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<cstdio>
#include<vector>
#include<queue>
#include<map>
#include<algorithm>
#include<queue>
#include<functional>
using namespace std;
int main(){
	int a;
	int b;
	int s;
	int t;
	vector<int> n[10000];
	int nn[10000];
	vector<int> x[10000];
	priority_queue<pair<int, int>, vector<pair<int, int> >, greater<pair<int, int> > >y;
	int z;
	long long d[10000];
	int e;
	int c[10000];
	int zz;
	pair<int, int>pai;
	for (int i = 0; i < 10000; i++){
		d[i] = 10000000000009;
		c[i] = 0;
	}
	scanf("%d", &a);
	for (int i = 0; i < a; i++){
		scanf("%d %d", &s, &b);
		for (int j = 0; j < b; j++){
			scanf("%d %d", &t, &e);
			n[s].push_back(t);
			nn[s]++;
			x[s].push_back(e);

		}
	}
	d[0] = 0;
	y.push(std::make_pair(d[0], 0));
	for (int i = 0; y.empty() == 0; i++){
		zz = 0;
		for (int j = 0; y.empty() == 0 && zz == 0; j++){
			pai = y.top();
			z = pai.second;
			if (c[z] == 0)zz++;
			else y.pop();
		}
		if (zz == 0)break;
		c[z] = 1;
		for (int j = 0; j < nn[z]; j++){
			if (d[z] + x[z][j] < d[n[z][j]])
			{
				d[n[z][j]] = d[z] + x[z][j];
				y.push(std::make_pair(d[n[z][j]], n[z][j]));
			}
		}
		y.pop();
	}
	for (int i = 0; i<a; i++)printf("%d %lld\n",i,d[i]);
		return 0;
}

C++: #include <iostream>
#include <cmath>
#include <vector>
#include <set>
#include <string>
#include <algorithm>

constexpr int INF = 10000001;

int main() {
    std::ios::sync_with_stdio(false);
    std::cin.tie(0);
    int n, u, k, vv, cc;
    std::cin >> n;
    std::vector<std::vector<int>> v(n), c(n);
    std::vector<int> d(n), p(n);
    std::set<int> v_s, s;
    for (int i=0; i<n; i++) {
        std::cin >> u >> k;
        for (int j=0; j<k; j++) {
            std::cin >> vv >> cc;
            v[u].push_back(vv);
            c[u].push_back(cc);
        }
        d[i] = INF;
        v_s.insert(i);
    }
    d[0] = 0;
    //v_s.erase(0);

    while (not v_s.empty()) {
        int mind=INF+1;
        int minnode;
        auto iter = v_s.begin();
        for (int i=0; i<v_s.size(); i++,iter++) {
            if (d[*iter] < mind) {
                mind = d[*iter];
                minnode = *iter;
            }
        }
        v_s.erase(minnode);
        s.insert(minnode);
        for (int i=0; i<v[minnode].size(); i++) {
            if (v_s.find(v[minnode][i]) != v_s.end() and mind + c[minnode][i] < d[v[minnode][i]]) {
                d[v[minnode][i]] = mind + c[minnode][i];
                p[v[minnode][i]] = minnode;
            }
        }
    }

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

    return 0;
}

C++: ///
// File:  alds1_12_c.cpp
// Author: ymiyamoto
//
// Created on Wed Oct 18 22:36:29 2017
//

#include <cstdint>
#include <iostream>
#include <queue>
#include <vector>

using namespace std;

#define SIZE 10000

struct route_t {
  uint32_t node;
  int64_t weight;

  bool operator<(const route_t &r) const
  {
    return weight > r.weight;
  }
};

static vector<route_t> graph[SIZE];
static int64_t costs[SIZE];
static bool visited[SIZE];
static priority_queue<route_t> q;

static void dikstra()
{
  q.push({0, 0});
  costs[0] = 0;

  while (!q.empty()) {
    route_t r = q.top();
    q.pop();

    if (!visited[r.node]) {
      visited[r.node] = true;
      for (uint32_t i = 0; i < graph[r.node].size(); i++) {
        int64_t cost = graph[r.node][i].weight;
        uint32_t node = graph[r.node][i].node;
        if (cost != -1) {
          if (costs[r.node] + cost < costs[node]) {
            costs[node] = costs[r.node] + cost;
          }
          q.push({node, cost});
        }
      }
    }
  }
}

int32_t main()
{
  uint32_t n;
  cin >> n;

  for (uint32_t i = 0; i < n; i++) {
    costs[i] = INT32_MAX;
  }

  for (uint32_t i = 0; i < n; i++) {
    uint32_t id, k;
    cin >> id >> k;
    for (uint32_t j = 0; j < k; j++) {
      route_t r;
      cin >> r.node >> r.weight;
      graph[id].push_back(r);
    }
  }

  dikstra();

  for (uint32_t i = 0; i < n; i++) {
    cout << i << " " << costs[i] << endl;
  }

  return 0;
}

C++: #include <iostream>
#include <cstdio>
#include <algorithm>
#include <queue>
#include <vector>
using namespace std;

const int NMAX = 10000;
const int AMAX = 9999999;

const int BLACK = 2;
const int GRAY = 1;
const int WHITE = 0;

vector<pair<int, int> > A[NMAX];
int c[NMAX];
int d[NMAX];
int n;

void dijkstra(int s) {
	for (int i = 0; i < n; i++) {
		c[i] = WHITE;
		d[i] = AMAX;
	}

	d[s] = 0;
	c[s] = GRAY;
	priority_queue<pair<int, int> > PQ;
	PQ.push(make_pair(d[s], s));

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

		c[u] = BLACK;

		if (d[u] < minw * (-1)) continue;

		for (int i = 0; i < A[u].size(); i++) {
			int v = A[u][i].first;
			int w = A[u][i].second;
			if (c[v] == BLACK) continue;

			if (d[v] > d[u] + w) {
				d[v] = d[u] + w;
				PQ.push(make_pair(d[v] * (-1), v));
				c[v] = GRAY;
			}
		}
	}
}

int main() {
	scanf("%d", &n);

	for (int i = 0; i < n; i++) {
		int u, k;
		scanf("%d %d", &u, &k);

		for (int j = 0; j < k; j++) {
			int v, c;
			scanf("%d %d", &v, &c);
			A[u].push_back(make_pair(v, c));
		}
	}

	dijkstra(0);

	for (int i = 0; i < n; i++) {
		printf("%d %d\n", i, d[i]);
	}

	return 0;
}