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>
#include<stdlib.h>

#define INF 1000000
#define NIL NULL
#define WHITE 5000
#define BLACK 5001

void initializeSingleSource(void);
void dijkstra(void);

int v[101][101],c[101][101];
int *d,*pi,*color,*k;
int n;

int main(){
  int i,j;
  int *u;

  scanf("%d",&n);

  u = malloc(sizeof(int)*n);
  d = malloc(sizeof(int)*n);
  pi = malloc(sizeof(int)*n);
  color = malloc(sizeof(int)*n);
  k = malloc(sizeof(int)*n);

  for(i = 0;i < n;i++){
    scanf("%d %d",&u[i],&k[i]);
    for(j = 0;j < k[i];j++){
      scanf("%d",&v[i][j]);
      scanf("%d",&c[i][j]);
    }
  }

  dijkstra();

  for(i = 0;i < n;i++){
    printf("%d %d\n",u[i],d[i]);
  }

  return 0;
}

void initializeSingleSource(){
  int i;
  for(i = 0;i < n;i++){
    d[i] = INF;
    pi[i] = NIL;
    color[i] = WHITE;
  }
  d[0] = 0;
}

void dijkstra(){
  int i,j,mincost,u1,v1;

  initializeSingleSource();

  while(1){
    mincost = INF;
    for(i = 0;i < n;i++){
      if(color[i] != BLACK && d[i] < mincost){
	mincost = d[i];
	u1 = i;
      }
    }

    if(mincost == INF)break;

    color[u1] = BLACK;

    for(v1 = 0;v1 < k[u1];v1++){
      if(color[v[u1][v1]] != BLACK && (d[u1] + c[u1][v1]) < d[v[u1][v1]]){
	pi[v[u1][v1]] = u1;
	d[v[u1][v1]] = d[u1] + c[u1][v1];
      }
    }
  }
}