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: WA: Presentation Error)

n = int(raw_input())

matrix = [[100001 for i in range(n)] for j in range(n)]

for i in range(n):
    line = raw_input()
    splited = line.split()
    splited = map(lambda x: int(x), splited)
    u = splited[0]
    k = splited[1]
    for j in range(k):
        matrix[u][splited[2 + j * 2]] = splited[2 + j * 2 + 1]

cost = [10000000000 for i in range(n)]
selected = []
now_node = 0
cost[now_node] = 0
while len(selected) != n + 1:
    selected.append(now_node)

    for (i, item) in enumerate(matrix[now_node]):
        if item < 100001 and cost[i] > item + cost[now_node] and cost[i] != -1:
            cost[i] = item + cost[now_node]
    now_node = -1
    for (i, item) in enumerate(cost):
        if i not in selected and now_node == -1:
            now_node = i
        elif i not in selected and item < cost[now_node]:
            now_node = i

for (i, item) in enumerate(cost):
    print i, " ", item