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: Accepted)

#include<stdio.h>
#include<stdlib.h>
  
#define INFTY 2097152//(1<<21)
 
struct ver{
    int weight;
    int key;
    struct ver *next;
};
  
void input(int);
void create(int,int,int);
void shortestpath(void);
int set(int*);
int heap(int*);
 
int n;
int *d;
struct ver *ver;
  
int main(void){
    int i;
    int id;
  
    scanf("%d",&n);
  
    d=(int*)malloc(sizeof(int)*n);
    ver=(struct ver*)malloc(sizeof(struct ver)*n);
    for(i=0;i<n;i++){
        ver[i].weight=-1;
        ver[i].key=-1;
        ver[i].next=NULL;
    }
  
    for(i=0;i<n;i++){
        scanf("%d",&id);
        input(id);  
    }
  
    shortestpath();
  
    for(i=0;i<n;i++) printf("%d %d\n", i, d[i]);
 
    free(d);
    return 0;
}
  
void input(int id){
    int k, u, c;
    int i;
 
    scanf("%d", &k);
    for(i = 0; i < k; i++){
        scanf("%d", &u);
        scanf("%d", &c);
        create(id, u, c);
    }
 
}
  
void create(int id, int u, int c){
    struct ver *new, *work;

    new=(struct ver*)malloc(sizeof(struct ver));
    new->next = NULL;
    new->weight = c;
    new->key = u;
  
    work = &ver[id];
    while(work->next != NULL){
      work = work->next;
    }
    work->next = new;
  
}
  
void shortestpath(void){
    int S[n];
    int i;
    int s, u;
    struct ver *work;
  
    for(i = 0; i < n; i++){
        S[i] = 0;
        d[i] = INFTY;
    }
    s = 0;
    d[s] = 0;
  
    while(set(S) == 0){
        u = heap(S);
        S[u] = 1;
        work = ver[u].next;
 
        while(work != NULL){
 
            if(S[work->key] == 1){
        }else if(d[u] + work->weight < d[work->key]){
                d[work->key] = d[u] + work->weight;
            }
            work = work->next;
 
        }
    }
}
  
int heap(int *s){
    int i;
    int min = INFTY;
    int u;
   
    for(i = 0; i < n; i++){
      if(s[i] == 1){
    continue;
      }
           
      if(d[i]<min){
    min=d[i];
    u=i;
      }
 
    }   
    return u;
}
 
int set(int *s){
    int i;
  
    for(i=0;i<n;i++){
        if(s[i]==0) return 0;
    }
    return 1;
}