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: Accepted)

import java.util.Scanner;
import java.io.IOException;
        public class Main {
                private final static int WHITE=0;
                private final static int GRAY=1;
                private final static int BLACK=2;
                private static int[][] M;
                private static int n;
                public static void main(String[] args) throws IOException {
                        final Scanner sc = new Scanner(System.in);
                        int i,j;
                        n=sc.nextInt();
                        M = new int[n][n];

        //??????????????????
                        for(i=0;i<n;i++)
                                for(j=0;j<n;j++) M[i][j]=Integer.MAX_VALUE;
                        int u,k,v,c;

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

                        dicstra();

                }

                public static void dicstra(){
                        int[] color = new int[n];
                        int[] depth = new int[n];
                        int i,j;
                        for(i=0;i<n;i++){
                                depth[i]=Integer.MAX_VALUE;
                                color[i]=WHITE;
                        }

                        depth[0]=0;
                        color[0]=GRAY;
                        int mincost;
                        int u;
                        while(true){
                                mincost=Integer.MAX_VALUE;
                                u=-1;
                                for(i=0;i<n;i++){
                                        if(color[i]!=BLACK && depth[i]<mincost){
                                                mincost = depth[i];
                                                u=i;
                                        }
                                }
                                if(mincost==Integer.MAX_VALUE) break;
                                color[u]=BLACK;

                                for(j=0;j<n;j++){
                                        if(color[j]!=BLACK && M[u][j]!=Integer.MAX_VALUE){
                                                if(depth[j]>depth[u]+M[u][j]){
                                                        depth[j]=depth[u]+M[u][j];
                                                        color[j]=GRAY;
                                                }
                                        }
                                }

                        }
                        for(i=0;i<n;i++){
                                System.out.println(i+" " + (depth[i]==Integer.MAX_VALUE ? -1 : depth[i]));
                        }
                }
        }