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 Python (judge verdict: Wrong Answer)

#!/usr/bin/python
from collections import defaultdict
import sys,csv,math,heapq
if sys.version_info[0]>=3: raw_input=input
INF=1<<29

def shortestPath(g,s,dist,prev):
	n = len(g)
	dist[s] = 0
	Q=[]
	heapq.heappush(Q,(0,-2,s))
	while Q:
		e=heapq.heappop(Q)
		if prev[e[2]]!=-1: continue
		prev[e[2]]=e[1]
		for f in g[e[2]]:
			if dist[f[2]]>e[0]+f[0]:
				dist[f[2]]=e[0]+f[0]
				heapq.heappush(Q,(e[0]+f[0],f[1],f[2]))

V,E,R=map(int,raw_input().split())
dist=[INF]*V
prev=[-1]*V
G=defaultdict(list)
for _ in range(E):
	s,t,d=map(int,raw_input().split())
	G[s].append([d,s,t])
	G[s].append([d,t,s])
shortestPath(G,R,dist,prev)
for e in dist:
	print('INF' if e==INF else e)