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.Queue;
import java.util.Scanner;
import java.util.ArrayList;
import java.util.Iterator;

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;
	
	private final int inf = Integer.MAX_VALUE;
	
	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;
	}
	
	
	public int getMinDistance(ArrayList<Integer> A, int[] d) {
		
		int min = inf;
		int minI = 0;
		
		for (int n : A) {
			//System.out.println(n + ", " + d[n]);
			//min = (d[n] < min) ? d[n] : min; 
			if (d[n] < min) {
				min = d[n];
				minI = n;
			}
		
		}
		
		return minI;
	
	}
	
	//implement the following	
	//argument is the vertex to go off of
	
	public int[] Dijkstra(int s) {
		
		//Initializing queue
		ArrayList<Integer> unsettled = new ArrayList<Integer>();
		unsettled.add(s);
		
		//Initializing distances
		int[] d = new int[totalVertex];
		for (int i = 0; i < totalVertex; i++) {
			if (i == s) { d[i] = 0; } 
			else { d[i] = inf; }
		}
				
		//The main processing loop
		while (!unsettled.isEmpty()) {
	
			int cur = getMinDistance(unsettled, d);
			//System.out.println(cur + ": " + d[cur]);
			
			//Get the neighbors to process
			LinkedList<Integer> neighbors = getUnsettledNeighbors(cur);
			
			//Process neighbors to settle this node
			for (int n : neighbors) {
				//add to processing queue
				if (!unsettled.contains(n)) { unsettled.add(n); }
				
				//update distance if necessary
				int len = d[cur] + getWeight(cur, n);
				if (len < d[n]) { d[n] = len; }
				
			}
		
		//Set the node you're processing to settled, and remove from unsettled
		ifSettled[cur] = true;
		unsettled.remove(new Integer(cur));
		
		}
		
		return d;	
	}
}

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]);
		}
	}
}