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: Runtime Error)

#include <stdio.h>
#define BLACK 1
#define WHITE 0
#define inf 1000000
int main(){
    int c, n, k, i, j, id, v[1000][1000], w[1000][1000], min, d[100], u=0, color[1000];
    scanf("%d",&n);
    for(i = 0; i < n;  i++){
        d[i] = inf;
        color[i] = WHITE;
        
        scanf("%d",&id);
        scanf("%d",&k);
        for(j = 0; j < k; j++){
            scanf("%d",&c);
            v[id][c] = 1;
            scanf("%d",&w[id][c]);
        }
    }
    d[0] = 0;
    while(1){
        min = inf;
        for(j = 0; j<n; j++){
            if(d[j] < min && color[j] == WHITE){
                min = d[j];
                u = j;
            }
        }
        if(min == inf) break;
        color[u] = BLACK;
        for(j = 1; j<n; j++){
            if(v[u][j] == 0) continue;
            if(d[u] + w[u][j] < d[j] && color[j] == WHITE) d[j] = d[u] + w[u][j];
        }
    }
    for(i = 0; i < n; i++) printf("%d %d\n",i, d[i]);
    return 0;
}