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)

n=int(input())
inf=10**15;d=[inf]*n;d[0]=0
node=[[]for _ in range(n)]
for i in range(n):
	x=list(map(int,input().split()))
	for j in range(x[1]):
		node[i].append((x[j*2+2],x[j*2+3]))
dis=[[inf]*n for _ in range(n)]
for i in range(n):
	dis[i][i]=0
for i in range(n):
	for x in node[i]:
		dis[i][x[0]]=x[1]
s=[False]*n
while True:
	min_cost=inf
	for i in range(n):
		if s[i]==0 and d[i]<min_cost:
			min_cost=d[i]
			u=i
	if min_cost==inf:
		break
	s[u]=True
	for i in range(n):
		if s[i]==False and dis[u][i]!=inf:
			if d[u]+dis[u][i]<d[i]:
				d[i]=d[u]+dis[u][i]		
for i in range(n):
	print(i,d[i])