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 <bits/stdc++.h>
using namespace std;
#define Rep(i, n) for (int i = 0; i < (int)(n); i++)
#define BitRep(i, n) for (int i = 0; i < (int)(1 << n); i++)
#define Sum(vec) accumulate(vec.begin(), vec.end(), 0)
#define Sort(vec) sort(vec.begin(), vec.end())
#define Reverse(vec) reverse(vec.begin(), vec.end())
#define Next_permutation(vec) next_permutation(vec.begin(), vec.end())

static const int MAX = 10000;
static const int INFTY = (1 << 20);
static const int WHITE = 0;
static const int GRAY = 1;
static 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();
    return 0;
}

C++: #include<iostream>
#include<cstdio>
#define INF 1<<30
#define FinishFunction return 0
#define MAX 1000000
using namespace std;
         
struct edge {
  int from,to,cost,k;
};
       
edge es[MAX];
       
int main(){
  int n,u,k,E,c,v;
  E = 0;
  scanf("%d",&n);
       
  for(int i=0;i<n;i++){
    scanf("%d %d",&u,&k);
          
    for(int j=0;j<k;j++){
      scanf("%d %d",&v,&c);
      es[E].from = u;
      es[E].to = v;
      es[E++].cost = c;
    }
  }
       
  // Ika berumanfo-do
  int d[MAX];
  for(int i=0;i<n;i++)d[i] = INF;
  d[0] = 0;
  while(true){
    bool update = false;
    for(int i=0;i<E;i++){
      edge e = es[i];
      if(d[e.from] != INF && d[e.to] > d[e.from] + e.cost){
    d[e.to] = d[e.from] + e.cost;
    update = true;
      }
    }
    if(!update)break;
  }
  for(int i=0;i<n;i++)cout << i << " " << d[i] << endl;
  FinishFunction;// return 0
}

C++: #include <bits/stdc++.h>

using namespace std;

vector<pair<int, int>> adja[10000];

#define INF (1LL << 30)

int main() {
	int n, id, k, a, b;

	cin >> n;
	for (int i = 0; i < n; ++i) {
		cin >> id >> k;
		for (int j = 0; j < k; ++j) {
			cin >> a >> b;
			adja[id].push_back(make_pair(a, b));
		}
	}

	priority_queue<pair<int, int>> que;
	que.push(make_pair(0, 0)); //cost, node
	long long cost[10000];
	fill(cost, cost + n, INF);

	while (!que.empty()) {
		for (int i = 0, size = que.size(); i < size; ++i) {
			pair<int, int> top = que.top();
			que.pop();

			if (cost[top.second] < top.first) {
				continue;
			}
			cost[top.second] = top.first;

			for (int j = 0, len = adja[top.second].size(); j < len; ++j) {
				que.push(make_pair(top.first + adja[top.second][j].second, adja[top.second][j].first));
			}
		}
	}

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

	return 0;
}

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

#define INF 2000000000
#define WH 0
#define GR 1
#define BK 2

int main() {
    int n;
    cin >> n;
    vector<pair<int, int>> adj[10000];
    for (int i = 0; i < n; i++) {
        int u, k;
        cin >> u >> k;
        for (int j = 0; j < k; j++) {
            int v, c;
            cin >> v >> c;
            adj[u].push_back(make_pair(v, c));
        }
    }

    int color[10000] = {};
    int d[10000];
    for (int i = 0; i < n; i++) {
        d[i] = INF;
    }

    int p[10000];
    for (int i = 0; i < n; i++) {
        p[i] = -1;
    }

    priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> PQ;  // (cost, unit)


    d[0] = 0;
    PQ.push(make_pair(0, 0));

    while (PQ.empty() == false) {
        pair<int, int> q = PQ.top(); PQ.pop();
        int u = q.second;

        if (d[u] < q.first) {
            continue;
        }

        color[u] = BK;

        for (int j = 0; j < adj[u].size(); j++) {
            int v = adj[u][j].first;
            int c = adj[u][j].second;
            if (color[v] != BK) {
                if (d[u] + c < d[v]) {
                    d[v] = d[u] + c;
                    PQ.push(make_pair(d[v], v));
                    p[v] = u;
                }
            }
        }
    }

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

    return 0;

}