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 <cassert>
#include <climits>
#include <algorithm>
#include <iostream>
#include <vector>
#include <list>
#include <string>
#include <queue>
#include <set>

/*
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while(????????????????????????????????§)
    list = ???????????????.Get????°?????????????????????????
    for(list)
        ?????????????????????
*/

class TVertex;
struct TPath
{
    int Cost;
    TVertex* Target;
    TPath(TVertex* ATarget, int ACost)
     : Target(ATarget), Cost(ACost) {}
    bool operator<(const TPath& Right)const
    {
        if(this->Cost  < 0) return false;
        if(Right.Cost < 0) return true;
        return this->Cost < Right.Cost;
    }
    bool operator>(const TPath& Right)const
    {
        return !((*this) < Right);
    }
};
class TVertex
{
    int FIndex;
    std::priority_queue<TPath, std::vector<TPath>, std::greater<TPath> > FList;
    int FDistance;

public:
    TVertex(int Index)
     : FIndex(Index), FDistance(INT_MAX)
    {}
    void Reserve(int Size)
    {
        // FList.reserve(Size);
    }
    void AddPath(const TPath& Path)
    {
        FList.push(Path);
    }
    void SortPath()
    {
        // std::sort(FList.begin(), FList.end(), Compare);
    }
    void PrintDistance(std::ostream& out)const
    {
        out << FIndex << " " << FDistance << std::endl;
    }
    int GetMinCostPath()const
    {
        if(FList.empty()) return INT_MAX;
        return FList.top().Cost + FDistance;
    }
    void PickupMinCostPath(int MinCost, std::list<TPath>& List)
    {
        while(FList.empty() == false && FList.top().Cost + FDistance == MinCost){
            List.push_back(TPath(FList.top().Target, FList.top().Cost + FDistance));
            FList.pop();
        }
    }
    bool SetDistance(int Distance)
    {
        if(FDistance < Distance) return false;
        FDistance = Distance;
        return true;
    }
};
class TGraph
{
    std::vector<TVertex*> FTable;
    std::set<TVertex*> FShortest;
    void Init(int n)
    {
        assert(n > 0);
        FTable.resize(n);
        for(int i = 0; i < n; ++i){
            FTable[i] = new TVertex(i);
        }
    }
    static bool CompareMinCost(const TVertex* Left, const TVertex* Right)
    {
        return Left->GetMinCostPath() < Right->GetMinCostPath();
    }
    void AddShortest(TVertex* Vertex, int Distance)
    {
        if(Vertex->SetDistance(Distance)){
            FShortest.insert(Vertex);
        }
    }
    std::list<TPath> PickupMinCostPath(int MinCost)
    {
        std::list<TPath> Result;
        for(std::set<TVertex*>::const_iterator It = FShortest.begin();
            It != FShortest.end(); ++It)
        {
            (*It)->PickupMinCostPath(MinCost, Result);
        }
        return Result;
    }
    void SetShortest(const std::list<TPath>& MinCostPathList)
    {
        for(std::list<TPath>::const_iterator It = MinCostPathList.begin();
            It != MinCostPathList.end(); ++It)
        {
            AddShortest(It->Target, It->Cost);
        }
    }
public:
    TGraph(int n)
    {
        Init(n);
    }
    void SetupVertex(std::istream& in)
    {
        int Index;
        in >> Index;
        assert(Index >= 0);
        assert(Index < FTable.size());
        int k;
        in >> k;
        FTable[Index]->Reserve(k);
        for(int i = 0; i < k; ++i){
            int v, c;
            in >> v >> c;
            FTable[Index]->AddPath(TPath(FTable[v], c));
        }
        FTable[Index]->SortPath();
    }
    void SearchShortest()
    {
        FTable[0]->SetDistance(0);
        FShortest.insert(FTable[0]);
        while(FShortest.size() != FTable.size()){
            int MinCost = (*std::min_element(FShortest.begin(), FShortest.end(), CompareMinCost))->GetMinCostPath();
            std::list<TPath> PathList = PickupMinCostPath(MinCost);
            SetShortest(PathList);
        }
    }
    void PrintDistance(std::ostream& out)
    {
        for(int i = 0; i < FTable.size(); ++i){
            FTable[i]->PrintDistance(out);
        }
    }
};

int main()
{
    std::cin.tie(0);
    std::ios::sync_with_stdio(false);
    int n;
    std::cin >> n;
    TGraph Graph(n);
    for(int i = 0; i < n; ++i){
        Graph.SetupVertex(std::cin);
    }
    Graph.SearchShortest();
    Graph.PrintDistance(std::cout);
    return 0;
    
}