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)

# 単一視点最短経路, Dijkstra(ダイクストラ)のアルゴリズム
from collections import deque

n = int(input())
# グラフの作成
INF = float('inf')
M = [[INF]*n for _ in range(n)]
d = [INF]*n
for _ in range(n):
    u, k, *v = map(int, input().split())
    if k == 0:
        continue
    cnt = 0
    for _ in range(k):
        M[u][v[cnt]] = v[cnt+1]
        cnt += 2

# アルゴリズム部分
def djikstra(n, M, d):
    d[0] = 0
    color = ['W']*n
    color[0] = 'G'
    while True:
        mincost = INF
        u = -1
        for i in range(n):
            if mincost > d[i] and color[i] != 'B':
                u = i
                mincost = d[i]
        if u == -1:
            break

        color[u] = 'B'
        for v in range(n):
            if color[v] != 'B' and M[u][v] != INF:
                if d[v] > d[u]+M[u][v]:
                    d[v] = d[u]+M[u][v]
                    color[v] = 'G'
    return d

D = djikstra(n, M, d)
for i, c in enumerate(D):
    print(i, c)