cp-library

C++ Library for Competitive Programming

View the Project on GitHub emthrm/cp-library

:warning: グラフ/区間に辺を張るテク
(test/graph/noshi_graph.test.cpp)

Depends on

Code

/*
 * @title グラフ/区間に辺を張るテク
 *
 * verification-helper: IGNORE
 * verification-helper: PROBLEM https://codeforces.com/problemset/problem/786/B
 */

#include <iostream>
#include <vector>

#include "emthrm/graph/noshi_graph.hpp"
#include "emthrm/graph/shortest_path/dijkstra.hpp"

int main() {
  int n, q, s;
  std::cin >> n >> q >> s;
  --s;
  emthrm::NoshiGraph<long long> graph(n);
  while (q--) {
    int t, v;
    std::cin >> t >> v;
    --v;
    if (t == 1) {
      int u, w;
      std::cin >> u >> w;
      --u;
      graph.add_edge(v, u, w);
    } else {
      int l, r, w;
      std::cin >> l >> r >> w;
      --l; --r;
      if (t == 2) {
        graph.add_edge(v, v + 1, l, r + 1, w);
      } else if (t == 3) {
        graph.add_edge(l, r + 1, v, v + 1, w);
      }
    }
  }
  emthrm::Dijkstra<long long> dijkstra(graph.graph);
  const std::vector<long long> ans = dijkstra.build(s);
  for (int i = 0; i < n; ++i) {
    std::cout << (ans[i] == dijkstra.inf ? -1 : ans[i]) << " \n"[i + 1 == n];
  }
  return 0;
}
#line 1 "test/graph/noshi_graph.test.cpp"
/*
 * @title グラフ/区間に辺を張るテク
 *
 * verification-helper: IGNORE
 * verification-helper: PROBLEM https://codeforces.com/problemset/problem/786/B
 */

#include <iostream>
#include <vector>

#line 1 "include/emthrm/graph/noshi_graph.hpp"



#include <bit>
#line 6 "include/emthrm/graph/noshi_graph.hpp"

#line 1 "include/emthrm/graph/edge.hpp"
/**
 * @title 辺
 */

#ifndef EMTHRM_GRAPH_EDGE_HPP_
#define EMTHRM_GRAPH_EDGE_HPP_

#include <compare>

namespace emthrm {

template <typename CostType>
struct Edge {
  CostType cost;
  int src, dst;

  explicit Edge(const int src, const int dst, const CostType cost = 0)
      : cost(cost), src(src), dst(dst) {}

  auto operator<=>(const Edge& x) const = default;
};

}  // namespace emthrm

#endif  // EMTHRM_GRAPH_EDGE_HPP_
#line 8 "include/emthrm/graph/noshi_graph.hpp"

namespace emthrm {

template <typename CostType>
struct NoshiGraph {
  std::vector<std::vector<Edge<CostType>>> graph;

  explicit NoshiGraph(const int n)
      : p2(std::bit_ceil(static_cast<unsigned int>(n))) {
    const int dbl = p2 << 1, hlf = p2 >> 1;
    graph.resize(dbl + p2);
    for (int i = 1; i < hlf; ++i) {
      add_edge(i + p2, (i << 1) + p2);
      add_edge(i + p2, (i << 1) + 1 + p2);
      add_edge((i << 1) + dbl, i + dbl);
      add_edge((i << 1) + 1 + dbl, i + dbl);
    }
    for (int src = p2 + hlf, dst = 0; dst < p2; ++src, dst += 2) {
      add_edge(src, dst);
      add_edge(src, dst + 1);
    }
    for (int src = 0, dst = dbl + hlf; src < p2; src += 2, ++dst) {
      add_edge(src, dst);
      add_edge(src + 1, dst);
    }
  }

  void add_edge(const int src, const int dst, const CostType cost = 0) {
    graph[src].emplace_back(src, dst, cost);
  }

  void add_edge(int src_l, int src_r, int dst_l, int dst_r,
                const CostType cost) {
    if (src_r <= src_l || dst_r <= dst_l) [[unlikely]] return;
    const int src_id = graph.size(), dst_id = src_id + 1;
    graph.emplace_back();
    graph.emplace_back();
    if ((dst_l += p2) & 1) add_edge(dst_id, dst_l++ - p2);
    if ((dst_r += p2) & 1) add_edge(dst_id, --dst_r - p2);
    for (dst_l >>= 1, dst_r >>= 1; dst_l < dst_r; dst_l >>= 1, dst_r >>= 1) {
      if (dst_l & 1) add_edge(dst_id, dst_l++ + p2);
      if (dst_r & 1) add_edge(dst_id, --dst_r + p2);
    }
    add_edge(src_id, dst_id, cost);
    if ((src_l += p2) & 1) add_edge(src_l++ - p2, src_id);
    if ((src_r += p2) & 1) add_edge(--src_r - p2, src_id);
    for (src_l >>= 1, src_r >>= 1; src_l < src_r; src_l >>= 1, src_r >>= 1) {
      if (src_l & 1) add_edge(src_l++ + (p2 << 1), src_id);
      if (src_r & 1) add_edge(--src_r + (p2 << 1), src_id);
    }
  }

 private:
  const int p2;
};

}  // namespace emthrm


#line 1 "include/emthrm/graph/shortest_path/dijkstra.hpp"



#include <algorithm>
#include <cassert>
#include <functional>
#include <limits>
#include <queue>
#include <utility>
#line 11 "include/emthrm/graph/shortest_path/dijkstra.hpp"

#line 1 "include/emthrm/graph/edge.hpp"
/**
 * @title 辺
 */

#ifndef EMTHRM_GRAPH_EDGE_HPP_
#define EMTHRM_GRAPH_EDGE_HPP_

#include <compare>

namespace emthrm {

template <typename CostType>
struct Edge {
  CostType cost;
  int src, dst;

  explicit Edge(const int src, const int dst, const CostType cost = 0)
      : cost(cost), src(src), dst(dst) {}

  auto operator<=>(const Edge& x) const = default;
};

}  // namespace emthrm

#endif  // EMTHRM_GRAPH_EDGE_HPP_
#line 13 "include/emthrm/graph/shortest_path/dijkstra.hpp"

namespace emthrm {

template <typename CostType>
struct Dijkstra {
  const CostType inf;

  Dijkstra(const std::vector<std::vector<Edge<CostType>>>& graph,
           const CostType inf = std::numeric_limits<CostType>::max())
      : inf(inf), is_built(false), graph(graph) {}

  std::vector<CostType> build(const int s) {
    is_built = true;
    const int n = graph.size();
    std::vector<CostType> dist(n, inf);
    dist[s] = 0;
    prev.assign(n, -1);
    std::priority_queue<std::pair<CostType, int>,
                        std::vector<std::pair<CostType, int>>,
                        std::greater<std::pair<CostType, int>>> que;
    que.emplace(0, s);
    while (!que.empty()) {
      const auto [d, ver] = que.top();
      que.pop();
      if (d > dist[ver]) continue;
      for (const Edge<CostType>& e : graph[ver]) {
        if (dist[ver] + e.cost < dist[e.dst]) {
          dist[e.dst] = dist[ver] + e.cost;
          prev[e.dst] = ver;
          que.emplace(dist[e.dst], e.dst);
        }
      }
    }
    return dist;
  }

  std::vector<int> build_path(int t) const {
    assert(is_built);
    std::vector<int> res;
    for (; t != -1; t = prev[t]) {
      res.emplace_back(t);
    }
    std::reverse(res.begin(), res.end());
    return res;
  }

 private:
  bool is_built;
  std::vector<int> prev;
  std::vector<std::vector<Edge<CostType>>> graph;
};

}  // namespace emthrm


#line 13 "test/graph/noshi_graph.test.cpp"

int main() {
  int n, q, s;
  std::cin >> n >> q >> s;
  --s;
  emthrm::NoshiGraph<long long> graph(n);
  while (q--) {
    int t, v;
    std::cin >> t >> v;
    --v;
    if (t == 1) {
      int u, w;
      std::cin >> u >> w;
      --u;
      graph.add_edge(v, u, w);
    } else {
      int l, r, w;
      std::cin >> l >> r >> w;
      --l; --r;
      if (t == 2) {
        graph.add_edge(v, v + 1, l, r + 1, w);
      } else if (t == 3) {
        graph.add_edge(l, r + 1, v, v + 1, w);
      }
    }
  }
  emthrm::Dijkstra<long long> dijkstra(graph.graph);
  const std::vector<long long> ans = dijkstra.build(s);
  for (int i = 0; i < n; ++i) {
    std::cout << (ans[i] == dijkstra.inf ? -1 : ans[i]) << " \n"[i + 1 == n];
  }
  return 0;
}
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