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 <iostream>
#include <algorithm>
#include <queue>
using namespace std;
#define MAX 10000
#define INFTY (1<<30)
#define rep(i,n)	for(int i=0;i<n;i++)
enum{
	white,
	gray,
	black,
};

int n;
vector<pair<int,int> >	adj[MAX];

void dijkstra(){
	priority_queue<pair<int,int> >	pq;
	int color[MAX];
	int d[MAX];
	rep(i,n){
		d[i]=INFTY;
		color[i]=white;
	}
	d[0]=0;
	pq.push(make_pair(0,0));
	color[0]=gray;
	while(!pq.empty()){
		pair<int,int> f=pq.top();	pq.pop();
		int u=f.second;
		color[u]=black;
		if(d[u]<f.first*(-1))	continue;
		rep(j,(int)adj[u].size()){
			int v=adj[u][j].first;
			if(color[v]==black)	continue;
			if(d[v]>d[u]+adj[u][j].second){
				d[v]=d[u]+adj[u][j].second;
				pq.push(make_pair(d[v]*(-1),v));
				color[v]=gray;
			}
		}
	}
	rep(i,n){
		cout<<i<<" "<<(d[i]==INFTY?-1:d[i])<<endl;
	}
}

int main(){
	int k,u,v,c;
	cin>>n;
	rep(i,n){
		cin>>u>>k;
		rep(j,k){
			cin>>v>>c;
			adj[u].push_back(make_pair(v,c));
		}
	}
	dijkstra();
	return 0;
}