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.*;
import java.io.*;

public class Main {
    
    public static void main(String[] args) {
        Main main = new Main();
        main.test();
    }
    
    int n;
    private void test() {
        Scanner input = new Scanner(System.in);
        n = input.nextInt();
        long[][] us = new long[n][n];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                us[i][j] = Integer.MAX_VALUE;
            }
            int u = input.nextInt();
            int k = input.nextInt();
            for (int j = 0; j < k; j++) {
                int v = input.nextInt();
                int c = input.nextInt();
                us[u][v] = c;
            }
        }
        us[0][0] = 0;
        
        vs = new long[n];
        Arrays.fill(vs, Integer.MAX_VALUE);
        vs[0] = 0;
        solv(us, 0);
        for (int i = 0; i < n; i++) {
            System.out.println(String.format("%d %d", i, vs[i]));
        }
    }
    
    long[] vs;
    void solv(long[][] us, int i) {
        boolean[] f = new boolean[n];
        for (int j = 0; j < n; j++) {
            if (i != j && vs[i] + us[i][j] < vs[j]) {
                vs[j] = vs[i] + us[i][j];
                f[j] = true;
            }
        }
        for (int j = 0; j < n; j++) {
            if(f[j])solv(us, j);
        }
    }
}

class Scanner {
    BufferedReader r;
    StreamTokenizer st;
    
    public Scanner(InputStream in) {
        r = new BufferedReader(new InputStreamReader(in));
        st = new StreamTokenizer(r);
    }
    
    public String next() {
        nextToken();
        return st.sval;
    }
    
    public Integer nextInt() {
        nextToken();
        return (int)st.nval;
    }
    
    private int nextToken() {
        int token = st.TT_EOF;
        try {
            token = st.nextToken();
        } catch (IOException e) {
        }
        return token;
    }
}