Problem:
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Single Source Shortest Path

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

$1 \leq n \leq 100$

$0 \leq c_i \leq 100,000$

$|E| \leq 10,000$

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 <limits.h>

#define INF INT_MAX

int** init( int n ) {
  /*
   * 初期値INFのn次正方行列を作成する
   */
  int i, j;
  int** a;

  a = (int**)malloc( sizeof( int* ) * n );
  for( i=0; i<n; i++ ) {
    a[i] = (int*)malloc( sizeof( int ) * n );
  }

  for( i=0; i<n; i++ ) {
    for( j=0; j<n; j ++ ) {
      a[i][j] = INF;
    }
  }

  return a;

}

void scanGraph( int** g, int n ) {
  int i;  
  int u, k, v;
  
  
  while( scanf( "%d%d", &u, &k ) != EOF ) {
    
    for( i=0; i<k; i++ ) {
      scanf( "%d", &v );
      scanf( "%d", &g[u][v] );
    }
    
  }
  
  return;
  
}


int* ssspForCost( int** g, int n ) {

  int i;
  int *dist, color[n], pi[n];
  int minCost, u;

  dist = malloc( sizeof( int ) * n );

  for( i=0; i<n; i++ ) {
    dist[i] = INF;
    color[i] = 0;
  }

  dist[0] = 0;

  while( 1 ) {
    minCost = INF;
    for( i=0; i<n; i++ ) {
      if( color[ i ] != 1 && dist[ i ] < minCost ) {
	minCost = dist[ i ];
	u = i;
      }
      
      if( minCost == INF ) {
	break;
      }
      
      for( i=0; i<n; i++ ) {
	if( g[u][i] != INF ) {
	  if( color[ i ] != 1 && dist[ u ] + g[ u ][ i ] < dist[ i ] ) {
	    pi[i] = u;
	    dist[i] =  dist[ u ] + g[ u ][ i ];
	  }
	}
      }
    }
  }
  
  return dist;
  
}   

void printDist( int* dist, int n ) {
  int i;

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

  return;

}

int main() {
  int n;
  int** g;
  int* dist;

  scanf( "%d", &n );
  g = init( n );

  scanGraph( g, n );

  dist = ssspForCost( g, n );

  printDist( dist , n );

  return 0;

}