Problem:
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Single Source Shortest Path II

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

$1 \leq n \leq 10,000$

$0 \leq c_i \leq 100,000$

$|E| < 500,000$

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: Memory Limit Exceeded)

import java.io.IOException;
import java.io.InputStream;
import java.util.NoSuchElementException;
import java.util.PriorityQueue;

public class Main {
	private static FastScanner sc = new FastScanner();
	static Node[] V;
	static PriorityQueue<Node> que = new PriorityQueue<>((a, b) -> a.d - b.d);

	public static void main(String[] args) {
		int n = sc.nextInt();
		
		V = new Node[n];
		for(int i=0; i<n; i++) {
			sc.nextInt();
			int k = sc.nextInt();
			int[] v = new int[n];
			int[] c = new int[n];
			for(int j=0; j<k; j++) {
				v[j] = sc.nextInt();
				c[j] = sc.nextInt();
			}
			V[i] = new Node(i == 0 ? 0 : Integer.MAX_VALUE, v, c);
		}
		que.add(V[0]);
		
		while(!que.isEmpty()) {
			Node node = que.poll();
			node.dijkstra();
		}
		
		StringBuilder ans = new StringBuilder();
		for(int i=0; i<n; i++) {
			ans.append(i);
			ans.append(" ");
			ans.append(V[i].d);
			ans.append("\n");
		}
		System.out.print(ans);
	}
	
	static class Node {
		int d;
		int[] v;
		int[] c;
		
		Node(int d, int[] v, int[] c) {
			this.d = d;
			this.v = v;
			this.c = c;
		}
		
		public void dijkstra() {
			for(int i=0; i<v.length; i++) {
				Node node = V[v[i]];
				if(node.d > d + c[i]) {
					if(que.contains(node)) {
						que.remove(node);
					}
					node.d = d + c[i];
					que.add(node);
				}
			}
		}
	}

	static class FastScanner {
	    private final InputStream in = System.in;
	    private final byte[] buffer = new byte[1024];
	    private int ptr = 0;
	    private int buflen = 0;
	    private boolean hasNextByte() {
	        if (ptr < buflen) {
	            return true;
	        }else{
	            ptr = 0;
	            try {
	                buflen = in.read(buffer);
	            } catch (IOException e) {
	                e.printStackTrace();
	            }
	            if (buflen <= 0) {
	                return false;
	            }
	        }
	        return true;
	    }
	    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
	    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
	    private void skipUnprintable() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;}
	    public boolean hasNext() { skipUnprintable(); return hasNextByte();}
	    public String next() {
	        if (!hasNext()) throw new NoSuchElementException();
	        StringBuilder sb = new StringBuilder();
	        int b = readByte();
	        while(isPrintableChar(b)) {
	            sb.appendCodePoint(b);
	            b = readByte();
	        }
	        return sb.toString();
	    }
	    public long nextLong() {
	        return Long.parseLong(next());
	    }
	    public int nextInt(){
	    	return Integer.parseInt(next());
	    }
	}
}