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++: #define _CRT_SECURE_NO_WARNINGS
#include <cstdio>
#include <cstdlib>
#include <string>
#include <iostream>
#include <climits>
#include <list>
#include <queue>

using namespace std;

static const int INFTY = -1;

int H;
int A[101];
int NodeNum[101];
int IndexInA[100];


int parent(int i) {
	return i / 2;
}

int left(int i) {
	return 2 * i;
}

int right(int i) {
	return 2 * i + 1;
}

void minHeapify(int i) {
	int l = left(i);
	int r = right(i);
	int smallest = i;
	if (l <= H && A[l] < A[i]) {
		smallest = l;
	}
	if (r <= H && A[r] < A[smallest]) {
		smallest = r;
	}
	if (smallest != i) {
		int temp = A[i];
		A[i] = A[smallest];
		A[smallest] = temp;
		temp = NodeNum[i];
		NodeNum[i] = NodeNum[smallest];
		NodeNum[smallest] = temp;
		IndexInA[NodeNum[i]] = i;
		IndexInA[NodeNum[smallest]] = smallest;

		minHeapify(smallest);
	}
}

void insert(int d, int nodeNum) {
	int i = ++H;
	A[i] = d;
	NodeNum[i] = nodeNum;
	IndexInA[nodeNum] = i;
	int p = parent(i);
	while (i > 1 && A[p] > A[i]) {
		int temp = A[p];
		A[p] = A[i];
		A[i] = temp;
		temp = NodeNum[p];
		NodeNum[p] = NodeNum[i];
		NodeNum[i] = temp;
		IndexInA[NodeNum[p]] = p;
		IndexInA[NodeNum[i]] = i;
		i = p;
		p = parent(i);
	}
}

int heapExtractMinNodeNum() {
	int minNodeNum = NodeNum[1];
	A[1] = A[H];
	NodeNum[1] = NodeNum[H];
	IndexInA[NodeNum[1]] = 1;
	H--;
	minHeapify(1);

	return minNodeNum;
}

void decrese(int i, int value) {
	A[i] = value;
	int p = parent(i);
	while (i > 1 && A[p] > A[i]) {
		int temp = A[p];
		A[p] = A[i];
		A[i] = temp;
		temp = NodeNum[p];
		NodeNum[p] = NodeNum[i];
		NodeNum[i] = temp;
		IndexInA[NodeNum[p]] = p;
		IndexInA[NodeNum[i]] = i;
		i = p;
		p = parent(i);
	}
}

int main() {
	int Dist[100];
	int AdjacenceyList[100][100];
	int AdjacenceyWeightList[100][100];
	int Degree[100];
	int i, j;
	int N;
	int W;
	//int Deg;
	//int MinTotalWeight = 0;
	int u, v;
	int k;
	bool inT[100];

	cin >> N;

	//for (i = 0; i < N; i++) {
	//	inT[i] = false;
	//	Dist[i] = INFTY;
	//	Deg = -1;
	//	for (j = 0; j < N; j++) {
	//		cin >> W;
	//		if (W != -1) {
	//			AdjacenceyList[i][++Deg] = j;
	//			AdjacenceyWeightList[i][Deg] = W;
	//		}
	//	}
	//	Degree[i] = Deg + 1;
	//}

	for (i = 0; i < N; i++) {
		inT[i] = false;
		Dist[i] = INFTY;
		cin >> u >> k;
		Degree[u] = k;
		for (j = 0; j < k; j++) {
			cin >> AdjacenceyList[u][j] >> AdjacenceyWeightList[u][j];
		}
	}


	H = 0;
	u = 0;
	inT[u] = true;
	Dist[u] = 0;
	for (i = 1; i <= N - 1; i++) {
		for (j = 0; j < Degree[u]; j++) {
			v = AdjacenceyList[u][j];
			if (inT[v] == false) {
				W = AdjacenceyWeightList[u][j];
				if (Dist[v] == INFTY) {
					//Dist[v] = W;
					//insert(W, v);
					Dist[v] = Dist[u] + W;
					insert(Dist[v], v);
				}
				//else if (W < Dist[v]) {
				else if(W + Dist[u] < Dist[v]){
					//Dist[v] = W;
					//decrese(IndexInA[v], W);
					Dist[v] = W + Dist[u];
					decrese(IndexInA[v], Dist[v]);
				}
			}
		}

		int minNodeNum = heapExtractMinNodeNum();
		inT[minNodeNum] = true;
		//MinTotalWeight += Dist[minNodeNum];
		u = minNodeNum;

	}

	//printf("%d\n", MinTotalWeight);

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

	return 0;
}

C++: #include <cstring>
#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
using namespace std;
#define pb push_back
#define fi first
#define se second
#define mkp make_pair
#define rep(i,n) for(int i=0; i<(n); ++i)
#define outl(x) cout << (x) << '\n'
#define FAST() cin.tie(0), ios::sync_with_stdio(false)
typedef pair<int,int> pii;
template<class A, class B>inline bool chmax(A &a, B b){return b>a ? a=b,1 : 0;}
template<class A, class B>inline bool chmin(A &a, B b){return b<a ? a=b,1 : 0;}
#define INF 0x3f3f3f3f

int N;
vector <pii> G[101];
int mcos[101];

void dijkstra(int s)
{
   priority_queue < pii, vector<pii>, greater<pii> > pq;
   pq.push( mkp(0, s) );
   memset( mcos, INF, sizeof(mcos) );
   mcos[s] = 0;
   while( !pq.empty() ){
      const pii tmp = pq.top(); pq.pop();
      if( mcos[tmp.se] < tmp.fi )continue;
      for( const auto& v : G[tmp.se] ){
         const int nc = v.fi + tmp.fi;
         if( chmin( mcos[v.se], nc )) pq.push( mkp(nc, v.se) );
      }
   }
}

signed main()
{
   FAST();
   cin >> N;

   rep(i, N){
      int u, k, to, c;
      cin >> u >> k;
      while(k--){
         cin >> to >> c;
         G[i].pb( mkp(c,to) );
      }
   }
   dijkstra(0);
   rep(i, N) cout << i << ' ' << mcos[i] << '\n';
}