Problem:
Single Source Shortest Path

For a given weighted graph G(V, E) and a source r, find the source shortest path to each vertex from the source (SSSP: Single Source Shortest Path).

Input

An edge-weighted graph G (V, E) and the source r.

|V| |E| r
s0 t0 d0
s1 t1 d1
:
s|E|-1 t|E|-1 d|E|-1

|V| is the number of vertices and |E| is the number of edges in G. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively. r is the source of the graph.

si and ti represent source and target vertices of i-th edge (directed) and di represents the cost of the i-th edge.

Output

Print the costs of SSSP in the following format.

c0
c1
:
c|V|-1

The output consists of |V| lines. Print the cost of the shortest path from the source r to each vertex 0, 1, ... |V|-1 in order. If there is no path from the source to a vertex, print INF.

Constraints

1 ≤ |V| ≤ 100000

0 ≤ di ≤ 10000

0 ≤ |E| ≤ 500000

There are no parallel edges

There are no self-loops

Sample Input 1

4 5 0
0 1 1
0 2 4
1 2 2
2 3 1
1 3 5

Sample Output 1

0
1
3
4

Sample Input 2

4 6 1
0 1 1
0 2 4
2 0 1
1 2 2
3 1 1
3 2 5

Sample Output 2

3
0
2
INF

Solution in Python3 (judge verdict: WA: Presentation Error)

def main():
    [V,E,r]=input().split(" ")
    V=int(V)
    E=int(E)
    r=int(r)
    edgeset=[]
    for i in range(E):
        [s,t,d]=input().split(" ")
        edgeset.append([int(s),int(t),int(d)])

    setS=[]
    setV=[i for i in range(V)]
    setdist=[500000*10000+1 for i in range(V)]

    setS.append(r)
    setV.pop(r)
    setdist[r]=0

    for i in range(V-1):
        nowvert=setS[-1]
        for j in range(len(edgeset)):
            if(nowvert==edgeset[j][0]):
                newdist=edgeset[j][2]+setdist[nowvert]
                olddist=setdist[edgeset[j][1]]
                if(newdist<olddist):
                    setdist[edgeset[j][1]]=newdist
        setVdist=[setdist[setV[k]] for k in range(len(setV))]
        position=setVdist.index(min(setVdist))
        setS.append(setV[position])
        setV.pop(position)
                    
    for i in range(V):
        if(setdist[i]==500000*10000+1):
            print('INF')
        else:
            print(setdist[i])
        print('\n')
    
    return 0

main()