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.LinkedList;
import java.util.Scanner;

class Graph {
	private int totalVertex;
	// adjMatrix[u][v] = 1 if there is an edge from u to v, otherwise 0
	private int[][] adjMatrix;
	// adjWeight[u][v] -- the weight of the edge from u to v if there is one
	private int[][] adjWeight;
	// if a node is settled (e.g., processed in the Dijkstra's algorithm)
	private Boolean[] ifSettled;

	public Graph() {
		totalVertex = 0;
	}

	public int getTotalVertex() {
		return totalVertex;
	}

	// load graph from standard input
	public void loadAdjMatrix() {
		Scanner in = new Scanner(System.in);
		totalVertex = in.nextInt();
		adjMatrix = new int[totalVertex][totalVertex];
		adjWeight = new int[totalVertex][totalVertex];
		ifSettled = new Boolean[totalVertex];
		int i, j;
		for (i = 0; i < totalVertex; i++) {
			ifSettled[i] = false;
			for (j = 0; j < totalVertex; j++) {
				adjMatrix[i][j] = adjWeight[i][j] = 0;
			}
		}
		int u, v;
		for (i = 0; i < totalVertex; i++) {
			u = in.nextInt();
			int degree = in.nextInt();
			for (j = 0; j < degree; j++) {
				v = in.nextInt();
				adjMatrix[u][v] = 1;
				adjWeight[u][v] = in.nextInt();
			}
		}
		in.close();
	}

	// return weight of the edge from u to v if there is one
	public int getWeight(int u, int v) {
		return adjWeight[u][v];
	}

	// return neighbors of u as a LinkedList
	public LinkedList<Integer> getNeighbors(int u) {
		LinkedList<Integer> tmp = new LinkedList<Integer>();
		for (int v = 0; v < totalVertex; v++) {
			if (adjMatrix[u][v] == 1)
				tmp.add(v);
		}
		return tmp;
	}

	// return unsettled neighbors of u as a LinkedList
	public LinkedList<Integer> getUnsettledNeighbors(int u) {
		LinkedList<Integer> tmp = new LinkedList<Integer>();
		for (int v = 0; v < totalVertex; v++) {
			if ((adjMatrix[u][v] == 1) && (ifSettled[v] == false))
				tmp.add(v);
		}
		return tmp;
	}

	// return the unsettled node that has the smallest dist
	public int getUnsettledNearest(int[] dist) {
		int md = Integer.MAX_VALUE;
		int mv = -1;
		int v;
		for (v = 0; v < totalVertex; v++) {
			if ((ifSettled[v] == false) && (dist[v] < md)) {
				md = dist[v];
				mv = v;
			}
		}
		return mv;
	}

	// implement the following
	public int[] Dijkstra(int s) {
		int[] out = new int[totalVertex];
		for (int i = 0; i < totalVertex; i++) { // Initialize
			out[i] = Integer.MAX_VALUE;
		}
		out[s] = 0;
		ifSettled[s] = true;

		int set = s;
		boolean cont = true;
		LinkedList<Integer> neighbors;

		while (cont) {
			neighbors = getUnsettledNeighbors(set); // Find next-closest vertex
			for (int i : neighbors) {
				if (out[i] > out[set] + getWeight(set, i)) {
					out[i] = out[set] + getWeight(set, i);
				}
			}
			set = getUnsettledNearest(out);
			ifSettled[set] = true;
			cont = false;
			for (int i = 0; i < totalVertex; i++) {
				if (ifSettled[i] == false) {
					cont = true;
				}
			}
		}
		return out;
	}
}

public class Main {
	public static void main(String[] argv) {
		Graph g = new Graph();
		g.loadAdjMatrix();
		int[] dist = g.Dijkstra(0);
		for (int i = 0; i < g.getTotalVertex(); i++) {
			System.out.println(i + " " + dist[i]);
		}
	}
}