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>
#include <algorithm>
#include <cmath>
#include <climits>
#include <string>
#include <vector>
#include <utility>
#include <functional>
#include <stack>
#include <queue>
#include <map>
#include <set>
#include <cassert>

using namespace std;

typedef long long ll;
typedef pair<ll, ll> P;

const ll MOD = ll(1e9) + 7;
const ll INF = LLONG_MAX;
const ll MAX_N = ll(1e5) + 5;
const double EPS = 10e-8;
const double PI = 3.14159265359;

#define REP(i, n) for (ll i = 0; i < n; i++)
#define REPR(i, n) for (ll i = n; i >= 0; i--)
#define FOR(i, m, n) for (ll i = m; i < n; i++)

int dx[] = {1, 0, -1, 0}, dy[] = {0, 1, 0, -1};

struct UF {
    static const int MAX_N = 100000;
    int p[MAX_N];
    int r[MAX_N];

    void init(int n) {
        REP(i, n) {
            p[i] = i;
            r[i] = 0;
        }
    }
    int find(int x) {
        if (p[x] == x) return x;
        return p[x] = find(p[x]);
    }
    void unite(int x, int y) {
        x = find(x);
        y = find(y);
        if (x == y) return;
        if (r[x] < r[y]) swap(x, y);
        if (r[x] == r[y]) r[x]++;
        p[y] = x;
    }
    bool same(int x, int y) { return find(x) == find(y); }
};

ll n, d[100000];
vector<P> g[100000];

void dijkstra(ll s) {
    fill(d, d + n, INF);
    d[s] = 0;
    priority_queue<P> que;
    que.push({0, s});
    while (!que.empty()) {
        P p = que.top();
        que.pop();
        ll u = p.second;
        if (p.first > d[u]) continue;
        REP(i, g[u].size()) {
            ll v = g[u][i].first, cost = g[u][i].second;
            if (d[v] > d[u] + cost) {
                d[v] = d[u] + cost;
                que.push({d[v], v});
            }
        }
    }
}

int main() {
    cin >> n;
    REP(i, n) {
        ll from, k;
        cin >> from >> k;
        REP(j, k) {
            ll to, c;
            cin >> to >> c;
            g[from].push_back({to, c});
        }
    }
    dijkstra(0);
    REP(i, n) printf("%ld %ld",i,d[i]);
    return 0;
}

C++: #include <iostream>
#include <algorithm>
#include <climits>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>

using namespace std;

int n;
vector<pair<int, int> > es[10001];
vector<int> d(10001);
vector<int> c(10001);

bool cmp(pair<int, int> a, pair<int, int> b) {
    return a.first < b.first;
}

priority_queue<pair<int, int>, vector<pair<int, int> >, greater<pair<int, int> > > q;

int MX = INT_MAX / 3;

void dijkstra() {
    for (int i = 0; i < n; ++i) {
        d[i] = MX;
        c[i] = 0;
    }
    q.push(make_pair(0, 0));
    d[0] = 0;

    while(!q.empty()) {
        auto next = q.top(); q.pop();
        if(next.first > d[next.second]) continue;

        c[next.second] = 1;
        for (auto v : es[next.second]) {
            if(d[next.second] + v.first < d[v.second] && c[v.second] == 0) {
                d[v.second] = d[next.second] + v.first;
                q.push(make_pair(d[v.second], v.second));
            }
        }
    }

}

int main() {
    cin >> 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;
            es[i].push_back(make_pair(c, v));
        }
    }
    dijkstra();

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

    return 0;
}

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

typedef pair<int, int> PII;
#define fi first
#define se second

const int N=10005;
vector<PII> g[N];
int dist[N];
bool vis[N];
int n;

void dijkstra(){
    dist[0]=0;
    priority_queue<PII, vector<PII>, greater<PII>> q;
    q.push({0, 0});
    while(!q.empty()){
        int node=q.top().se;
        q.pop();
        if(vis[node]) continue;
        vis[node]=true;
        for(auto &e: g[node]){
            int v=e.fi;
            int w=e.se;
            if(dist[v]>dist[node]+w){
                dist[v]=dist[node]+w;
                q.push({dist[v], v});
            }
        }
    }
}

int main(){
    memset(dist, 0x3f, sizeof dist);
    memset(vis, 0x00, sizeof vis);
    cin>>n;
    for(int i=0; i<n; ++i){
        int u, k;
        cin>>u>>k;
        for(int j=0; j<k; ++j){
            int v, w;
            cin>>v>>w;
            g[u].push_back({v, w});
        }
    }
    
    dijkstra();
    for(int i=0; i<n; ++i) cout<<i<<" "<<dist[i]<<endl;
    
    return 0;
}