C ++优先级字典

Question

I need a container to store pairs, I have two operations:

1. update value by key
2. get the key with maximum value.

For the first operation, map is a good structure. For the second operation, seems priority queue is a good one. How would you do this? Is there anyway to have both of the two operations done without having a O(n) loop? Thanks.

Answer 1

An asymptotically efficient solution to this would be to use a combination of a hash table and a Fibonacci heap. You would use the hash table to be able to access the value associated with any particular key in O(1) time, and would use the Fibonacci heap to be able to quickly look up the key/value pair with the lowest value (doing so in O(1)).

If you want to change the value associated with a key, if you are increasing the value, you can do so in (amortized) O(1) time by using the increase-key operation on the Fibonacci heap, which has O(1) amortized time. If you are decreasing the value, it will take O(log n) time to delete the element out of the Fibonacci heap and then reinsert it.

Overall, this gives a time complexity of

• Insert a new element: O(1) for hash, O(1) for insert into Fibonacci heap: O(1) time .
• Delete an element: O(1) for hash, O(log n) for delete from Fibonacci heap: O(log n) time .
• Find top element: O(1) for lookup in Fibonacci heap: O(1) time.
• Increase a value: O(1) for hash, O(1) for increase-key: O(1) time.
• Decrease a value: O(1) for hash, O(log n) for delete/insert: O(log n) time.

Hope this helps!

Answer 2

Create a heap structure (for the second bullet) and put each of its nodes in a map (for the first bullet).

EDIT: An implementation of min heap I had done some time in the past

#ifndef MINHEAP_H
#define MINHEAP_H

//////////////////////// MinHeap with Map for Data ////////////////////////

template <class T, class M = int> class MinHeap {
    T*          array;
    unsigned const int  arr_max;
    unsigned int        elements;
    M           map;

    void percolate_down(unsigned int i=0) {
        unsigned int n = elements-1, min;
        do {
            unsigned int l = 2*i + 1, r = 2*i + 2;
            if (l <= n && array[i] > array[l]) min = l;
            else min = i;
            if (r <= n && array[i] > array[r] && array[l] > array[r]) min = r;
            if (i != min) {
                T temp = array[i];
                array[i] = array[min];
                array[min] = temp;
                map.update(array[i], i);
                map.update(array[min], min);
                i = min;
            } else break;
        } while (i < n);
    }
    void percolate_up(unsigned int i) {
        while (i && array[(i-1)/2] > array[i]) {
            T temp = array[i];
            array[i] = array[(i-1)/2];
            array[(i-1)/2] = temp;
            map.update(array[i], i);
            map.update(array[(i-1)/2], (i-1)/2);
            i = (i-1)/2;
        }
    }
public:
    MinHeap(const int max) : array(new T[max]), arr_max(max), elements(0), map(max) {}
    ~MinHeap(void) { delete[] array; }

    bool empty(void) const { return elements == 0; }
    unsigned int capacity(void) const { return arr_max; }
    unsigned int size(void) const { return elements; }
    const M& heapmap(void) const { return map; }
    const T& peek(unsigned int i=0) const { return array[i]; }

    bool insert(T& element) {
        if (arr_max == elements) return false;

        unsigned int k = elements++;
        map.update(element, k);
        array[k] = element;
        percolate_up(k);
        return true;
    }
    unsigned int mass_insert(T copy[], unsigned int n) {
        unsigned int i = 0;     
        for( ; i < n ; i++) if (!insert(copy[i])) break;
        return i;
    }
    bool delete_min(void) {
        if (elements == 0) return false;

        map.update(array[0], arr_max+1);
        array[0] = array[--elements];
        map.update(array[0], 0);
        percolate_down();
        return true;
    }
    bool delete_element(unsigned int i) {
        if (i > elements) return false;

        map.update(array[i], arr_max+1);
        T temp = array[i];      
        array[i] = array[--elements];
        map.update(array[i], i);
        if (array[i] > temp) percolate_down(i);
        else if (temp > array[i]) percolate_up(i);
        return true;
    }
    bool update(unsigned int i, T& element) {
        if (i > elements) return false;

        map.update(array[i], arr_max+1);
        T temp = array[i];      
        array[i] = element;
        map.update(array[i], i);
        if (array[i] > temp) percolate_down(i);
        else if (temp > array[i]) percolate_up(i);
        return true;
    }

//  void print() { using namespace std; for (unsigned int i=0 ; i < elements ; i++) cout << array[i] << " | "; cout << endl; }


    // Iterators
/*
    friend class Const_Iterator;

    class Const_Iterator {
        MinHeap<T>* heap;
        unsigned int    index;
        Const_Iterator(MinHeap<T>* h, unsigned int i) : heap(h), index(i) {}
    public:
        Const_Iterator(const Const_Iterator& clone) : heap(clone.heap), index(clone.index) {}

        friend Const_Iterator MinHeap<T>::begin(void);
    };

    Const_Iterator begin(void) { return Const_Iterator(this, 0); }
*/
};

//////////////////////////////////////////////////////////////////////////////


//////////////////////// MinHeap without Map for Data ////////////////////////

template <class T> class MinHeap <T, int> {
    T*          array;
    unsigned const int  arr_max;
    unsigned int        elements;

    void percolate_down(unsigned int i=0) {
        unsigned int n = elements-1, min;
        do {
            unsigned int l = 2*i + 1, r = 2*i + 2;
            if (l <= n && array[i] > array[l]) min = l;
            else min = i;
            if (r <= n && array[i] > array[r] && array[l] > array[r]) min = r;
            if (i != min) {
                T temp = array[i];
                array[i] = array[min];
                array[min] = temp;
                i = min;
            } else break;
        } while (i < n);
    }
    void percolate_up(unsigned int i) {
        while (i && array[(i-1)/2] > array[i]) {
            T temp = array[i];
            array[i] = array[(i-1)/2];
            array[(i-1)/2] = temp;
            i = (i-1)/2;
        }
    }
public:
    MinHeap(const int max) : array(new T[max]), arr_max(max), elements(0) {}
    ~MinHeap(void) { delete[] array; }

    bool empty(void) const { return elements == 0; }
    unsigned int capacity(void) const { return arr_max; }
    unsigned int size(void) const { return elements; }
    const T& peek(unsigned int i=0) const { return array[i]; }

    bool insert(T& element) {
        if (arr_max == elements) return false;

        unsigned int k = elements++;
        array[k] = element;
        percolate_up(k);
        return true;
    }
    unsigned int mass_insert(T copy[], unsigned int n) {
        unsigned int i = 0;     
        for( ; i < n ; i++) if (!insert(copy[i])) break;
        return i;
    }
    bool delete_min(void) {
        if (elements == 0) return false;

        array[0] = array[--elements];
        percolate_down();
        return true;
    }
    bool delete_element(unsigned int i) {
        if (i > elements) return false;

        T temp = array[i];      
        array[i] = array[--elements];
        if (array[i] > temp) percolate_down(i);
        else if (temp > array[i]) percolate_up(i);
        return true;
    }
    bool update(unsigned int i, T& element) {
        if (i > elements) return false;

        T temp = array[i];      
        array[i] = element;
        if (array[i] > temp) percolate_down(i);
        else if (temp > array[i]) percolate_up(i);
        return true;
    }

//  void print() { using namespace std; for (unsigned int i=0 ; i < elements ; i++) cout << array[i] << " | "; cout << endl; }
};

//////////////////////////////////////////////////////////////////////////////

#endif // MINHEAP_H

Answer 3

boost :: bimap可以做你想要的，反向映射用于实现＃2。

Answer 4

According to my C++0x standard, The fundamental property of iterators of associative containers is that they iterate through the containers in the non-descending order of keys where non-descending is defined by the comparison that was used to construct them.

So just use a map. Random lookup is O(log(n)), and to get the highest element takes O(1) time.

value getHighest(map<key, value>& map) {
    assert(map.empty() == false);
    return (--map.end())->second;
}

Answer 5

我认为bimap是最好的路线