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<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 <iostream>
#include <cstdio>
#include <climits>
#include <cstring>

using namespace std;

#define SWAP(type, a, b) do { type t = a; a = b; b = t; } while(0)

typedef struct {
    int* verIdx;
    int num;
} Heap;

typedef struct _node {
    int toIdx;
    int weight;
    struct _node* next;
} Node;

typedef struct {
    Node* head;
} List;

int* d; 
List* list;
int n;

void makeMinHeap(Heap *heap, int idx);
void insert(Heap *heap, int key);
int extract(Heap *heap);

static inline int getParent(int idx) { return idx / 2; }
static inline int getLeft(int idx) { return idx * 2; }
static inline int getRight(int idx) { return idx * 2 + 1; }
static inline bool isCorrectHeapIdx(int idx, int heapSize) { return idx <= heapSize && 1 <= idx; }
static inline bool isEmpty(Heap *heap) { return heap->num <= 0; }

static inline int getMinCost(int idx) {
    return d[idx];
}

void makeMinHeap(Heap *heap, int idx) {
    int left = getLeft(idx);
    int right = getRight(idx);

    int minIdx = idx;
    if(isCorrectHeapIdx(left, heap->num) && getMinCost(heap->verIdx[minIdx]) > getMinCost(heap->verIdx[left])) {
        minIdx = left;
    } if(isCorrectHeapIdx(right, heap->num) && getMinCost(heap->verIdx[minIdx]) > getMinCost(heap->verIdx[right])) {
        minIdx = right;
    }

    if(minIdx != idx) {
        SWAP(int, heap->verIdx[minIdx], heap->verIdx[idx]);
        makeMinHeap(heap, minIdx);
    }
}

void insert(Heap *heap, int* key) {
    heap->verIdx[++heap->num] = *key;
    for(int i = getParent(heap->num); i >= 1; i = getParent(i)) {
        makeMinHeap(heap, i);
    }
}

void extract(Heap *heap, int* key) {
    *key = heap->verIdx[1];
    heap->verIdx[1] = heap->verIdx[heap->num--];
    makeMinHeap(heap, 1);
}

static inline void set(Node* ptr, int toIdx, int weight, Node* next) {
    ptr->toIdx = toIdx;
    ptr->weight = weight;
    ptr->next = next;
}

void addList(int s, int t, int weight) {
    Node* next = list[s].head;
    Node* newNode = new Node();

    list[s].head = newNode;
    set(newNode, t, weight, next);
}

void solve(int s) {
    Heap que;
    bool* isAddS = new bool[n]();

    que.verIdx = new int[n * n];
    que.num = 0;

    d = new int[n];
    d[s] = 0;
    for(int i = 0; i < n; i++) {
        if(s != i) {
            d[i] = INT_MAX;
        }
    }
    
    insert(&que, &s);

    while(1) {
        int u;
        while(1) {
            if(isEmpty(&que)) {
                return;
            } 

            extract(&que, &u);
            if(!isAddS[u]) {
                break;
            }
        }

        isAddS[u] = true;

        Node* ptr = list[u].head;
        while(ptr != NULL) {
            int v = ptr->toIdx;
            if(!isAddS[v]) {
                int weight = ptr->weight;
                if(d[u] + weight < d[v]) {
                    d[v] = d[u] + weight;
                }
                insert(&que, &v);
            }
            ptr = ptr->next;
        }
    }

    return;
}

int main() {

    scanf("%d", &n);

    list = new List[n];
    for(int i = 0; i < n; i++) {
        list[i].head = NULL;
    }
    

    for(int i = 0; i < n; i++) {
        int s;
        int deg;

        scanf("%d %d", &s, &deg);
        for(int j = 0; j < deg; j++) {
            int t;
            int w;

            scanf("%d %d", &t, &w);

            addList(s, t, w);
        }
    }

    solve(0);

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