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: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>
#define MAX 10000
#define INF 1000000
#define true 1
#define false 0

int p[MAX], d[MAX], is_visited[MAX];

typedef struct _n {
  int id, weight;
  struct _n *next;
} node;
node G[MAX];

void add(int origin, int direction, int weight) {
  node *p, *new;
  p = &G[origin];

  while(p->next != NULL)
    p = p->next;

  new = (node *)malloc(sizeof(node));
  p->next = new;
  new->id = direction;
  new->weight = weight;
}

node *find(int origin, int direction) {
  node *p;

  p = &G[origin];
  while(p->next != NULL && p->id != direction)
    p = p->next;

  if(p->id == direction)
    return p;
  else
    return false;
}

int is_connected(int origin, int direction) {
  if(find(origin, direction))
    return true;
  else
    return false;
}

int weight_between(int origin, int direction) {
  node *t;

  t = find(origin, direction);
  return t->weight;
}

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

  d[0] = 0;
  p[0] = -1;

  while(1) {
    mincost = INF;

    for(i = 0;i < MAX;i++) {
      if(!is_visited[i] && d[i] < mincost) {
        mincost = d[i];
        u = i;
      }
    }

    if(mincost == INF) return;
    is_visited[u] = true;

    for(i = 0;i < MAX;i++) {
      if(!is_visited[i] && is_connected(u, i)) {
        weight = d[u] + weight_between(u, i);
        if(weight < d[i]) {
          d[i] = weight;
          p[i] = u;
        }
      }
    }
  }
}

int main() {
  int n, i, j, k, u, v, w;

  for(i = 0;i < MAX;i++) {
    p[i] = -1;
    d[i] = INF;
    G[i].id = i;
    G[i].weight = INF;
    G[i].next = NULL;
  }

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

  dijkstra();

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

  return 0;
}