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 <climits>
#include <functional>
#include <iostream>
#include <queue>
#include <utility>
#include <vector>
using namespace std;

int main() {
	int n, u, k, v, c;
	cin >> n;
	vector<vector<pair<int, int>>> a(n);
	for (int i = 0; i < n; ++i) {
		cin >> u >> k;
		for (int j = 0; j < k; ++j) {
			cin >> v >> c;
			a[u].emplace_back(v, c);
		}
	}
	priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> b;
	b.emplace(0, 0);
	vector<bool> d(n);
	vector<int> e(n, INT_MAX);
	e[0] = 0;
	while (!b.empty()) {
		pair<int, int> f = b.top();
		b.pop();
		d[f.second] = true;
		for (int i = 0; i < a[f.second].size(); ++i) {
			if (!d[a[f.second][i].first]) {
				if (a[f.second][i].second + e[f.second] < e[a[f.second][i].first]) {
					e[a[f.second][i].first] = a[f.second][i].second + e[f.second];
					b.emplace(e[a[f.second][i].first], a[f.second][i].first);
				}
			}
		}
	}
	for (int i = 0; i < n; ++i) cout << i << ' ' << e[i] << endl;
}

C++: #include <iostream>
#include <cstdlib>
using namespace std;

#define INF 100000000

typedef struct state {
  int pos, cost;
} state;

state A[2000001];
int N = 0;

int parent (int i) { return i/2;}
int left ( int i) {return i * 2;}
int right ( int i ) {return i * 2 + 1;}

void swap( state* a, state* b ) {
  state tmp = *a;
  *a = *b;
  *b = tmp;
}

void minHeapify ( int i ) {
  int l = left(i);
  int r = right(i);
  int small;

  if ( l <= N && A[l].cost < A[i].cost ) small = l;
  else small = i;

  if ( r <= N && A[r].cost < A[small].cost ) small = r;

  if ( small != i ) {
    swap ( &A[i], &A[small] );
    minHeapify(small);
  }
}

state heapExtractMin() {
  if ( N < 1 ) return (state) {0,0};
  state min = A[1];
  A[1] = A[N];
  N--;
  minHeapify(1);
  return min;
}

void heapIncreaseKey( int i , state key ) {
  if ( key.cost > A[i].cost) return;

  A[i] = key;
  while ( i > 1 && A[parent(i)].cost > A[i].cost ) {
    swap( &A[i], &A[parent(i)]);
    i = parent(i);
  }
}

void minHeapInsert( state key ) {
  N++;
  A[N] = (state) { INF, INF };
  heapIncreaseKey(N, key);
}

typedef struct edge{
  int to,cost;
} edge;

edge* G[10000];
int size[10000];
int n;
int d[10000];
edge e;
state s;

int main() {
  int a,b;
  cin >> n;
  for ( int i = 0; i < n; i++ ) {
    cin >> a >> b;
    G[a] = (struct edge*)malloc( sizeof(edge )*b );
    size[a] = b;
    for ( int j = 0; j < b; j++ ) {
      cin >> G[a][j].to >> G[a][j].cost;
    }
    d[i] = INF;
  }
  d[0] = 0;
  minHeapInsert ( (state{0,0} ) );
  while(N!=0) {
    s = heapExtractMin();
    if ( s.cost > d[s.pos]) continue;
    for ( int i = 0; i < size[s.pos]; i++ ) {
      e = G[s.pos][i];
      if ( d[e.to] <= d[s.pos] + e.cost ) continue;
      d[e.to] = d[s.pos] + e.cost;
      minHeapInsert((state){e.to,d[e.to]});
    }
  }
  for ( int i = 0; i < n; i++ ) {
    cout << i << " " << d[i] << endl;
  }
}

C++: #include <algorithm>
#include <iostream>
#include <queue>
using namespace std;
static const int MAX = 10000;
static const int INFTY = (1 << 20);
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() {
  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;

    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;
        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]) << endl;
  }
}

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();

  return 0;
}

C++: #include<stdio.h>
#include<algorithm>
#include<queue>
#include<vector>
#include<string.h>
using namespace std;
#define NIL -2000000001
#define INFTY 2000000001
#define MAX 100001
#define WHITE 0
#define GRAY 1
#define BLACK 2

int n = 0;
int color[MAX], d[MAX];
vector<pair<int, int> > G[MAX];


void sp() {
  for ( int i = 0; i < n; i++ ) {
    color[i] = WHITE;
    d[i] = INFTY;
  }
  priority_queue<pair<int, int> > PQ;
  PQ.push(make_pair(0, 0));
  d[0] = 0;
  color[0] = GRAY;

  while (true) {
    int mincost;
    int u; //訪問する頂点

    // for (int i = 0; i < n; i++) {
    //   if (color[i] != BLACK && d[i] < mincost) {
    //     mincost = d[i];
    //     u = i;
    //   }
    // }

    pair<int, int> f = PQ.top();
    PQ.pop();
    u = f.second;
    mincost = (-1)*f.first;

    color[u] = BLACK;

    // u周りの頂点vの情報を入れる
    for (int i = 0; i < G[u].size(); i++) {
      int v = G[u][i].first;
      if (color[v] != BLACK && d[u]+G[u][i].second < d[v]) {
        d[v] = d[u]+G[u][i].second;
        color[v] = GRAY;
        PQ.push(make_pair(-d[v], v));
      }
    }
    if (PQ.empty()) break;
  }

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

int main() {
  scanf("%d", &n);
  for ( int i = 0; i < n; i++ ) {
    int stash, k;
    scanf("%d %d", &stash, &k);
    for ( int j = 0; j < k; j++) {
      int v;
      scanf("%d", &v);
      int g;
      scanf("%d", &g);
      G[i].push_back(make_pair(v, g));
    }
  }

  sp();

  return 0;
}