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 N 100000
#define INF 1000000

typedef struct{
  int g, b,  c; 
}Place;

int n, d[N];
Place a[500000];

void root(int);

int main(){
 int i, j;
 int x, y, count;
 count =0;
 scanf("%d",&n);
for(i=0;i<n;i++)
 for(i=0;i<n;i++){
 scanf("%d%d",&y,&x);
 for(j=0;j<x;j++){
 a[count].b =y;
 scanf("%d%d",&a[count].g,&a[count].c);
 count++;
}
}

 root(count);

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

 return 0;
}

void root(int x){
  int i, flag;
   flag=1;

 for(i = 0 ; i < n ; i++) d[i] = INF;
 d[0] = 0;

 while(flag != 0){
 flag = 0;
 for(i = 0 ; i < x ; i++){
 if(a[i].c + d[a[i].b] < d[a[i].g]){
	d[a[i].g] = a[i].c + d[a[i].b];
	flag = 1;
 }
 }
}
}