Dijkstra-Radix-Heap(単一始点最短路) (graph/shortest-path/dijkstra-radix-heap.hpp)

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Last update: 2026-08-10 10:02:02+00:00
Include: #include "graph/shortest-path/dijkstra-radix-heap.hpp"

Depends on

Verified with

test/verify/aoj-grl-1-a-3.test.cpp

Code

#pragma once

#include <algorithm>
#include <limits>
#include <tuple>
#include <vector>

#include "../../structure/heap/radix-heap.hpp"
#include "../graph-template.hpp"

/**
 * @brief Dijkstra-Radix-Heap(単一始点最短路)
 */
template <typename T>
std::vector<T> dijkstra_radix_heap(Graph<T>& g, int s) {
  const auto INF = std::numeric_limits<T>::max();
  std::vector<T> dist(g.size(), INF);

  RadixHeap<T, int> heap;
  dist[s] = 0;
  heap.push(dist[s], s);
  while (!heap.empty()) {
    T cost;
    int idx;
    std::tie(cost, idx) = heap.pop();
    if (dist[idx] < cost) continue;
    for (auto& e : g.g[idx]) {
      auto next_cost = cost + e.cost;
      if (dist[e.to] <= next_cost) continue;
      dist[e.to] = next_cost;
      heap.push(dist[e.to], e.to);
    }
  }
  return dist;
}

#line 2 "graph/shortest-path/dijkstra-radix-heap.hpp"

#include <algorithm>
#include <limits>
#include <tuple>
#include <vector>

#line 2 "structure/heap/radix-heap.hpp"

#line 4 "structure/heap/radix-heap.hpp"
#include <array>
#include <cstddef>
#include <cstdint>
#include <iterator>
#include <utility>
#line 10 "structure/heap/radix-heap.hpp"

template <typename key_t, typename val_t>
struct RadixHeap {
  static constexpr int bit = sizeof(key_t) * 8;
  std::array<std::vector<std::pair<key_t, val_t> >, bit> vs;

  std::size_t sz;
  key_t last;

  RadixHeap() : sz(0), last(0) {}

  bool empty() const { return sz == 0; }

  std::size_t size() const { return sz; }

  inline int getbit(int a) const { return a ? bit - __builtin_clz(a) : 0; }

  inline int getbit(std::int64_t a) const {
    return a ? bit - __builtin_clzll(a) : 0;
  }

  void push(const key_t& key, const val_t& val) {
    sz++;
    vs[getbit(key ^ last)].emplace_back(key, val);
  }

  std::pair<key_t, val_t> pop() {
    if (vs[0].empty()) {
      int idx = 1;
      while (vs[idx].empty()) idx++;
      last = std::min_element(vs[idx].begin(), vs[idx].end())->first;
      for (auto& p : vs[idx]) vs[getbit(p.first ^ last)].emplace_back(p);
      vs[idx].clear();
    }
    --sz;
    auto res = vs[0].back();
    vs[0].pop_back();
    return res;
  }
};
#line 2 "graph/graph-template.hpp"

#line 4 "graph/graph-template.hpp"
#include <iostream>
#line 6 "graph/graph-template.hpp"

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 {
  std::vector<std::vector<Edge<T> > > g;
  int es;

  Graph() = default;

  explicit Graph(int n) : g(n), es(0) {}

  std::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;
      std::cin >> a >> b;
      a += padding;
      b += padding;
      T c = T(1);
      if (weighted) std::cin >> c;
      if (directed)
        add_directed_edge(a, b, c);
      else
        add_edge(a, b, c);
    }
  }

  inline std::vector<Edge<T> >& operator[](const int& k) { return g[k]; }

  inline const std::vector<Edge<T> >& operator[](const int& k) const {
    return g[k];
  }
};

template <typename T = int>
using Edges = std::vector<Edge<T> >;
#line 10 "graph/shortest-path/dijkstra-radix-heap.hpp"

/**
 * @brief Dijkstra-Radix-Heap(単一始点最短路)
 */
template <typename T>
std::vector<T> dijkstra_radix_heap(Graph<T>& g, int s) {
  const auto INF = std::numeric_limits<T>::max();
  std::vector<T> dist(g.size(), INF);

  RadixHeap<T, int> heap;
  dist[s] = 0;
  heap.push(dist[s], s);
  while (!heap.empty()) {
    T cost;
    int idx;
    std::tie(cost, idx) = heap.pop();
    if (dist[idx] < cost) continue;
    for (auto& e : g.g[idx]) {
      auto next_cost = cost + e.cost;
      if (dist[e.to] <= next_cost) continue;
      dist[e.to] = next_cost;
      heap.push(dist[e.to], e.to);
    }
  }
  return dist;
}