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: Wrong Answer)

#!/usr/bin/python3
n = int(input())
inf = 100 * 100000

M = [[inf for i in range(n)] for j in range(n)]

for i in range(n):
    L = list(map(int, input().split()))
    u = L[0]
    k = L[1]
    v = L[2::2]
    c = L[3::2]
    for j in range(k):
        M[u][v[j]] = M[v[j]][u] = c[j]

S = set()
V = set(range(n))
S.add(0)
d = [inf for i in range(n)]
d[0] = 0
count = 0
while len(V - S) != 0 and count < 10:
    T = V - S
    nd = [inf for i in range(n)]
    for s in S:
        for m, c in enumerate(M[s]):
            if d[s] + c < nd[m] and m in T:
                nd[m] = d[s] + c

    min_nd = min(nd)
    u = nd.index(min_nd)
    S.add(u)
    d[u] = min_nd

    count += 1

for i, v in enumerate(d):
    print(i, v)