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: Time Limit Exceeded)

import java.util.Scanner;


public class Main {

	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		int edgeCnt = Integer.parseInt(s.nextLine());
		int[][] input = new int[edgeCnt][];
		for(int i=0 ; i<edgeCnt ; i++) {
			String[] tmp = s.nextLine().split(" ");
			int[] inner = new int[edgeCnt];
			for(int j=0 ; j<edgeCnt ; j++) {
				inner[j] = -1;
			}
			for(int k=0 ; k<Integer.parseInt(tmp[1]) ; k++) {
				inner[Integer.parseInt(tmp[k*2+2])] = Integer.parseInt(tmp[k*2+3]);
			}
			input[Integer.parseInt(tmp[0])] = inner;
		}
		int[] result = solve(input);
		for(int a=0 ; a<result.length ; a++) {
			System.out.println(a + " " + result[a]);
		}
	}

	public static int[] solve(int[][] input) {
		int[] result = new int[input.length];
		for(int i=0 ; i<input.length ; i++) {
			result[i] = Integer.MAX_VALUE;
		}
		result[0] = 0;
		boolean[] alreadyVisit = new boolean[input.length];
		int minValue = Integer.MAX_VALUE;
		int minEdge = -1;
		while(true) {
			minEdge = -1;
			minValue = Integer.MAX_VALUE;
			for(int j=0 ; j<input.length ; j++) {
				if(minValue>result[j] && !alreadyVisit[j]) {
					minValue = result[j];
					minEdge = j;
				}
			}
			if(minEdge==-1)
				break;
			alreadyVisit[minEdge] = true;
			for(int k=0 ; k<input[minEdge].length ; k++) {
				if(input[minEdge][k] != -1) {
					if(result[k]>result[minEdge]+input[minEdge][k]) {
						result[k] = result[minEdge]+input[minEdge][k];
					}
				}
			}
		}
		return result;
	}

}