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 <sstream>
#include <cstdio>
#include <cmath>
#include <cctype>
#include <string>
#include <vector>
#include <list>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <algorithm>
#include <functional>

using namespace std;
using ll = long long int;
#define rep(i,n) for(int i = 0; i < n; i++)
#define FOR(i, a, b)  for(int i = (a); i < (b) ; i++)

#define pb push_back
#define SORT(v,n) sort(v, v+n)
#define ALL(x) (x).begin(),(x).end()
#define debug(x) cerr << #x << ": " << x << '\n'
#define elif else if
#define itn ll
#define int ll
const int INF = 100100100;
const int MOD = (int)1e9 + 7;
const double EPS = 1e-9;
///                →,↑,←,↓,↗,↖,↙,↘
int dx[8] = { 1, 0, -1, 0, 1, -1, -1, 1 };
int dy[8] = { 0, 1, 0, -1, 1, 1, -1, -1 };

typedef vector<vector<int>> vvi;
typedef vector<vector<vector<int>>> vvvi;

static const int MAX = 100;
static const int White = 0;
static const int Gray = 1;
static const int Black = 2;


int n, M[MAX][MAX];
int d[MAX], p[MAX],color[MAX];

void dijkstra() {
	rep(i, n) {
		color[i] = White;
		d[i] = INF;
		p[i] = -1;
	}
	d[0] = 0;
	while (true) {
		int u, mincost = INF;
		rep(i, n) {
			if (color[i] != Black and d[i] < mincost) {
				u = i;
				mincost = d[i];
			}
		}
		if (mincost == INF) break;
		color[u]  = Black;
		int v;
		rep(v, n) {
			if (color[v] != Black and M[u][v] != INF) {
				if (d[u] + M[u][v] < d[v]) {
					d[v] = d[u] + M[u][v];
					p[v] = u;
					color[v] = Gray;
				}
			}
		}
	}
	rep(i, n) {
		cout << i << ' ' << d[i] << '\n';
	}
}

signed main() {
	ios::sync_with_stdio(false);
	int i, j, k;
	cin >> n;
	rep(i, n) {
		rep(j, n) {
			M[i][j] = INF;
		}
	}
	rep(i, n) {
		int u, k;
		cin >> u >> k;
		rep(j, k) {
			int c,v;
			cin >> v >> c;
			M[u][v] = c;
		}
	}
	dijkstra();
	return 0;
}

C++: #include<iostream>
#include<vector>
#include<climits>
#include<cmath>
#include<queue>
 
using namespace std;
 
struct edge {
  int to, cost;
};
 
struct state {
  int pos, cost;
 
  bool operator < (const state& s) const {
    return cost > s.cost;
  }
};
 
int main() {
  int n; cin >> n;
 
  vector< vector<edge> > edges(n, vector<edge>());
  for (int i = 0; i < n; i++) {
    int u, k; cin >> u >> k;
 
    while (k--) {
      int to, cost; cin >> to >> cost;
      edges[u].push_back((edge) { to, cost});
    }
  }
 
  priority_queue<state> queue;
  vector<int> costs(n, INT_MAX);
  costs[0] = 0;
  queue.push((state) {0, 0});
 
  while(!queue.empty()) {
    const state now = queue.top();
    queue.pop();
 
    
     
    for (int i = 0; i < edges[now.pos].size(); i++) {
      state nex = now;
      nex.pos = edges[now.pos][i].to;
      nex.cost += edges[now.pos][i].cost;
      if (costs[nex.pos] > nex.cost) {
        costs[nex.pos] = nex.cost;
        queue.push(nex);
      }
    }
  }
 
  for (int i = 0; i < n; i++)
    cout << i << " " << costs[i] << endl;
   
  return 0;
}

C++: #include <iostream>
#include <queue>
#include <vector>

using namespace std;

#define INF (10000001)

typedef pair<int, int> Edge;

int main()
{
    priority_queue<Edge,vector<Edge>,greater<Edge> > pq;
    vector<vector<Edge> > e;
    vector<int> d;
    Edge etemp;
    int n,u,k,v,c;
    cin >> n;
    e.resize(n);
    d.resize(n);
    for(int i=0; i<n; ++i) {
        cin >> u >> k;
        for(int j=0; j<k; ++j) {
            cin >> v >> c;
            e[u].push_back(Edge{c,v});
        }
        d[u]=INF;
    }

    d[0]=0;
    for(auto x : e[0]) {
        pq.push(x);
    }
    while(!pq.empty()) {
        etemp=pq.top(); pq.pop();
        v=etemp.second;
        c=etemp.first;
        if(d[v]<c) continue;
        d[v]=c;
        for(auto x : e[v]) {
            if(d[x.second]<=c+x.first) continue;
            pq.push(Edge{c+x.first,x.second});
        }
    }
    for(int i=0; i<n; ++i) {
        cout << i << " " << d[i] << endl;
    }
    return 0;
}