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.Scanner;

public class Main {

    private static final int MAX_N = 100;
    private static final int INF = 1 << 21;
    private static final int WHITE = 0;
    private static final int GRAY = 1;
    private static final int BLACK = 2;

    private static int n;
    private static int[][] M = new int[MAX_N][MAX_N];


    private static void dijkstra() {
        // initialize
        int[] color = new int[MAX_N]; // visited or not
        int[] d = new int[MAX_N]; // min edge

        for (int i = 0; i < n; i++) {
            color[i] = WHITE;
            d[i] = INF;
        }

        // start node
        d[0] = 0;
        color[0] = GRAY;

        while (true){
            int u = -1;
            int minv = INF;

            // find minimum value vertex
            for (int i = 0; i < n; i++) {
                if (color[i] != BLACK && d[i] < minv){
                    minv = d[i];
                    u = i;
                }
            }

            // didn't find any vertex
            if (u == -1)
                break;
            color[u] = BLACK;

            // add new edges
            for (int v = 0; v < n; v++) {
                if (color[v] != BLACK && M[u][v] != INF){
                    if (d[v] > M[u][v] + d[u]) {
                        d[v] = M[u][v] + d[u];
                        color[v] = GRAY;
                    }
                }

            }

        }

        for (int i = 0; i < n; i++) {
            System.out.println(
                    i + " " + (d[i] == INF ? -1 : d[i])
            );
        }

    }

    private static void input() {
        Scanner scanner = new Scanner(System.in);
        n = scanner.nextInt();

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                M[i][j] = INF;
            }
        }

        for (int i = 0; i < n; i++) {
            int u = scanner.nextInt();
            int k = scanner.nextInt();
            for (int j = 0; j < k; j++) {
                M[u][scanner.nextInt()] = scanner.nextInt();
            }
        }
    }

    public static void main(String[] args){
        input();
        dijkstra();
    }
}