This documentation is automatically generated by online-judge-tools/verification-helper
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_1_A"
#include <iostream>
#include <limits>
#include "graph/dijkstra.hpp"
#include "macros.hpp"
using namespace std;
int main(){
long long N, E, R;
cin >> N >> E >> R;
Graph<long long> G(N);
G.read(E, 0, true, true);
ShortestPath<long long> sp = dijkstra(G, R);
const long long INF = numeric_limits<long long>::max();
rep(i, N){
if (sp.dist[i] == INF) {
cout << "INF" << endl;
} else {
cout << sp.dist[i] << endl;
}
}
}#line 1 "test/graph/dijkstra.aoj_GRL_1_A.test.cpp"
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_1_A"
#include <iostream>
#include <limits>
#line 3 "graph/dijkstra.hpp"
#include <queue>
#include <vector>
#include <algorithm>
#line 4 "graph/graphTemplate.hpp"
using namespace std;
template <typename T = int>
struct Edge {
int from, to;
T cost;
int idx;
Edge() = default;
Edge(int from, int to, T cost = 1, int idx = -1)
: from(from), to(to), cost(cost), idx(idx) {}
operator int() const { return to; }
};
template <typename T = int>
struct Graph {
vector<vector<Edge<T>>> g;
int es;
Graph() = default;
explicit Graph(int n) : g(n), es(0) {}
size_t size() const { return g.size(); }
void add_directed_edge(int from, int to, T cost = 1) {
g[from].emplace_back(from, to, cost, es++);
}
void add_edge(int from, int to, T cost = 1) {
g[from].emplace_back(from, to, cost, es);
g[to].emplace_back(to, from, cost, es++);
}
void read(int M, int padding = -1, bool weighted = false,
bool directed = false) {
for (int i = 0; i < M; i++) {
int a, b;
cin >> a >> b;
a += padding;
b += padding;
T c = T(1);
if (weighted) {
cin >> c;
}
if (directed) {
add_directed_edge(a, b, c);
} else {
add_edge(a, b, c);
}
}
}
inline vector<Edge<T>> &operator[](const int &k) { return g[k]; }
inline const vector<Edge<T>> &operator[](const int &k) const { return g[k]; }
};
template <typename T>
using Edges = vector<Edge<T>>;
#line 8 "graph/dijkstra.hpp"
using namespace std;
template <typename T = int>
struct ShortestPath {
vector<T> dist;
vector<int> from, id;
};
template <typename T>
ShortestPath<T> dijkstra(const Graph<T> &g, int s) {
ShortestPath<T> sp;
const auto INF = numeric_limits<T>::max();
sp.dist.resize(g.size(), INF);
sp.dist[s] = 0;
sp.from.resize(g.size(), -1);
sp.id.resize(g.size(), -1);
using Pi = pair<T, int>;
priority_queue<Pi, vector<Pi>, greater<>> pq;
pq.emplace(0, s);
while (!pq.empty()) {
auto [cost, idx] = pq.top();
pq.pop();
if (sp.dist[idx] < cost) continue;
for (auto &e : g[idx]) {
auto next_cost = cost + e.cost;
if (sp.dist[e.to] <= next_cost) continue;
sp.dist[e.to] = next_cost;
sp.from[e.to] = idx;
sp.id[e.to] = e.idx;
pq.emplace(sp.dist[e.to], e.to);
}
}
return sp;
};
#line 2 "macros.hpp"
#define rep(i, n) for (int i = 0; i < (n); i++)
#line 7 "test/graph/dijkstra.aoj_GRL_1_A.test.cpp"
using namespace std;
int main(){
long long N, E, R;
cin >> N >> E >> R;
Graph<long long> G(N);
G.read(E, 0, true, true);
ShortestPath<long long> sp = dijkstra(G, R);
const long long INF = numeric_limits<long long>::max();
rep(i, N){
if (sp.dist[i] == INF) {
cout << "INF" << endl;
} else {
cout << sp.dist[i] << endl;
}
}
}