Dijkstra法(Radix Heap)
(graph/dijkstra_radix_heap.cpp)

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• Last update: 2020-05-02 12:50:18+09:00

説明

単一始点最短路を求める。負辺があると正しく動作しない。 $O(V \log E)$

Depends on

• datastructure/radixheap.cpp

Verified with

• test/yosupo_shortest_path_radix_heap.test.cpp

Code

template <typename T>
struct edge {
    int from, to; T cost;
    edge(int to, T cost) : from(-1), to(to), cost(cost) {}
    edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}
};

#include "../datastructure/radixheap.cpp"

template <typename T>
vector<T> dijkstra(int s,vector<vector<edge<T>>> &G){
    auto n = G.size();
    vector<T> d(n, INF<T>);
    RadixHeap<ll, int> Q;
    d[s] = 0;
    Q.emplace(0, s);
    while(!Q.empty()){
        T cost; int i;
        tie(cost, i) = Q.top(); Q.pop();
        if(d[i] < cost) continue;
        for (auto &&e : G[i]) {
            auto cost2 = cost + e.cost;
            if(d[e.to] <= cost2) continue;
            d[e.to] = cost2;
            Q.emplace(d[e.to], e.to);
        }
    }
    return d;
}

/**
 * @brief Dijkstra法(Radix Heap)
 * @docs _md/dijkstra.md
 */

#line 1 "graph/dijkstra_radix_heap.cpp"
template <typename T>
struct edge {
    int from, to; T cost;
    edge(int to, T cost) : from(-1), to(to), cost(cost) {}
    edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}
};

#line 1 "datastructure/radixheap.cpp"
template <class K, class V>
class RadixHeap {
    static constexpr int bit_length = sizeof(K)*8;
    K last;
    size_t sz, cnt;
    
    array<vector<pair<K, V>>, bit_length> v;
    static inline int bsr(int x){
        return x ? bit_length-__builtin_clz(x) : 0;
    }
    static inline int bsr(ll x){
        return x ? bit_length-__builtin_clzll(x) : 0;
    }

    void pull() {
        if(cnt < v[0].size()) return;;
        int i = 1;
        while(v[i].empty()) i++;
        last = min_element(v[i].begin(),v[i].end())->first;
        for (auto &&x : v[i]) v[bsr(x.first ^ last)].push_back(x);
        v[i].clear();
    }
public:
    RadixHeap() : last(0), sz(0), cnt(0) {}
    void emplace(K x, V val){
        sz++;
        v[bsr(x^last)].emplace_back(x, val);
    }

    pair<K, V> top() {
        pull();
        return v[0][cnt];
    }

    void pop() {
        pull();
        sz--;
        cnt++;
    }

    size_t size() const { return sz; }
    bool empty() const { return !sz; }
};
#line 9 "graph/dijkstra_radix_heap.cpp"

template <typename T>
vector<T> dijkstra(int s,vector<vector<edge<T>>> &G){
    auto n = G.size();
    vector<T> d(n, INF<T>);
    RadixHeap<ll, int> Q;
    d[s] = 0;
    Q.emplace(0, s);
    while(!Q.empty()){
        T cost; int i;
        tie(cost, i) = Q.top(); Q.pop();
        if(d[i] < cost) continue;
        for (auto &&e : G[i]) {
            auto cost2 = cost + e.cost;
            if(d[e.to] <= cost2) continue;
            d[e.to] = cost2;
            Q.emplace(d[e.to], e.to);
        }
    }
    return d;
}

/**
 * @brief Dijkstra法(Radix Heap)
 * @docs _md/dijkstra.md
 */

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