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: Memory Limit Exceeded)

#include<stdio.h>

#define MAX 10001
static const int INF = (1 << 21);

int n;
int d[MAX],key1[MAX],key2[MAX],G[MAX][MAX];

void SingleSourceShortestPathII(void){
  int i,j;
  int min,youso;

  for(i = 0;i < n;i++){
    d[i] = INF;
    key1[i] = 0;
    key2[i] = -1;
  }
  d[0] = 0;

  while(1){
    min = INF;
    youso = -1;

    for(i = 0;i < n;i++){
      if(!key1[i] && d[i] < min){
	youso = i;
	min = d[i];
      }
    }
    if(youso == -1){
      break;
    }
    key1[youso] = 1;

    for(j = 0;j < n;j++){
      if(d[j] > d[youso] + G[youso][j]){
	d[j] = d[youso] + G[youso][j];
	key2[j] = youso;
      }
    }
  }
}

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

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

  SingleSourceShortestPathII();

  for(i = 0;i < n;i++){
    printf("%d %d\n",i,(d[i] == INF?-1:d[i]));
  }
  return 0;
}