Language: C++

#include <algorithm>
#include <bits/stdc++.h>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <list>
#include <map>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <vector>
using namespace std;

#define rep(X, S, E) for (int(X) = (S); (X) < (E); ++(X))
#define rrep(X, S, E) for (int(X) = (E)-1; (X) >= (S); --(X))
#define itrep(X, Y) for (auto(X) = (Y).begin(); (X) != (Y).end(); (X)++)
#define all(X) (X).begin(), (X).end()
#define sortDecending(X) sort(all(X), greater<ll>()) //降順
#define sortAscending(X) sort(all(X))                //昇順
#define pb push_back
#define mp make_pair
#define fi first
#define sc second
#define print(x) cout << x << endl
#define printDouble(x) cout << fixed << setprecision(13) << x << endl
#define chmin(x, y) x = min(x, y)
#define chmax(x, y) x = max(x, y)

typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<bool> vb;
typedef priority_queue<ll, vl> decendingQueue;              //降順
typedef priority_queue<ll, vl, greater<ll>> ascendingQueue; //昇順
const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};
const ll INF = 9 * 1e18;
const ll MOD = 1e9 + 7;

long long gcd(long long m, long long n) {
  if (m < n)
    return gcd(n, m);
  if (n == 0)
    return m;
  return gcd(n, m % n);
}

long long lcm(long long m, long long n) {
  // m * nでlong型のオーバフローを発生させないため、先に割り算から行う
  return m * (n / gcd(m, n));
}

// auto mod int
// https://youtu.be/L8grWxBlIZ4?t=9858
// https://youtu.be/ERZuLAxZffQ?t=4807 : optimize
// https://youtu.be/8uowVvQ_-Mo?t=1329 : division
const int mod = 1000000007;
struct mint {
  ll x; // typedef long long ll;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}
  mint &operator+=(const mint a) {
    if ((x += a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator-=(const mint a) {
    if ((x += mod - a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const {
    mint res(*this);
    return res += a;
  }
  mint operator-(const mint a) const {
    mint res(*this);
    return res -= a;
  }
  mint operator*(const mint a) const {
    mint res(*this);
    return res *= a;
  }
  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }

  // for prime mod
  mint inv() const { return pow(mod - 2); }
  mint &operator/=(const mint a) { return (*this) *= a.inv(); }
  mint operator/(const mint a) const {
    mint res(*this);
    return res /= a;
  }
};

// combination mod prime
// https://www.youtube.com/watch?v=8uowVvQ_-Mo&feature=youtu.be&t=1619
struct combination {
  vector<mint> fact, ifact;
  combination(int n) : fact(n + 1), ifact(n + 1) {
    assert(n < mod);
    fact[0] = 1;
    for (int i = 1; i <= n; ++i)
      fact[i] = fact[i - 1] * i;
    ifact[n] = fact[n].inv();
    for (int i = n; i >= 1; --i)
      ifact[i - 1] = ifact[i] * i;
  }
  mint operator()(int n, int k) {
    if (k < 0 || k > n)
      return 0;
    return fact[n] * ifact[k] * ifact[n - k];
  }
};

vector<long long> SieveOfEratosthenes(int max) {
  vector<long long> sieve;
  vector<long long> primes;

  for (int i = 1; i < max + 1; ++i) {
    sieve.push_back(i);
  }

  sieve[0] = 0;
  for (int i = 2; i < max + 1; ++i) {
    if (sieve[i - 1] != 0) {
      primes.push_back(sieve[i - 1]);
      for (int j = 2 * sieve[i - 1]; j < max + 1; j += sieve[i - 1]) {
        sieve[j - 1] = 0;
      }
    }
  }
  return primes;
}

class UnionFindTree {
private:
  vector<int> par;
  vector<int> rnk;
  vector<int> siz;

public:
  UnionFindTree(int n) {
    par.assign(n, -1);
    rnk.assign(n, -1);
    siz.assign(n, -1);

    for (int i = 0; i < n; ++i) {
      par[i] = i;
      rnk[i] = 0;
      siz[i] = 1;
    }
  }

  int find(int x) {
    if (par[x] == x)
      return x;
    else
      return par[x] = find(par[x]);
  }

  bool same(int x, int y) { return find(x) == find(y); }

  void unite(int x, int y) {
    x = find(x);
    y = find(y);
    if (x == y)
      return;
    if (rnk[x] < rnk[y]) {
      par[x] = y;
      siz[y] += siz[x];
    } else {
      par[y] = x;
      siz[x] += siz[y];
      if (rnk[x] == rnk[y])
        ++rnk[x];
    }
  }

  int size(int x) {
    x = find(x);
    return siz[x];
  }
};

class Edge {
public:
  ll from;
  ll to;
  double cost;

  Edge() {}
  Edge(ll from, ll to, double cost) {
    this->from = from;
    this->to = to;
    this->cost = cost;
  }

  bool operator<(const Edge &edge) const {
    return cost < edge.cost; //昇順
  }
};

class Graph {
public:
  ll nodes; // ノード数
  vector<Edge> edges;

  Graph() {}
  Graph(ll nodes) { this->nodes = nodes; }
  void addEdge(ll from, ll to, double cost) {
    this->edges.push_back(Edge(from, to, cost));
  }
};

// クラスカル法
// 連結グラフの最小全域木を求める
class Kruskal {
private:
  Graph graph;
  vector<Edge> MinimumSpanningTree;
  ll minimumCost;
  void searchMinimumSpanningTree() {
    UnionFindTree uf(graph.nodes);
    sort(all(graph.edges));
    itrep(edge, graph.edges) {
      if (!uf.same(edge->from, edge->to)) {
        uf.unite(edge->from, edge->to);
        MinimumSpanningTree.push_back(*edge);
      }
    }
  }

public:
  Kruskal(Graph graph) { this->graph = graph; }
  ll getMinimumSpanningTreeCost() {
    searchMinimumSpanningTree();
    ll cost = 0;
    itrep(it, MinimumSpanningTree) { cost += it->cost; }
    return cost;
  }
};

// ダイクストラ法 O((E+V)logV)
// 最小経路問題を解くためのアルゴリズム。辺の重みに負数を含む場合は利用不可
// 無向グラフの場合はコメントアウト箇所をコメントイン
class Dijkstra {
private:
  Graph graph;
  map<ll, vector<Edge>> fromPaths;
  vector<double> distances;
  vl srcs;

public:
  Dijkstra(Graph graph) {
    this->graph = graph;
    itrep(edge, graph.edges) {
      fromPaths[edge->from].push_back(*edge);
      fromPaths[edge->to].push_back(Edge(edge->to, edge->from, edge->cost));
    }
  }
  void searchMinimumPathFrom(ll src) {
    // 複数回呼ばれる度に計算する
    distances = vector<double>(graph.nodes + 1, INF);
    srcs = vl(graph.nodes + 1, INF);

    // 距離が近い順番に捜査していく
    priority_queue<pair<double, ll>,
                   vector<pair<double, ll>, greater<pair<double, ll>>>>
        pq;
    distances[src] = 0;
    srcs[src] = -1;

    pq.push(mp(0.0, src));
    while (!pq.empty()) {
      int u = pq.top().second;
      pq.pop();

      itrep(edge, fromPaths[u]) {
        int v = edge->to;
        double w = edge->cost;
        if (distances[v] > distances[u] + w) {
          distances[v] = distances[u] + w;
          srcs[v] = u;
          pq.push(mp(distances[v], v));
        }
      }
    }
  };
  double getDistance(ll n) { return distances[n]; }
  ll getFrom(ll n) { return srcs[n]; }
};

// ベルマンフォード O(|V||E|)
// 負コストが含まれていても最短経路問題を解くためのアルゴリズム。閉路の検出も可能
// 有向グラフ
class BellmanFord {
private:
  Graph graph;
  // 閉路が含まれるかは個々のノードごとに管理する必要あり
  vector<bool> hasNegativeCycles;
  vector<ll> distances;
  vl srcs;

public:
  BellmanFord(Graph graph) {
    ll nodes = graph.nodes + 1;

    this->graph = graph;
    distances = vector<ll>(nodes, INF);
    hasNegativeCycles = vector<bool>(nodes, false);
  }
  void searchMinimumPathFrom(ll src) {
    distances[src] = 0;

    for (ll i = 0; i < graph.nodes - 1; i++) {
      itrep(edge, graph.edges) {
        ll u = edge->from;
        ll v = edge->to;
        ll w = edge->cost;
        if (distances[u] != INF) {
          chmin(distances[v], distances[u] + w);
        }
      }
    }

    itrep(edge, graph.edges) {
      ll u = edge->from;
      ll v = edge->to;
      ll w = edge->cost;
      if (distances[u] == INF) {
        continue;
      }
      if (distances[u] + w < distances[v]) {
        hasNegativeCycles[v] = true;
      }
    }

    for (ll i = 0; i < graph.nodes; i++) {
      itrep(edge, graph.edges) {
        ll u = edge->from;
        ll v = edge->to;
        ll w = edge->cost;
        if (distances[u] == INF) {
          continue;
        }
        chmin(distances[v], distances[u] + w);
        if (hasNegativeCycles[u] == true) {
          hasNegativeCycles[v] = true;
        }
      }
    }
  }
  ll getDistance(ll n) { return distances[n]; }
  bool hasNegativeCycle(ll n) { return hasNegativeCycles[n]; }
  ll getFrom(ll n) { return srcs[n]; }
};

// O(V^3) 有向グラフ
class WarshallFloyd {
private:
  Graph graph;
  int nodes = this->graph.nodes + 1;
  vector<vector<ll>> distances;

public:
  WarshallFloyd(Graph graph) {
    this->graph = graph;
    nodes = this->graph.nodes + 1;
    this->distances = vector<vector<ll>>(nodes, vector<ll>(nodes, INF));
    itrep(edge, graph.edges) {
      int from = edge->from;
      int to = edge->to;
      int cost = edge->cost;
      distances[from][to] = cost;
    }
  }
  void searchMinimumPath() {
    for (int k = 0; k < nodes; k++) {
      for (int i = 0; i < nodes; i++) {
        for (int j = 0; j < nodes; j++) {
          if (distances[i][k] == INF || distances[k][j] == INF) {
            continue;
          }
          if (distances[i][k] + distances[k][j] < distances[i][j]) {
            distances[i][j] = distances[i][k] + distances[k][j];
          }
        }
      }
    }
  }
  ll getDistance(int from, int to) { return distances[from][to]; }
};

double calcCost(ll x1, ll y1, ll r1, ll x2, ll y2, ll r2) {
  double dist = sqrt(((double)x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
  return max(0.0, dist - r1 - r2);
}

void solve(long long x_s, long long y_s, long long x_t, long long y_t,
           long long N, std::vector<long long> x, std::vector<long long> y,
           std::vector<long long> r) {
  Graph g(N + 2); // start:N, end:N+1
  rep(i, 0, N) {
    g.addEdge(i, N, calcCost(x[i], y[i], r[i], x_s, y_s, 0));
    g.addEdge(i, N + 1, calcCost(x[i], y[i], r[i], x_t, y_t, 0));
  }
  rep(i, 0, N) {
    rep(j, i + 1, N) {
      g.addEdge(i, j, calcCost(x[i], y[i], r[i], x[j], y[j], r[j]));
    }
  }

  Dijkstra dijkstra(g);
  dijkstra.searchMinimumPathFrom(N);
  printDouble(dijkstra.getDistance(N + 1));
}

int main() {
  long long x_s;
  scanf("%lld", &x_s);
  long long y_s;
  scanf("%lld", &y_s);
  long long x_t;
  scanf("%lld", &x_t);
  long long y_t;
  scanf("%lld", &y_t);
  long long N;
  scanf("%lld", &N);
  std::vector<long long> x(N);
  std::vector<long long> y(N);
  std::vector<long long> r(N);
  for (int i = 0; i < N; i++) {
    scanf("%lld", &x[i]);
    scanf("%lld", &y[i]);
    scanf("%lld", &r[i]);
  }
  solve(x_s, y_s, x_t, y_t, N, std::move(x), std::move(y), std::move(r));
  return 0;
}


Compiler output:
In file included from /usr/include/c++/14/vector:66,
                 from /usr/include/c++/14/functional:64,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:53,
                 from a.cc:2:
/usr/include/c++/14/bits/stl_vector.h: In instantiation of 'struct std::_Vector_base<std::pair<double, long long int>, std::greater<std::pair<double, long long int> > >':
/usr/include/c++/14/bits/stl_vector.h:428:11:   required from 'class std::vector<std::pair<double, long long int>, std::greater<std::pair<double, long long int> > >'
  428 |     class vector : protected _Vector_base<_Tp, _Alloc>
      |           ^~~~~~
a.cc:287:70:   required from here
  287 |                    vector<pair<double, ll>, greater<pair<double, ll>>>>
      |                                                                      ^~
/usr/include/c++/14/bits/stl_vector.h:87:28: error: no type named 'value_type' in 'struct std::greater<std::pair<double, long long int> >'
   87 |         rebind<_Tp>::other _Tp_alloc_type;
      |                            ^~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_vector.h:89:9: error: no type named 'value_type' in 'struct std::greater<std::pair<double, long long int> >'
   89 |         pointer;
      |         ^~~~~~~
/usr/include/c++/14/bits/stl_vector.h: In instantiation of 'class std::vector<std::pair<double, long long int>, std::greater<std::pair<double, long long int> > >':
a.cc:287:70:   required from here
  287 |                    vector<pair<double, ll>, greater<pair<double, ll>>>>
      |                                                                      ^~
/usr/include/c++/14/bits/stl_vector.h:518:20: error: '_M_allocate' has not been declared in 'std::vector<std::pair<double, long long int>, std::greater<std::pair<double, long long int> > >::_Base'
  518 |       using _Base::_M_allocate;
      |                    ^~~~~~~~~~~
/usr/include/c++/14/bits/stl_vector.h:519:20: error: '_M_deallocate' has not been declared in 'std::vector<std::pair<double, long long int>, std::greater<std::pair<double, long long int> > >::_Base'
  519 |       using _Base::_M_deallocate;
      |                    ^~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_vector.h:521:20: error: '_M_get_Tp_allocator' has not been declared in 'std::vector<std::pair<double, long long int>, std::greater<std::pair<double, long long int> > >::_Base'
  521 |       using _Base::_M_get_Tp_allocator;
      |                    ^~~~~~~~~~~~~~~~~~~
In file included from /usr/include/c++/14/bits/stl_algobase.h:59,
                 from /usr/include/c++/14/algorithm:60,
                 from a.cc:1:
/usr/include/c++/14/bits/stl_vector.h: In instantiation of 'std::_Vector_base<_Tp, _Alloc>::_Vector_impl::_Vector_impl() [with _Tp = std::pair<double, long long int>; _Alloc = std::greater<std::pair<double, long long int> >]':
/usr/include/c++/14/type_traits:1110:25:   required by substitution of 'template<class _Tp, class ... _Args> using std::__is_constructible_impl = std::__bool_constant<__is_constructible(_Tp, _Args ...)> [with _Tp = std::vector<std::pair<double, long long int>, std::greater<std::pair<double, long long int> > >; _Args = {}]'
 1110 |       = __bool_constant<__is_constructible(_Tp, _Args...)>;
      |                         ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/type_traits:1124:12:   required from 'struct std::is_default_constructible<std::vector<std::pair<double, long long int>, std::greater<std::pair<double, long long int> > > >'
 1124 |     struct is_default_constructible
      |            ^~~~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/14/type_traits:183:35:   required by substitution of 'template<class ... _Bn> std::__detail::__first_t<std::integral_constant<bool, true>, typename std::enable_if<(bool)(_Bn::value), void>::type ...> std::__detail::__and_fn(int) [with _Bn = {std::is_default_constructible<std::less<std::pair<double, long long int> > >, std::is_default_constructible<std::vector<std::pair<double, long long int>, std::greater<std::pair<double, long long int> > > >}]'
  183 |                                       __enable_if_t<bool(_Bn::value)>...>;
      |                                                               ^~~~~
/usr/include/c++/14/type_traits:199:42:   required from 'struct std::__and_<std::is_default_constructible<std::less<std::pair<double, long long int> > >, std::is_default_constructible<std::vector<std::pair<double, long long int>, std::greater<std::pair<double, long long int> > > > >'
  199 |     : decltype(__detail::__and_fn<_Bn...>(0))
      |                ~~~~~~~~~~~~~~~~~~~~~~~~~~^~~
/usr/include/c++/14/bits/stl_queue.h:551:43:   required by substitution of 'template<class _Seq, class _Requires> std::priority_queue<std::pair<double, long long int>, std::vector<std::pair<double, long long int>, std::greater<std::pair<double, long long int> > > >::priority_queue() [with _Seq = std::vector<std::pair<double, long long int>, std::greater<std::pair<double, long long int> > >; _Requires = <missing>]'
  551 |       template<typename _Seq = _Sequence, typename _Requires = typename
      |                                           ^~~~~~~~
a.cc:288:9:   required from here
  288 |         pq;
      |         ^~
/usr/include/c++/14/bits/stl_vector.h:136:24: error: no type named 'value_type' in 'struct std::greater<std::pair<double, long long int> >'
  136 |         _Vector_impl() _GLIBCXX_NOEXCEPT_IF(
      |                        ^~~~~~~~~~~~~~~~~~~~
a.cc: In member function 'void Dijkstra::searchMinimumPathFrom(ll)':
a.cc:294:18: error: 'class std::priority_queue<std::pair<double, long long int>, std::vector<std::pair<double, long long int>, std::greater<std::pair<double, long long int> > > >' has no member named 'top'; did you mean 'pop'?
  294 |       int u = pq.top().second;
      |                  ^~~
      |                  pop
In file included from /usr/include/c++/14/queue:66,
                 from /usr/include/x86_64-linux-gnu/c++/14/bits/stdc++.h:157:
/usr/include/c++/14/bits/stl_queue.h: In instantiation of 'void std::priority_queue<_Tp, _Sequence, _Compare>::push(value_type&&) [with _Tp = std::pair<double, long long int>; _Sequence = std::vector<std::pair<double, long long int>, std::greater<std::pair<double, long long int> > >; _Compare = std::less<std::pair<double, long long int> >; value_type = std::pair<double, long long int>]':
a.cc:292:12:   required from here
  292 |     pq.push(mp(0.0, src));
      |     ~~~~~~~^~~~~~~~~~~~~~
/usr/include/c++/14/bits/stl_queue.h:747:26: error: 'class std::vector<std::pair<double, long long int>, std::greater<std::pair<double, long long int> > >' has no member named 'begin'
  747 |         std::push_heap(c.begin(), c.end(), comp);
      |                        ~~^~~~~
/usr/include/c++/14/bits/stl_queue.h:747:37: error: 'class std::vector<std::pair<double, long long int>, std::greater<std::pair<double, long long int> > >' has no member named 'end'
  747 |         std::push_heap(c.begin(), c.end(), comp);
      |                                   ~~^~~
/usr/include/c++/14/bits/stl_queue.h: In instantiation of 'void std::priority_queue<_Tp, _Sequence, _Compare>::pop() [with _Tp = std::pair<double, long long int>; _Sequence = std::vector<std::pair<double, long long int>, std::greater<std::pair<double, long long int> > >; _Compare = std::less<std::pair<double, long long int> >]':
a.cc:295:13:   required from here
  295 |       pq.pop();
      |       ~~~~~~^~
/usr/include/c++/14/bits/stl_queue.h:774:25: error: 'class std::vector<std::pair<double, long long int>, std::greater<std::pair<double, long long int> > >' has no member named 'begin'
  774 |         std::pop_heap(c.begin(), c.end(), comp);
      |                       ~~^~~~~
/usr/include/c++/14/bits/stl_queue.h:774:36: error: 'class std::vector<std::pair<double, long long int>, std::greater<std::pair<double, long long int> > >' has no member named 'end'
  774 |         std::pop_heap(c.begin(), c.end(), comp);
      |                                  ~~^~~
/usr/include/c++/14/bits/stl_vector.h: In instantiation of 'std::_Vector_base<_Tp, _Alloc>::_Vector_impl::_Vector_impl() [with _Tp = std::pair<double, long long int>; _Alloc = std::greater<std::pair<double, long long int> >]':
/usr/include/c++/14/bits/stl_vector.h:314:7:   required from 'std::priority_queue<_Tp, _Sequence, _Compare>::priority_queue() [with _Seq = std::vector<std::pair<double, long long int>, std::greater<std::pair<double, long long int> > >; _Requires = void; _Tp = std::pair<double, long long int>; _Sequence = std::vector<std::pair<double, long long int>, std::greater<std::pair<double, long long int> > >; _Compare = std::less<std::pair<double, long long int> >]'
  314 |       _Vector_base() = default;
      |       ^~~~~~~~~~~~
a.cc:288:9:   required from here
  288 |         pq;
      |         ^~
/usr/include/c++/14/bits/stl_vector.h:141:26: error: no type named 'value_type' in 'struct std::greater<std::pair<double, long long int> >'
  141 |         : _Tp_alloc_type()
      |                          ^