Go: package main

import (
	"bufio"
	"container/heap"
	"fmt"
	"os"
)

type Item struct {
	value    int // The value of the item; arbitrary.
	priority int // The priority of the item in the queue.
	// The index is needed by update and is maintained by the heap.Interface methods.
	index int // The index of the item in the heap.
}
type PriorityQueue []*Item

func (pq PriorityQueue) Len() int { return len(pq) }
func (pq PriorityQueue) Less(i, j int) bool {
	return pq[i].priority < pq[j].priority
}
func (pq PriorityQueue) Swap(i, j int) {
	pq[i], pq[j] = pq[j], pq[i]
	pq[i].index = i
	pq[j].index = j
}
func (pq *PriorityQueue) Push(x interface{}) {
	n := len(*pq)
	item := x.(*Item)
	item.index = n
	*pq = append(*pq, item)
}
func (pq *PriorityQueue) Pop() interface{} {
	old := *pq
	n := len(old)
	item := old[n-1]
	item.index = -1 // for safety
	*pq = old[0 : n-1]
	return item
}

type Q struct {
	pq *PriorityQueue
	ds map[int]int // It has always same value as pq. For random access.
}

func newQ() *Q {
	pq := new(PriorityQueue)
	heap.Init(pq)
	return &Q{
		pq: pq,
		ds: make(map[int]int),
	}
}
func (q *Q) pop() (u, d int) {
	item := heap.Pop(q.pq).(*Item)
	delete(q.ds, item.value)
	return item.value, item.priority
}
func (q *Q) get(u int) (int, bool) { // returns d
	d, ok := q.ds[u]
	return d, ok
}
func (q *Q) set(u, d int) {
	q.ds[u] = d
	for _, item := range *q.pq {
		if item.value != u {
			continue
		}

		item.priority = d
		heap.Fix(q.pq, item.index)
		return
	}
	heap.Push(q.pq, &Item{
		priority: d,
		value:    u,
	})
}
func (q *Q) len() int {
	return len(q.ds)
}

func main() {
	r := bufio.NewReader(os.Stdin)

	var n int
	fmt.Fscan(r, &n)
	cs := make([]map[int]int, n) // []v_i -> c_i
	for h := 0; h < n; h++ {
		var u, k int
		fmt.Fscan(r, &u, &k)
		m := make(map[int]int)
		for i := 0; i < k; i++ {
			var v, c int
			fmt.Fscan(r, &v, &c)
			m[v] = c
		}

		cs[u] = m
	}

	q := newQ()
	q.set(0, 0)
	visited := make(map[int]struct{})
	out := make([]int, n)

	for q.len() > 0 {
		u, d := q.pop()
		for uu, c := range cs[u] {
			// Consider the connection between u and uu.
			if _, ok := visited[uu]; ok {
				continue
			}
			dd := d + c
			if d, ok := q.get(uu); !ok || d > dd {
				q.set(uu, dd)
			}
		}

		out[u] = d
		visited[u] = struct{}{}
	}

	for u, d := range out {
		fmt.Println(u, d)
	}
}

C++: #include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

int main()
{
	int n, u, k, v1, c1;
	const int INF = 1000000;
	
	cin >> n;
	
	vector<vector<int> > v(n), c(n);
	vector<int> w(n, INF);
	vector<bool> f(n, false);

	for (int i = 0; i < n; i++) {
		cin >> u >> k;
		for (int j = 0; j < k; j++) {
			cin >> v1 >> c1;
			v[u].push_back(v1);
			c[u].push_back(c1);
		}
	}

	w[0] = 0;

	while (true) {
		int k = -1;
		for (int i = 0; i < n; i++)
			if (!f[i] && (k == -1 || w[i] < w[k]))
				k = i;

		if (k == -1)
			break;

		f[k] = true;

		for (int i = 0; i < (int)v[k].size(); i++)
			w[v[k][i]] = min(w[v[k][i]], w[k] + c[k][i]);
	}

	for (int i = 0; i < n; i++)
		cout << i << " " << w[i] << endl;

	return 0;
}

C++: #include<iostream>
#include<algorithm>
#include<queue>
using namespace std;
const int MAX = 10000;
const int INFTY = (1 << 20);
const int WHITE = 0;
const int GRAY = 1;
const int BLACK = 2;
int n;
vector<pair<int, int>> adj[MAX];
void dijkstra()
{
	priority_queue<pair<int, int>> PQ;
	int color[MAX];
	int d[MAX];
	for (int i = 0; i < n; i++)
	{
		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;
		for (int j = 0; j < adj[u].size(); j++)
		{
			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;
			}
		}
	}
	for (int i = 0; i < n; i++)
		cout << i << " " << (d[i] == INFTY ? -1 : d[i]) << endl;
}
int main()
{
	int k, u, v, c;
	cin >> n;
	for (int i = 0; i < n; i++)
	{
		cin >> u >> k;
		for (int j = 0; j < k; j++)
		{
			cin >> v >> c;
			adj[u].push_back(make_pair(v, c));
		}
	}
	dijkstra();
}

C++: //Single Source Shortest Path II
#include <iostream>
#include <vector>
#include <queue>
#include <climits>

using namespace std;

static const int N = 10000;
static const int WHITE = 0;
static const int BLACK = 1;
int n, colors[N], d[N];
vector<pair<int, int> > G[N];


void dijkstra() {
    priority_queue<pair<int, int>, vector<pair<int, int> >, greater<pair<int, int> > > PQ;
    for(int i = 0; i < N; i++) {
        colors[i] = WHITE;
        d[i] = INT_MAX;
    }
    d[0] = 0;
    PQ.push(make_pair(0, 0));
    while(!PQ.empty()) {
        pair<int, int> f = PQ.top();
        PQ.pop();
        int u = f.second;
        if(colors[u] == BLACK) continue;
        for(int i = 0; i < G[u].size(); i++) {
            if(d[G[u][i].first] > f.first + G[u][i].second) {
                d[G[u][i].first] = f.first + G[u][i].second;
                PQ.push(make_pair(d[G[u][i].first], G[u][i].first));
            }

        }
    }
}

int main() {
    int u, k, v, c;
    cin >> n;
    for(int i = 0; i < n; i++) {
        cin >> u >> k;
        for(int j = 0; j < k; j++) {
            cin >> v >> c;
            G[u].push_back(make_pair(v, c));
        }
    }

    dijkstra();

    for(int i = 0; i < n; i++) {
        cout << i << " " << d[i] << endl;
    }
}

C++: #include<iostream>
#include<vector>
#include<stack>

#define INF (1 << 21)

int main() {
	int node_num;

	std::cin >> node_num;
	std::vector<std::vector<int> > node(node_num, std::vector<int>(node_num, -1));

	for (size_t i = 0; i < node.size(); i++) {
		int out, node_number;
		std::cin >> node_number >> out;
		for (int j = 0; j < out; j++) {
			int to, distance;
			std::cin >> to >> distance;
			node[node_number][to] = distance;
		}
	}

	std::vector<int> distance(node.size(), INF);
	std::stack<int> s;
	distance[0] = 0;

	s.push(0);
	while(!s.empty()) {
		int node_number = s.top(); s.pop();
		for (size_t j = 0; j < node[node_number].size(); j++) {
			if (node[node_number][j] != -1 && node[node_number][j] + distance[node_number] < distance[j]) {
				distance[j] = node[node_number][j] + distance[node_number];
				s.push(j);
			}
		}
	}

	for (size_t i = 0; i < distance.size(); i++) {
		std::cout << i << " " << distance[i] << std::endl;
	}
}

C++: #include<bits/stdc++.h>
using namespace std;

#define fi first
#define se second

vector<pair<int,int> >adj[10010];
priority_queue<pair<int,int> > pq;
int nodes[10010];

int main(){
	memset(nodes,-1,sizeof(nodes));
	int n,node,k,v,c;
	cin>>n;
	for (int i=0; i<n; ++i) {
		cin>>node>>k;
		for (int j=0; j<k; ++j) {
			cin>>v>>c;
			adj[node].push_back(make_pair(v,c));
		}
	}
	pq.push(make_pair(0,0));
	while(!pq.empty()){
		pair<int,int> cur=pq.top();
		pq.pop();
		if(nodes[cur.se]!=-1){//kalo udh didatengin
			continue;
		}
		else nodes[cur.se]=-cur.fi;
		for(int i=0;i<adj[cur.se].size();i++){
			pq.push(make_pair(-adj[cur.se][i].se+cur.fi,adj[cur.se][i].fi));
		}
	}
	for (int i=0; i<n; ++i) {
		cout<<i<<" "<<nodes[i]<<endl;
	}
	return 0;
}