Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

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: Accepted)

#include <stdio.h>
#include <stdlib.h>
#define MAX_N 10001
#define INF (1<<28);
#define QUEUE_SIZE 20001;

typedef struct Node * NodePointer;

typedef struct Node {
  NodePointer next;
  int v, c;
} Node;

int N;
NodePointer E[MAX_N] = {};
NodePointer tail[MAX_N] = {};
int cost[MAX_N];

NodePointer makeNode(int v, int c) {
  NodePointer node = (NodePointer)malloc(sizeof(Node));
  node->next = NULL;
  node->v = v;
  node->c = c;
  return node;
}

void addEdge(int u, int v, int c) {
  tail[u]->next = makeNode(v,c);
  tail[u] = tail[u]->next;
}

int daiku() {
  int i, j;
  int mini, id;
  int vis[MAX_N];
  NodePointer np;
  for(i = 0; i < N; ++i) {
    cost[i] = INF;
    vis[i] = 0;
  }
  cost[0] = 0;
  while(1) {
    mini = INF;
    id = -1;
    for(i = 0; i < N; ++i) {
      if(vis[i]) continue;
      if(cost[i] < mini) {
        mini = cost[i];
        id = i;
      }
    }
    if(id == -1) break;
    vis[id] = 1;
    for(np = E[id]->next; np != NULL; np = np->next) {
      if(vis[np->v]) continue;
      j = cost[id] + np->c;
      if(j < cost[np->v]) cost[np->v] = j;
    }
  }
}

int main() {
  int i, j, k;
  int id, v, c;
  int tmp;

  for(i = 0; i < MAX_N; ++i) {
    E[i] = makeNode(-1,-1);
    tail[i] = E[i];
  }

  scanf("%d", &N);
  for(i = 0; i < N; ++i) {
    scanf("%d %d", &id, &k);
    while(k--) {
      scanf("%d %d", &v, &c);
      addEdge(id,v,c);
    }
  }

  daiku();

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

  return 0;
}