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 <vector>

using namespace std;

struct Info{
	Info(int arg_weight,short arg_to){
		weight = arg_weight;
		to = arg_to;
	}
	int weight;
	short to;
};


int main(){
	int n,count=0,t,min,min_index,tmp,left_node,right_node,dist,t_to_i;
	scanf("%d",&n);
	vector<Info> V[n];

	int P[n],zero_dist[n];

	for(int i=0;i<n;i++){
		P[i]=0;
		zero_dist[i] = 10000001;
	}
	zero_dist[0] = 0;
	P[0]=1;

	for(int i=0;i<n;i++){
		scanf("%d %d",&left_node,&tmp);
		if(left_node == 0){
			for(int k=0;k<tmp;k++){
				scanf("%d %d",&right_node,&dist);
				zero_dist[right_node] = dist;
			}
		}else{
			for(int k=0;k<tmp;k++){
				scanf("%d %d",&right_node,&dist);
				V[left_node].push_back(Info(dist,right_node));
			}
		}
	}

	while(count<n-1){

		min=10000001;
		for(int i=1;i<n;i++){
			if(P[i]==0&&zero_dist[i]<min){
				min_index = i;
				min = zero_dist[i];
			}
		}
		t = min_index;
		P[t]=1;
		count++;

		for(int i=1;i<n;i++){
			t_to_i = 10000001;
			for(int k=0;k<V[t].size();k++){
				if(V[t][k].to == i){
					t_to_i = V[t][k].weight;
					break;
				}
			}
			if(zero_dist[i] > zero_dist[t]+t_to_i){
				zero_dist[i]=zero_dist[t]+t_to_i;
			}
		}
	}

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

    return 0;
}