repeat(INFTY, n).ToArray();
        var parent = Enumerable.Repeat(-1, n).ToArray();
        var Color = Enumerable.Repeat("WHITE", n).ToArray();
        d[0] = 0;
        Color[0] = "GRAY";
        while (true) {
            int mincost = INFTY;
            int u = -1;
            for (int i = 0; i < n; i++) {
                if (Color[i] != "BLACK" && d[i] < mincost) {
                    mincost = d[i];
                    u = i;
                }
            }
            if (u==-1) {
                break;
            }
            Color[u] = "BLACK";
            for (int v = 0; v < n; v++) {
                if (Color[v] != "BLACK" && G[u, v] != INFTY) {
                    if (d[u]+G[u,v] < d[v]) {
                        d[v] = d[u] + G[u, v];
                        parent[v] = u;
                        Color[v] = "GRAY";
                    }
                }
            }
            
        }
        for (int i = 0; i < n; i++) {
            Console.WriteLine(i + " " + (d[i] == INFTY ? -1 : d[i]));
        }
    }
}