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 Python (judge verdict: Accepted)

import heapq

def dijkstra(G, s):
    n = len(G)
    INF = float("inf")
    d = [INF] * n
    d[s] = 0
    pq = []
    heapq.heappush(pq, (0, s)) # (cost, vertex)
    while pq:
        c, v = heapq.heappop(pq)
        if d[v] < c:
            continue
        for nv, nc in G[v]:
            if d[nv] > d[v] + nc:
                d[nv] = d[v] + nc
                heapq.heappush(pq, (d[nv], nv))
    return d

n = input()
G = [[] for i in xrange(n)]
for i in xrange(n):
    li = map(int, raw_input().split())
    for j in xrange(li[1]):
        G[i].append((li[2 * (j + 1)], li[2 * (j + 1) + 1]))

d = dijkstra(G, 0)
for i, c in enumerate(d):
    print i, c