Go: package main

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

var scanner = bufio.NewScanner(os.Stdin)

func nextString() string {
	scanner.Scan()
	return scanner.Text()
}

func nextInt() int {
	n, err := strconv.Atoi(nextString())
	if err != nil {
		fmt.Printf("strconv.Atoi failed: %v\n", err)
	}
	return n
}

var infty = 1000000000

type DirectedGraphNodeID int

type DirectedGraphNode struct {
	key         DirectedGraphNodeID
	adjacents   []*DirectedGraphNode
	costs       []int
	distance    int
	predecessor *DirectedGraphNode
}

func newDirectedGraph(nNodes int) *DirectedGraph {
	graph := DirectedGraph{}
	graph.nodes = make([]*DirectedGraphNode, nNodes)
	for i := 0; i < nNodes; i++ {
		node := DirectedGraphNode{}
		node.key = DirectedGraphNodeID(i)
		node.distance = infty
		graph.nodes[i] = &node
	}
	return &graph
}

type DirectedGraph struct {
	nodes []*DirectedGraphNode
}

func (g *DirectedGraph) setAdjacency(i, j DirectedGraphNodeID, cost int) {
	g.nodes[i].adjacents = append(g.nodes[i].adjacents, g.nodes[j])
	g.nodes[i].costs = append(g.nodes[i].costs, cost)
}

func (g *DirectedGraph) print() {
	for i := 0; i < len(g.nodes); i++ {
		node := g.nodes[i]
		key := node.key
		strings := []string{strconv.Itoa(int(key)), strconv.Itoa(node.distance)}
		for j := 0; j < len(node.adjacents); j++ {
			nodeJ := fmt.Sprintf("(%v, %v)", node.adjacents[j].key, node.costs[j])
			strings = append(strings, nodeJ)
		}
		fmt.Printf("%v\n", strings)
	}
}

func (g *DirectedGraph) relaxEdge(l, r *DirectedGraphNode, w int) {
	if r.distance > l.distance+w {
		// fmt.Printf("%v -> %v, %v\n", l.key, r.key, l.distance+w)
		r.distance = l.distance + w
		r.predecessor = l
	}
}

func main() {
	scanner.Split(bufio.ScanWords)

	nNodes := nextInt()
	graph := newDirectedGraph(nNodes)

	for i := 0; i < nNodes; i++ {
		iNode := DirectedGraphNodeID(nextInt())
		nAdjacent := nextInt()
		for j := 0; j < nAdjacent; j++ {
			jNode := DirectedGraphNodeID(nextInt())
			cost := nextInt()
			graph.setAdjacency(iNode, jNode, cost)
		}
	}

	graph.nodes[0].distance = 0
	for iNode := 0; iNode < nNodes; iNode++ {
		for iLeft := 0; iLeft < len(graph.nodes); iLeft++ {
			nodeLeft := graph.nodes[iLeft]
			for iRight := 0; iRight < len(nodeLeft.adjacents); iRight++ {
				nodeRight := nodeLeft.adjacents[iRight]
				cost := nodeLeft.costs[iRight]
				graph.relaxEdge(nodeLeft, nodeRight, cost)
			}
		}
	}

	// graph.print()

	for iNode := 0; iNode < len(graph.nodes); iNode++ {
		node := graph.nodes[iNode]
		fmt.Println(node.key, node.distance)
	}
}

C++: #include <bits/stdc++.h>
#pragma GCC diagnostic ignored "-Wsign-compare"
#pragma GCC diagnostic ignored "-Wconversion"

using namespace std;

#define FOR(i, a, b) for (ll i = (a); i < (b); i++)
#define RFOR(i, a, b) for (ll i = (b)-1; i >= (a); i--)
#define rep(i, n) for (ll i = 0; i < (n); i++)
#define rep1(i, n) for (ll i = 1; i <= (n); i++)
#define rrep(i, n) for (ll i = (n)-1; i >= 0; i--)

#define pb push_back
#define mp make_pair
#define fst first
#define snd second
#define show(x) cout << #x << " = " << x << endl
#define chmin(x, y) x = min(x, y)
#define chmax(x, y) x = max(x, y)
#define pii pair<int, int>

namespace is_stl_container_impl
{
template <typename T>
struct is_stl_container : false_type {
};
template <typename T, size_t N>
struct is_stl_container<array<T, N>> : true_type {
};
template <typename... Args>
struct is_stl_container<vector<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<deque<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<list<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<forward_list<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<set<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<multiset<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<map<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<multimap<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<unordered_set<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<unordered_multiset<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<unordered_map<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<unordered_multimap<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<stack<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<queue<Args...>> : true_type {
};
template <typename... Args>
struct is_stl_container<priority_queue<Args...>> : true_type {
};
}  // namespace is_stl_container_impl

//type trait to utilize the implementation type traits as well as decay the type
template <typename T>
struct is_stl_container {
    static constexpr bool const value = is_stl_container_impl::is_stl_container<decay_t<T>>::value;
};

template <typename T>
typename enable_if<is_stl_container<T>::value, ostream&>::type operator<<(ostream& os, const T& container)
{
    os << "[";
    for (const auto& p : container) {
        os << p << ",";
    }
    os << "]";
    return os;
}

template <typename S, typename T>
ostream& operator<<(ostream& os, const pair<S, T>& p)
{
    os << "(" << p.first << "," << p.second
       << ")";
    return os;
}

using ll = long long;
constexpr ll MOD = 1000000007;

template <typename T>
constexpr T INF = numeric_limits<T>::max() / 100;

struct DGraph {
    using T = ll;
    DGraph(const int v) : V{v}
    {
        edge.resize(v);
        rev_edge.resize(v);
    }
    struct Edge {
        Edge(const int from, const int to, const T cost) : from{from}, to{to}, cost{cost} {}
        const int from;
        const int to;
        const T cost;
        bool operator<(const Edge& e) const
        {
            return cost != e.cost ? cost < e.cost : to < e.to;
        }
    };
    void addEdge(const int from, const int to, const T cost)
    {
        edge[from].push_back(Edge{from, to, cost});
        rev_edge[to].push_back(Edge(to, from, cost));
    }
    vector<vector<Edge>> edge;
    vector<vector<Edge>> rev_edge;
    const int V;
};

void Dijkstra(const DGraph& g, const int s, vector<DGraph::T>& d)
{
    using T = DGraph::T;
    assert(s < g.V);
    assert(d.size() == g.V);
    using P = pair<T, int>;
    priority_queue<P, vector<P>, greater<P>> q;
    for (int i = 0; i < g.V; i++) {
        d[i] = INF<T>;
    }
    d[s] = 0;
    q.push(make_pair(0, s));
    while (not q.empty()) {
        const P& p = q.top();
        const T cost = p.first;
        const int v = p.second;
        q.pop();
        if (d[v] < cost) {
            continue;
        }
        for (const auto& e : g.edge[v]) {
            if (d[e.to] > d[v] + e.cost) {
                d[e.to] = d[v] + e.cost;
                q.push(make_pair(d[e.to], e.to));
            }
        }
    }
}

int main()
{
    int V, E, r;
    cin >> V >> E >> r;
    DGraph g{V};
    for (int i = 0; i < E; i++) {
        int s, t;
        ll c;
        cin >> s >> t >> c;
        g.addEdge(s, t, c);
    }
    vector<long long> d(V);
    Dijkstra(g, r, d);
    for (int i = 0; i < V; i++) {
        if (d[i] != INF<ll>) {
            cout << d[i] << endl;
        } else {
            cout << "INF" << endl;
        }
    }
    return 0;
}