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 Python3 (judge verdict: Runtime Error)

from heapq import heappush, heappop
from enum import Enum, auto

INFTY = float('inf')

class Color(Enum):
    WHITE = auto()
    GRAY = auto()
    BLACK = auto()

n = int(input())
M = [[-1 for i in range(n)] for i in range(n)]
adj_list = []
for i in range(n):
    u, k, *kv = list(map(int, input().split(' ')))
    if k == 0: continue
    adj_list.append(kv)
    for j in range(0,2*k,2):
        M[i][kv[j]] = kv[j+1]
colors = []
d = []

def dijkstra(s):
    global d
    colors = [Color.WHITE for i in range(n)]
    d = [INFTY for i in range(n)]
    pque = []
    d[0] = 0

    heappush(pque, (0, s))

    while len(pque) >= 1:
        vert_u = heappop(pque)
        u = vert_u[1]
        colors[u] = Color.BLACK
        if d[u] < vert_u[0]: continue
        i = 0
        while i <= len(adj_list[u])-2:
            v = adj_list[u][i]
            if colors[v] != Color.BLACK:
                if d[u] + adj_list[u][i+1] < d[v]:
                    d[v] = d[u] + adj_list[u][i+1]
                    colors[v] = Color.GRAY
                    heappush(pque, (d[v], v))
            i += 2

dijkstra(0)
for i in range(n):
    print(i, d[i])