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 MAX 1000  // Gの頂点数の最大値
#define INF 10000000

int G[MAX][MAX];
int d[MAX];
char color[MAX];
int n;

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

int main(){

  int u,k,i,j,v,c;
  
  /* 入力 */
  scanf("%d",&n); //n:Gの頂点数

  for(i = 0; i < n;i++){ // 初期化
    for(j = 0;j < n;j++){
      G[i][j] = INF;
    }
  }

  for(i = 0;i < n;i++){
    scanf("%d %d",&u,&k); // u:頂点の番号 , k:uの出次数
    for(j = 0;j < k;j++){
      scanf("%d %d",&v,&c); // v:uに隣接する頂点の番号, c: 重み
      G[u][v] = c; // G[u][v]にはuとvをつなぐ辺の重みを入れる
    }
  }

  dijkstra();
  
  return 0;
}

void initializeSingleSource(void)
{
  int v;

  for(v = 0;v < MAX;v++){
    d[v] = INF; // 始点からvまでの重みの合計
    color[v] = 'W';
  }
  d[0] = 0;
  color[0] = 'G';
}

void dijkstra(void)
{
  int mincost,i,u,v;

  initializeSingleSource(); // 初期化

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

    if(mincost == INF) break;

    color[u] = 'B';

    for(v = 0;v < n;v++){
      if(color[v] != 'B' && G[u][v] != INF){	 
	if(d[v] > d[u] + G[u][v]){
	d[v] = d[u] + G[u][v];
	color[v] = 'G';
	}
      }
    }

  }

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