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 Python3 (judge verdict: Accepted)

def dijkstra(n):
    distance_list[0] = 0
    while True:
        min_distance = 10**9
        u = -1
        for i in range(n):
            distance = distance_list[i]
            if flag_list[i] < 2 and distance < min_distance:
                min_distance = distance
                u = i
        if u == -1:
            break
        flag_list[u] = 2
        for v in range(n):
            edge = m_list[u][v]
            if flag_list[v] < 2 and -1 < edge:
                if distance_list[u] + edge < distance_list[v]:
                    distance_list[v] = distance_list[u] + edge
                    p[v] = u
                    flag_list[v] = 1


if __name__ == "__main__":
    n = int(input())
    m_list = [[-1]*n  for _ in range(n)]
    for i in range(n):
        in_list = list(map(int, input().split()))
        adj_num = in_list[1]
        tmp = []
        if adj_num > 0:
            for j in range(adj_num):
                m_list[i][in_list[j*2+2]] = in_list[j*2+3]

    flag_list = [0]*n # 0: 未到達, 1: 処理中, 2: 完了
    distance_list = [10**9]*n
    p = [-1]*n
    dijkstra(n)
    for i, d in enumerate(distance_list):
        print(i, d)