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>
#include <stdlib.h>
#define N 10000
#define INF 200000
#define WHITE 0
#define GRAY 1
#define BLACK 2

int G[N][N], n;

void dijkstra(void) {
  int *d, *color;
  int i, u, mincost;

  d = (int*)malloc(sizeof(int) * n);
  color = (int*)malloc(sizeof(int) * n);
  for(i = 0; i < n; i++) {
    d[i] = INF;
    color[i] = WHITE;
  }
  d[0] = 0;

  while(1){
    mincost = INF;
    for(i = 0; i < n; i++) {
      if(color[i] != BLACK && d[i] < mincost){
        mincost = d[i];
        u = i;
      }
    }
    if(mincost == INF) break;
    color[u] = BLACK;
    for(i = 0; i < n; i++) {
      if(color[i] != BLACK && G[u][i] != INF && d[u] + G[u][i] < d[i]) {
        d[i] = d[u] + G[u][i];
      }
    }
  }
  for(i = 0; i < n; i++) {
    printf("%d %d\n", i, d[i]);
  }
}

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