Go: package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

const BIG_COST = 200000

type Path struct {
	node int
	cost int
}

func main() {
	sc := bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)

	nNodes := scanInt(sc)

	// 各頂点につながる頂点一覧を得るための隣接リスト
	graph := make([][]Path, nNodes)

	for i := 0; i < nNodes; i++ {
		u := scanInt(sc)
		k := scanInt(sc)
		graph[i] = make([]Path, k)
		for d := 0; d < k; d++ {
			graph[u][d] = Path{
				node: scanInt(sc),
				cost: scanInt(sc),
			}
		}
	}

	// 0 から各頂点への最小コストを保存する配列
	minCosts := make([]int, nNodes)

	minCosts[0] = 0
	for i := 1; i < nNodes; i++ {
		minCosts[i] = BIG_COST
	}

	// 各頂点が調査済みかどうかを保持する配列
	checked := make([]bool, nNodes)

	// 最小コストのパスを高速に取得するためのヒープ。
	// コストが小さいものほどルートに来るようにする。
	heap := NewHeap(func(a, b Path) bool {
		return a.cost < b.cost
	})

	heap.insert(Path{node: 0, cost: 0})
	for heap.size > 0 {
		u := heap.extractMax()

		// 隣接行列を使っていた時とは違い、ヒープには
		// 同じノードへのパスが複数含まれうる。そのため既によりコストの低い
		// パスが見つかっている場合は無視する。
		if minCosts[u.node] < u.cost {
			continue
		}

		checked[u.node] = true

		for _, v := range graph[u.node] {
			cost := v.cost + u.cost
			if !checked[v.node] && cost < minCosts[v.node] {
				minCosts[v.node] = cost
				heap.insert(Path{node: v.node, cost: cost})
			}
		}
	}

	w := bufio.NewWriter(os.Stdout)
	for i, cost := range minCosts {
		fmt.Fprintf(w, "%d %d\n", i, cost)
	}
	w.Flush()
}

func scanInt(sc *bufio.Scanner) int {
	sc.Scan()
	v, _ := strconv.Atoi(sc.Text())
	return v
}

// --- From ALDS1_9_C: Priority Queue

type Heap struct {
	size   int
	heap   []Path
	isHigh func(a, b Path) bool
}

func NewHeap(isHigh func(a, b Path) bool) Heap {
	heap := make([]Path, 1) // 先頭は不使用
	return Heap{size: 0, heap: heap, isHigh: isHigh}
}

func (h *Heap) insert(v Path) {
	h.size += 1
	if h.size > len(h.heap)-1 {
		h.heap = append(h.heap, v)
	} else {
		h.heap[h.size] = v
	}

	for i := h.size; i > 1; {
		parent := i / 2
		if h.isHigh(h.heap[parent], h.heap[i]) {
			break
		}
		h.heap[i], h.heap[parent] = h.heap[parent], h.heap[i]
		i = parent
	}
}

func (h *Heap) extractMax() Path {
	if h.size <= 0 {
		panic("cannot extract from empty heap")
	}

	max := h.heap[1]
	h.heap[1] = h.heap[h.size]
	h.size -= 1
	h.maxHeapify(1)

	return max
}

func (h *Heap) maxHeapify(idx int) {
	left := idx * 2
	right := left + 1
	largest := idx

	if left <= h.size {
		if h.isHigh(h.heap[left], h.heap[idx]) {
			largest = left
		}
		if right <= h.size && h.isHigh(h.heap[right], h.heap[largest]) {
			largest = right
		}
	}

	if largest != idx {
		h.heap[idx], h.heap[largest] = h.heap[largest], h.heap[idx]
		h.maxHeapify(largest)
	}
}

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

typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll,ll> P;
typedef pair<ll,P>  PP;
typedef vector<ll> Vector;
typedef vector<Vector> DVector;
typedef priority_queue<P, vector<P>, greater<P>> PQueue;

#define fi          first
#define se          second
#define sfi         se.fi
#define sse         se.se
#define pb          push_back
#define INF         INT_MAX
#define MOD         1000000007
#define bcnt        __builtin_popcount
#define all(x)      (x).begin(),(x).end()
#define uni(x)      x.erase(unique(all(x)),x.end())
#define ub(x,y)     (upper_bound(all(x),y)-x.begin())
#define lb(x,y)     (lower_bound(all(x),y)-x.begin())
#define rep(i,n)    repl(i,0,n-1)
#define usort(x)    sort(all(x))
#define dsort(x)    sort(all(x),greater<ll>())
#define mkp(x,y)    make_pair(x,y)
#define mmax(x,y)   (x>y?x:y)
#define mmin(x,y)   (x<y?x:y)
#define maxch(x,y)  x=mmax(x,y)
#define minch(x,y)  x=mmin(x,y)
#define exist(x,y)  (find(all(x),y)!=x.end())
#define each(itr,v) for(auto itr:v)
#define repl(i,a,b) for(ll i=(ll)(a);i<=(ll)(b);i++)
vector<vector<P>> costs;
ll n;
Vector mincost;
void djk(ll start){
  PQueue pq;
  mincost.resize(n,INF);
  mincost[start] = 0;
  pq.push({0,start});
  while(pq.size()){
    P state = pq.top();pq.pop();
    if(mincost[state.se] < state.fi)continue;
    each(itr,costs[state.se])if(mincost[itr.fi] > mincost[state.se] + itr.se){
      mincost[itr.fi] = mincost[state.se] + itr.se;
      pq.push({mincost[itr.fi],itr.fi});
    }
  }
}

int main(){
  cin.sync_with_stdio(false);
  cin >> n;
  costs.resize(n);
  rep(i,n){
    ll u,k;
    cin >> u >> k;
    rep(j,k){
      ll v,c;
      cin >> v >> c;
      costs[u].pb({v,c});
    }
  }
  djk(0);
  rep(i,n)cout << i << " " << mincost[i] << endl;
}

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

//def
#define debug(x) cout << #x << ": " << x << '\n'
#define out(x) cout << x << '\n'
#define repeat(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
#define revrepeat(i, a, b) for (int i = (int)(b)-1; i >= (int)(a); i--)
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
#define revrep(i, n) for (int i = (int)(n)-1; i >= 0; i--)
#define foreach(e, v) for (auto &e : v)
#define all(x) (x).begin(), (x).end()
#define CYES cout << "Yes" << endl
#define CNO cout << "No" << endl
#define SPC(x) cout << fixed << setprecision(x)
#define ZERO(a) memset(a, 0, sizeof(a))
#define MINUS(a) memset(a, 0xff, sizeof(a))

typedef long long ll;
typedef long double ld;
typedef vector<int> vi;
typedef vector<vector<int>> vii;
typedef vector<ll> vl;
typedef vector<vector<ll>> vll;
typedef pair<int, int> P;
constexpr int MOD = 1e9 + 7;
constexpr int INF = __INT_MAX__;               // 2^31 - 1
constexpr long long INFLL = __LONG_LONG_MAX__; // 2^61 - 1
constexpr int MAX_N = 1e5 + 5;
constexpr double PI = acos(-1);

int pre[MAX_N];
long long d[MAX_N];
bool seen[MAX_N];
struct Edge {
    int to;
    long long cost;
};
// require: cost value is positive
// O(nlog|v|)
void dijkstra(int s, vector<vector<Edge>> &graph) {
    fill(pre, pre + MAX_N, -1);
    fill(seen, seen + MAX_N, false);
    fill(d, d + MAX_N, INF);

    auto comPair = [](const P one, const P two) {
        return one.second > two.second;
    };
    // que(v, distance)
    priority_queue<P, vector<P>, decltype(comPair)> que(comPair);
    que.emplace(0, 0);
    d[0] = 0;
    seen[0] = true;

    while (!que.empty()) {
        int u = que.top().first;
        que.pop();

        for (auto e : graph[u]) {
            int v = e.to;
            int c = e.cost;

            if (not seen[v] and d[v] > d[u] + c) {
                d[v] = d[u] + c;
                pre[v] = u;
                que.emplace(v, d[v]);
            }
        }
        seen[u] = true;
    }
};

int main() {
    int n;
    cin >> n;
    vector<vector<Edge>> graph(n);
    int k;
    rep(i, n) {
        cin >> k;
        cin >> k;
        rep(j, k) {
            Edge e;
            cin >> e.to >> e.cost;
            graph[i].push_back(e);
        }
    }
    dijkstra(0, graph);
    rep(i, n) {
        cout << i << ' ' << d[i] << endl;
    }
}