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>
using namespace std;
#define MAX 10005
#define INFTY INT_MAX

struct Node {
    int point;
    int weight;
    Node() {}
    Node(int p, int w) {
        point = p;
        weight = w;
    }
};

bool operator<(Node left, Node right) {
    return (left.weight > right.weight);
}

vector<vector<Node> > vec(MAX);
vector<Node> ve;
priority_queue<Node> pq;
Node node;
int n;

void dijkstra() {
    int d[MAX], color[MAX];
    for (int i = 0; i < n; i++) {
        d[i] = INFTY;
        color[i] = 0;
    }
    d[0] = 0;
    pq.push(Node(0, d[0]));
    while (!pq.empty()) {
        node = pq.top();
        pq.pop();
        int u = node.point;
        color[u] = 1;
        if (d[u] < node.weight)
            continue;
        for (int i = 0; i < vec[u].size(); i++) {
            int v = vec[u][i].point;
            int c = vec[u][i].weight;
            if (d[u] + c < d[v]) {
                d[v] = d[u] + c;
                pq.push(Node(v, d[v]));
            }
        }
    }
    for (int i = 0; i < n; i++) {
        cout << i << " " << d[i] << endl;
    }
}

int main(void) {
    cin >> n;
    int u, k;
    for (int i = 0; i < n; i++) {
        ve.clear();
        cin >> u >> k;
        while (k--) {
            cin >> node.point >> node.weight;
            ve.push_back(node);
        }
        vec[u] = ve;
    }

    dijkstra();
}

C++: #include <iostream>
#include <iomanip>
#include <vector>
#include <stack>
#include <queue>
#include <set>
#include <map>
#include <algorithm>
#include <cstdio>
#include <utility>
#include <string>
#include <cmath>
#include <cstdlib>
#include <cstring>

using namespace std;

typedef uint64_t u64;
typedef int64_t s64;
typedef uint32_t u32;
typedef int32_t s32;
typedef vector<s32> vs32;
typedef vector<u32> vu32;
typedef vector<s64> vs64;
typedef vector<u64> vu64;

const double PI=3.14159265358979323846;

#define MAX(x, y) ((x) < (y) ? (y) : (x))
#define MIN(x, y) ((x) > (y) ? (y) : (x))

#define rep(i, N) for(int i = 0; i < N; ++i)

#define CEIL(x, y) (((x) + (y) - 1) / (y))
#define MOD 1000000007ULL

class Graph
{
public:
    enum
    {
        WHITE = 0,
        GRAY = 1,
        BLACK = 2,
    };

    Graph() {}
    Graph(int n)
    : color(n, WHITE), M(n), d(n, INFTY)
    {}
    ~Graph() {}

    void dijkstra(int s)
    {
        d[s] = 0;
        priority_queue< pair<int, int> > pq;

        pq.push(make_pair(0, s));
        while (!pq.empty())
        {
            pair<int, int> du = pq.top(); pq.pop(); 

            int u = du.second;
            int minv = -du.first;

            color[u] = BLACK;

            if (d[u] < -minv) continue;

            for (auto dv : M[u])
            {
                int v = dv.first;
                int w = dv.second;
                if (color[v] != BLACK && d[v] > d[u] + w)
                {
                    d[v] = d[u] + w;
                    color[v] = GRAY;
                    pq.push(make_pair(-d[v], v));
                }
            }
        }
    }

    static const int INFTY = 1e9;
    vs32 color;
    vector< vector< pair<int, int> > > M;
    vs32 d;
};

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);

    int n;
    cin >> n;

    Graph g(n);

    int u, v;
    int w;
    int c;
    rep (i, n)
    {
        cin >> u >> c;
        rep (j, c)
        {
            cin >> v >> w;
            g.M[u].emplace_back(v, w);
        }
    }

    g.dijkstra(0);
    rep (i, n)
    {
        cout << i << " " << g.d[i] << "\n";
    }
    return 0;
}

C++: #include <iostream>
#include <algorithm>
#include <queue>
using namespace std;
static const int MAX = 10000;
static const int INFTY = (1<<21);
static const int WHITE = 0;
static const int GRAY = 1;
static const int BLACK = 2;

int n;
vector<pair<int, int> > adj[MAX];

void dijkstra();


int main() {
    int k, u, v, c;

    cin >> n;
    for ( int i = 0; i < n; i++ ) {
        cin >> u >> k;
        for ( int j = 0; j < k; j++ ) {
            cin >> v >> c;
            adj[u].push_back(make_pair(v, c));
        }
    }

    dijkstra();

}



void dijkstra() {
    priority_queue<pair<int, int> > PQ;
    int color[MAX];
    int d[MAX];
    for ( int i = 0; i < n; i++) {
        d[i] = INFTY;
        color[i] = WHITE;
    }

    d[0]  = 0;
    PQ.push(make_pair(0, 0));
    color[0] = GRAY;

    while ( !PQ.empty()) {
        pair<int, int> f = PQ.top(); PQ.pop();
        int u = f.second;

        color[u] = BLACK;

        // take the minimum value, ignore if it is not the shortest
        if ( d[u] < f.first * (-1) ) continue;

        for ( int j = 0; j < adj[u].size(); j++ ) {
            int v = adj[u][j].first;
            if (color[v] == BLACK) continue;
            if ( d[v] > d[u] + adj[u][j].second) {
                d[v] = d[u] + adj[u][j].second;
                // multiple (-1) because of priority large value in priority_queue
                PQ.push(make_pair(d[v] * (-1), v));
                color[v] = GRAY;
                }
        }
    }

    for ( int i = 0; i < n; i++ ) {
        cout << i << " " << ( d[i] == INFTY ? -1 : d[i] ) << '\n';
    }
}