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;

namespace dijkstra_n {
template<class W>
struct Edge {
	using type = Edge<W>;
	int to;
	W w;
	template<class... Args> Edge(int t, Args... args) : to(t), w(args...) {}
	inline bool operator<(const Edge& rhs) const { return w < rhs.w; }
	inline bool operator>(const type& rhs) const { return rhs < *this; }
	inline bool operator>=(const type& rhs) const { return !(*this < rhs); }
	inline bool operator<=(const type& rhs) const { return !(rhs < *this); }
	inline bool operator==(const type& rhs) const { return !(*this < rhs) && !(rhs < *this); }
	inline bool operator!=(const type& rhs) const { return (*this < rhs) || (rhs < *this); }
};
template<class W>
struct Edges : private vector<vector<Edge<W>>> {
	using type = vector<vector<Edge<W>>>;
	template<class... Args> Edges(Args... args) : type(args...) {}
	template<class... Args> void add_edge(int u, int v, Args... args) {
		(*this)[u].emplace_back(v, args...);
	}
	using type::begin; using type::end; using type::rbegin; using type::rend;
	using type::cbegin; using type::cend; using type::crbegin; using type::crend;
	using type::size; using type::operator[]; using type::at; using type::back; using type::front;
	using type::reserve; using type::resize; using type::assign; using type::shrink_to_fit;
	using type::clear; using type::erase; using type::insert; using type::swap; 
	using type::push_back; using type::pop_back; using type::emplace_back; using type::empty;
};
template<class W>
struct Graph {
	const int sz;
	Edges<W> e;
	Graph(int n) : sz(n), e(sz) {}
	template<class... Args> void add_edge(int u, int v, Args... args) {
		e.add_edge(u, v, args...);
	}
	int size() {
		return sz;
	}
};
template<class W, class T = W>
struct Graph_D : public Graph<W> {
	vector<T> dist;
	Graph_D(int n) : Graph<W>(n), dist(n) {}
};
template<class W, class T>
void Dijkstra(Graph_D<W, T>& g, int start, T INF_COST) {
	auto& dist = g.dist;
	auto& e = g.e;
	for (auto& ww : dist) ww = INF_COST;
	using Q_T = pair<T, int>;
	priority_queue<Q_T, vector<Q_T>, greater<>> q;
	q.emplace(0, start);
	while (!q.empty()) {
		auto a = q.top();
		q.pop();
		if (a.first >= dist[a.second]) continue;
		dist[a.second] = a.first;
	for (auto& p : e[a.second]) {
			if (p.w == INF_COST) continue;
			if (a.first + p.w < dist[p.to]) q.emplace(a.first + p.w, p.to);
		}
	}
}
}
using dijkstra_n::Dijkstra;
template<class T, class U = T> using graph = dijkstra_n::Graph_D<T, U>;

int main() {
    int n; cin >> n;
    graph<int> g(n);
    for (int i = 0; i < n; i++) {
        int v, k; cin >> v >> k;
        while (k--) {
            int u, c; cin >> u >> c;
            g.add_edge(v, u, c);
        }
    }
    Dijkstra(g, 0, INT_MAX);
    for (int i = 0; i < n; i++) {
        cout << i << " " << g.dist[i] << endl;
    }
}

C++: #include <cassert>
#include <climits>
#include <algorithm>
#include <iostream>
#include <vector>
#include <list>
#include <string>


class TVertex;
struct TPath
{
    int Cost;
    TVertex* Target;
    TPath(TVertex* ATarget, int ACost)
     : Target(ATarget), Cost(ACost) {}
};
bool Compare(const TPath& Left, const TPath& Right)
{
    if(Left.Cost  < 0) return false;
    if(Right.Cost < 0) return true;
    return Left.Cost < Right.Cost;
}
class TVertex
{
    int FIndex;
    std::vector<TPath> FList;
    int FDistance;

public:
    TVertex(int Index)
     : FIndex(Index), FDistance(INT_MAX)
    {}
    void Reserve(int Size)
    {
        FList.reserve(Size);
    }
    void AddPath(const TPath& Path)
    {
        FList.push_back(Path);
    }
    void SortPath()
    {
        std::sort(FList.begin(), FList.end(), Compare);
    }
    void PrintDistance(std::ostream& out)const
    {
        out << FIndex << " " << FDistance << std::endl;
    }
    void BreadthFirstSearch(int Distance)
    {
        if(FDistance <= Distance) return;
        FDistance = Distance;
        for(std::vector<TPath>::iterator It = FList.begin(); It != FList.end(); ++It){
            It->Target->BreadthFirstSearch(Distance + It->Cost);
        }
    }
};
class TGraph
{
    std::vector<TVertex*> FTable;
    void Init(int n)
    {
        assert(n > 0);
        FTable.resize(n);
        for(int i = 0; i < n; ++i){
            FTable[i] = new TVertex(i);
        }
    }
public:
    TGraph(int n)
    {
        Init(n);
    }
    
    void SetupVertex(std::istream& in)
    {
        int Index;
        in >> Index;
        assert(Index >= 0);
        assert(Index < FTable.size());
        int k;
        in >> k;
        FTable[Index]->Reserve(k);
        for(int i = 0; i < k; ++i){
            int v, c;
            in >> v >> c;
            FTable[Index]->AddPath(TPath(FTable[v], c));
        }
        FTable[Index]->SortPath();
    }
    void BreadthFirstSearch()
    {
        FTable[0]->BreadthFirstSearch(0);
    }
    void PrintDistance(std::ostream& out)
    {
        for(int i = 0; i < FTable.size(); ++i){
            FTable[i]->PrintDistance(out);
        }
    }
};

int main()
{
    std::cin.tie(0);
    std::ios::sync_with_stdio(false);
    int n;
    std::cin >> n;
    TGraph Graph(n);
    for(int i = 0; i < n; ++i){
        Graph.SetupVertex(std::cin);
    }
    Graph.BreadthFirstSearch();
    Graph.PrintDistance(std::cout);
    return 0;
    
}