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 N 100000
#define INF 1000000
 
typedef struct{
    int go,back,cost;
}Date;
 
int n,d[N];
Date a[500000];
void root(int);
 
int main(void){
    int i,j,u,k,count=0;
    scanf("%d",&n);
    for(i=0;i<n;i++) {
        scanf("%d%d",&u,&k);
        for(j=0;j<k;j++){
            a[count].back=u;
            scanf("%d%d",&a[count].go,&a[count].cost);
            count++;
        }
    }
    root(count);
    for(i=0;i<n;i++) printf("%d %d\n",i,d[i]);
    return 0;
}
 
void root(int b){
    int i,flag=1;
     
    for(i=0;i<n;i++) d[i]=INF;
    d[0]=0;
     
    while(flag!=0){
        flag=0;
        for(i=0;i<b;i++){
            if(a[i].cost+d[a[i].back]<d[a[i].go]){
                d[a[i].go]=a[i].cost+d[a[i].back];
                flag=1;
            }
        }
    }
}