Problem:
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Single Source Shortest Path II

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

$1 \leq n \leq 10,000$

$0 \leq c_i \leq 100,000$

$|E| < 500,000$

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 C (judge verdict: Time Limit Exceeded)

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

#define NODE_NUM 10000


int wght[NODE_NUM];
int visited[NODE_NUM];

typedef struct VERTEX{
    int idx;
    int w;
}VERTEX;

void search(int node_idx, int w, VERTEX ** A, int* num, int n){
    
    int i, weight, next;
    
    if (visited[node_idx] == 1) {
        return;
    }
    
    for (i=0; i < num[node_idx]; i++) {
        
        next = A[node_idx][i].idx;
        
        if ( visited[next]) {
            continue;
        }
        
        weight = A[node_idx][i].w;
        
        if( wght[next] > w + weight )
        {
            wght[next] = w + weight;
            visited[node_idx] = 1;
            search(next, w + weight, A, num, n);
            visited[node_idx] = 0;
        }
    }

    return;

}


int main( ){
    
    int i, j, k, v, c, u, n , *num;
    VERTEX ** A;
    
    scanf("%d", &n);
    A = malloc(sizeof(VERTEX) * n);
    num = malloc(sizeof(int) * n);
    
    for (i=0; i <n; i++) {
        wght[i] = 300000000;
    }
    wght[0] = 0;
    
    
    
    for (i=0; i<n; i++){
        
        scanf("%d", &u);
        scanf("%d", &k);
        A[u] = malloc(sizeof(VERTEX) * k);
        num[u] = k;
        
        for (j = 0; j < k; j++) {
            scanf("%d %d", &v, &c);
            A[u][j].idx = v;
            A[u][j].w = c;
        }
    }
    
    search(0, 0, A, num, n);
    
    for (i=0; i<n; i++) {
        printf("%d %d\n", i, wght[i]);
    }
    
    
    return 0;
}