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)

import sys

INFTY=sys.maxsize
WHITE=0
GRAY=1
BLACK=2

def readinput():
    n=int(input())
    nMap=[]
    for _ in range(n):
        nMap.append([INFTY]*n)

    for _i in range(n):
        l=list(map(int,input().split()))
        i=l[0]
        for jj in range(l[1]):
            j=l[2+jj*2]
            w=l[2+jj*2+1]
            nMap[i][j]=w
    return n, nMap

color=[]
d=[]
p=[]

def dijkstra(s,n,nMap):
    global color
    global d
    global p
    
    color=[WHITE]*n
    d=[INFTY]*n
    p=[-1]*n

    d[s]=0
    p[s]=-1

    while True:
        mincost=INFTY
        for i in range(n):
            if color[i]!=BLACK and d[i] < mincost:
                mincost=d[i]
                u=i
        if mincost==INFTY:
            break
        color[u]=BLACK

        for v in range(n):
            if color[v]!=BLACK and nMap[u][v]!=INFTY:
                if d[u]+nMap[u][v] < d[v]:
                    d[v]=d[u]+nMap[u][v]
                    p[v]=u
                    color[v]=GRAY

def main(n,nMap):

    dijkstra(0,n,nMap)
    for i in range(n):
        print('{} {}'.format(i,d[i]))

if __name__=='__main__':
    n,nMap=readinput()
    main(n,nMap)