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>
#define INF 1e9
using namespace std;
typedef pair<uint32_t,uint32_t> P;

int bitSearchReverse(uint32_t x){
    if(x==0)return -1;
    return 31-__builtin_clz(x);
}
struct RadixHeap{
    vector<P>v[33];
    uint32_t last,sz;
    RadixHeap(){
        last=sz=0;
    }
    void push(P p){
        assert(last<=p.first);
        sz++;
        v[bitSearchReverse(p.first^last)+1].push_back({p.first,p.second});
    }
    P top(){
        return pop(false);
    }
    P pop(bool f=true){
        assert(sz);
        if(!v[0].size()){
            int i=1;
            while(!v[i].size())++i;
            last=min_element(v[i].begin(),v[i].end())->first;
            for(P p:v[i])v[bitSearchReverse(p.first^last)+1].push_back(p);
            v[i].clear();
        }
        P r=v[0].back();
        if(f){
            sz--;
            v[0].pop_back();
        }
        return r;
    }
    int size(){
        return sz;
    }
    bool empty(){
        return sz==0;
    }
    void clear(){
        last=sz=0;
        for(auto a:v)a.clear();
    }
};
struct Graph{
    Graph(int n):E(n),d(n){}
    vector<vector<P>>E;
    vector<uint32_t>d;
    void add_edge(int a,int b,uint32_t c){
        E[a].emplace_back(b,c);
    }
    void dijkstra(int s){
        RadixHeap H;
        fill(d.begin(),d.end(),INF);
        H.push({d[s]=0,s});
        while(H.size()){
            P e=H.top();H.pop();
            if(e.first>d[e.second])continue;
            for(P& a:E[e.second]){
                uint32_t x=a.first,y=a.second+e.first;
                if(y<d[x])d[x]=y,H.push({y,x});
            }
        }
    }
};

main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    int N;
    cin>>N;
    Graph G(N);
    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;
            G.add_edge(u,v,c);
        }
    }
    G.dijkstra(0);
    for(int i=0;i<N;++i)
        cout<<i<<' '<<G.d[i]<<endl;
}

/***************************************

referred
https://github.com/yosupo06/Algorithm/blob/master/datastructure/buf/RadixHeap.h

****************************************/

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

using namespace std;
const int INF = 1e18;

struct edge
{
    int to;
    int cost;
};
using Graph = vector<vector<edge>>;

#define WHITE 0
#define GRAY 1
#define BLACK 2

int n;
Graph G;

void dijkstra(int start)
{
    int seen[10010];
    int dist[10010];

    priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
    for (int i = 0; i < n; i++)
    {
        seen[i] = (i == start) ? GRAY : WHITE;
        dist[i] = (i == start) ? 0 : INF;
        pq.push(make_pair(dist[i], i));
    }

    while (!pq.empty())
    {
        auto now = pq.top();
        pq.pop();
        int u = now.second;
        int distU = now.first;

        seen[u] = BLACK;

        for (auto ne : G[u])
        {
            int v = ne.to;
            int cv = ne.cost;
            if (dist[u] + cv < dist[v])
            {
                dist[v] = dist[u] + cv;
                pq.push(make_pair(dist[v], v));
                seen[v] = GRAY;
            }
        }
    }

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

void solve()
{

    // remove the bottom 3 lines when you submit this code.
    std::ifstream in("sample.txt");
    std::cin.rdbuf(in.rdbuf());

    cin.tie(0);
    ios::sync_with_stdio(false);

    cin >> n;
    G.resize(n);

    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;
            G[u].push_back((edge){v, c});
        }
    }

    dijkstra(0);
}

signed main()
{
    solve();
    return 0;
}

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

using namespace std;

typedef pair<int,int> P;

struct edge
{
    int to,cost;
    edge(int _to=0,int _cost=0)
    {
        to=_to;cost=_cost;
    }
};

int n;
vector<edge> G[10010];

int d[10010];
const int INF=1e9+7;

void dijkstra(int s)
{
    fill(d,d+n,INF);

    d[s]=0;
    priority_queue<P,vector<P>,greater<P> > q;
    q.push(P(0,s));

    while(!q.empty())
    {
        P tmp=q.top();q.pop();
        int v=tmp.second;
        if(d[v]<tmp.first) continue;
        for(int i=0;i<G[v].size();i++)
        {
            edge e=G[v][i];
            if(d[e.to]>d[v]+e.cost)
            {
                d[e.to]=d[v]+e.cost;
                q.push(P(d[e.to],e.to));
            }
        }
    }
}

int main()
{

    ios::sync_with_stdio(false);
    cin.tie(0);cout.tie(0);
    while(cin>>n)
    {
        int a,b,c,dd;
        for(int i=0;i<n;i++)
        {
            G[i].clear();
            cin>>a>>b;
            for(int j=0;j<b;j++)
            {
                cin>>c>>dd;
                G[a].push_back(edge(c,dd));
            }
        }

        dijkstra(0);

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



    return 0;
}