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.util.ArrayDeque;
import java.util.Arrays;
import java.util.Deque;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		new Main().run();
	}

	int n;
	boolean[] color;
	int[][] map;
	int INF = 1 << 24;

	private void run() {
		Scanner scanner = new Scanner(System.in);
		n = scanner.nextInt();
		map = new int[n][n];
		for (int[] a : map)
			Arrays.fill(a, INF);
		for (int i = 0; i < n; i++) {
			int u = scanner.nextInt();
			int k = scanner.nextInt();
			for (int j = 0; j < k; j++) {
				int v = scanner.nextInt();
				int c = scanner.nextInt();
				map[u][v] = c;
			}

		}
		dijkstra();
	}

	private void dijkstra() {
		int[] d = new int[n];
		color = new boolean[n];
		Arrays.fill(d, INF);
		d[0] = 0;
		Deque<Integer> deque = new ArrayDeque<Integer>();
		deque.push(0);
		while (!deque.isEmpty()) {
			int u = deque.poll();
			color[u] = true;
			int minv = INF;
			int next = -1;
			for (int i = 0; i < n; i++) {
				if (d[i] > d[u] + map[u][i]) {
					d[i] = d[u] + map[u][i];
				}
				if (!color[i] && minv > d[i]) {
					minv = d[i];
					next = i;
				}

			}
			if (next != -1)
				deque.push(next);
		}
		for (int i = 0; i < n; i++) {
			System.out.printf("%d %d\n", i, d[i] == INF ? -1 : d[i]);
		}

	}
}