Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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 {
 
    public static void main(String[] args){
 
        Scanner scan = new Scanner(System.in);
 
        int n = scan.nextInt();
        SSSPath sp = new SSSPath(n);
 
        for (int i = 0; i < n; i++) {
            int u = scan.nextInt();
            int k = scan.nextInt();
            for (int j = 0; j < k; j++)
                sp.addPath(u, scan.nextInt(), scan.nextInt());
        }
        sp.setPath(0);
 
        for (int i = 0; i < n; i++)
            System.out.println(i + " " + sp.getResult(i));
 
        scan.close();
        System.exit(0);
    }
}
 
class SSSPath {
    int[][] cost;
    int[] reach;
 
    public SSSPath(int n) {
        reach = new int[n];
        for (int i = 0; i < n; i++)
            reach[i] = -1;
 
        cost = new int[n][n];
        for (int x = 0; x < n; x++)
            for (int y = 0; y < n; y++)
                cost[x][y] = -1;
    }
 
    public int getResult(int i) {
        return reach[i];
    }
 
    public void setPath(int from) {
        reach[from] = 0;
        setP(from);
    }
 
    private void setP(int from) {
        for (int to = 0; to < cost[from].length; to++)
            if (cost[from][to] > 0) {
                int d = reach[from] + cost[from][to];
                if (reach[to] == -1 || reach[to] > d) {
                    reach[to] = d;
                    setP(to);
                }
            }
    }
 
    public void addPath(int from, int to, int c) {
        cost[from][to] = c;
    }
 
}