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 C (judge verdict: Accepted)

#include <stdio.h>
#include <string.h>
#include <stdlib.h>

#define BUF_SIZE 30

int get_int3(int *a1, int *a2, int *a3) {
#ifdef BUF_SIZE
  char line[BUF_SIZE];
  if(!fgets(line, BUF_SIZE, stdin)) return -1;
  sscanf(line, "%d %d %d", a1, a2, a3);
#else
#error
#endif
  return 0;
}

#define VERTEX_MAX 100000
#define EDGE_MAX 500000
// [# of heads(: VERTEX_MAX)] + [# of elems( <= EDGE_MAX)]
#define POOL_MAX (VERTEX_MAX+EDGE_MAX+10)
#define WEIGH_MAX 0x3f3f3f3f

struct edge {
    int src;
    int dst;
    int cost;
};

int main(void) {
    int vs, es, start;
    get_int3(&vs, &es, &start);
    struct edge edges[EDGE_MAX];
    int i;
    for(i = 0; i < es; i++) {
        struct edge *e = &edges[i];
        get_int3(&e->src, &e->dst, &e->cost);
    }
    // initialization
    int min_dist[VERTEX_MAX];
    memset(min_dist, 0x3f, VERTEX_MAX*sizeof(int));
    min_dist[start] = 0;
    while(1) {
        int updated = 0;
        for(i = 0; i < es; i++) {
            struct edge *e = &edges[i];
            if(min_dist[e->src] == WEIGH_MAX) continue;
            int new = min_dist[e->src] + e->cost;
            if(new < min_dist[e->dst]) {
                min_dist[e->dst] = new;
                updated = 1;
            }
        }
        if(!updated) break;
    }
    for(i = 0; i < vs; i++) {
        if(min_dist[i] == WEIGH_MAX) {
            printf("INF\n");
        } else {
            printf("%d\n", min_dist[i]);
        }
    }
    return 0;
}