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.Arrays;
import java.util.Scanner;
 
class Main{
    public static void main(String args[]){
        Scanner sc=new Scanner(System.in);
            int number=sc.nextInt();
            int max=100000000;
            
            
            int[] initial=new int[number+1];
            int[][] graph=new int[number+1][number+1];
            Arrays.fill(initial, max); //setting up the graph and filling
            //starter array with max values
            for(int i=0; i<number; i++) {
                int u=sc.nextInt();
                int k=sc.nextInt();
                
                for(int j=0; j<k; j++){
                    int v=sc.nextInt();
                    int c=sc.nextInt();
                    
                    graph[u][v]=c;//Filling in the graph
                }
            }
            initial[0]=0;
            
            for(int t=0; t<number; t++) {
                boolean update=false;
                
                for(int i=0; i<number; i++) {
                    for(int j=0; j<number; j++) {
                    	
                        if(initial[i]<max && graph[i][j]>0) {
                            if(initial[j]>initial[i]+graph[i][j]) {//Updating the max value
                                initial[j]=initial[i]+graph[i][j]; //And updating to least
                                					//later.
                                update=true;
                            }
                        }
                    }
                }
                if(! update) break;
            }
            //Print Answer
            for(int i=0; i<number; i++) {
                System.out.println(i+" "+initial[i]);
            }
        }
    }