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.io.IOException;
import java.io.InputStream;
import java.io.PrintStream;
import java.util.Arrays;
import java.util.NoSuchElementException;
public class Main {
    private static final PrintStream ps     = System.out;
    private static final InputStream IS     = System.in;
    private static final byte[]      BUFFER = new byte[1024];
    private static int               ptr    = 0;
    private static int               buflen = 0;

    public static void main(String[] args) {
        final int max = Integer.MAX_VALUE;
        int n = ni();
        int[][] g = new int[n][n];
        for (int i = 0; i < n; i++) {
            Arrays.fill(g[i], max);
        }
        
        for (int i = 0; i < n; i++) {
            int u = ni();
            int m = ni();
            for (int j = 0; j < m; j++) {
                g[u][ni()] = ni();
            }
        }
        
//        UArr.printArr2D(g);
        int[] d = dijkstra(g, 0);
        for (int i = 0; i < n; i++) {
            ps.println(i + " " + d[i]);
        }
    }
    
    
    static int[] dijkstra(int[][] g, int from) {
        final int MAX = Integer.MAX_VALUE;
        int n = g.length;
        
        int[] d = new int[n];
        Arrays.fill(d, MAX);
        d[from] = 0;
        
        boolean[] visited = new boolean[n];
        
        while (true) {
            int u = -1;
            int min = MAX;
            for (int i = 0; i < n; i++) {
                if (!visited[i] && d[i] < min) {
                    u = i;
                    min = d[i];
                }
            }
            if (min == MAX) break;
            
            visited[u] = true;
            for (int i = 0; i < n; i++) {
                if (g[u][i] != MAX) {
                    d[i] = Math.min(d[i], d[u] + g[u][i]);
                }
            }
        }
        return d;
    }

    private static boolean hasNextByte() {
        if (ptr < buflen)
            return true;
        else {
            ptr = 0;
            try {
                buflen = IS.read(BUFFER);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0)
                return false;
        }
        return true;
    }

    private static int readByte() {
        if (hasNextByte())
            return BUFFER[ptr++];
        else
            return -1;
    }

    private static boolean isPrintableChar(int c) {
        return 33 <= c && c <= 126;
    }

    public static boolean hasNext() {
        while (hasNextByte() && !isPrintableChar(BUFFER[ptr]))
            ptr++;
        return hasNextByte();
    }

    public static String n() {
        if (!hasNext())
            throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    public static long nl() {
        if (!hasNext())
            throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b)
            throw new NumberFormatException();
        while (true) {
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            } else if (b == -1 || !isPrintableChar(b))
                return minus ? -n : n;
            else
                throw new NumberFormatException();
            b = readByte();
        }
    }

    public static int ni() {
        long nl = nl();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
            throw new NumberFormatException();
        return (int) nl;
    }

    public static double nextDouble() {
        return Double.parseDouble(n());
    }

    private static int[] nia(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = ni();
        return a;
    }

    private static long[] nla(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = nl();
        return a;
    }

    private static String[] na(int n) {
        String[] a = new String[n];
        for (int i = 0; i < n; i++)
            a[i] = n();
        return a;
    }

    private static int[][] nia2(int n, int m) {
        int[][] a = new int[n][m];
        for (int i = 0; i < n; i++)
            a[i] = nia(m);
        return a;
    }

    private static long[][] nla2(int n, int m) {
        long[][] a = new long[n][m];
        for (int i = 0; i < n; i++)
            a[i] = nla(m);
        return a;
    }

    private static char[][] nca2(int n) {
        char[][] a = new char[n][];
        for (int i = 0; i < n; i++)
            a[i] = n().toCharArray();
        return a;

    }
}