Design an efficient data structure for given operations | GeeksforGeeks


Design an efficient data structure for given operations


Design a Data Structure for the following operations. The data structure should be efficient enough to accommodate the operations according to their frequency.
1) findMin() : Returns the minimum item.
   Frequency: Most frequent

2) findMax() : Returns the maximum item.
    Frequency: Most frequent

3) deleteMin() : Delete the minimum item.
    Frequency: Moderate frequent 

4) deleteMax() : Delete the maximum item.
    Frequency: Moderate frequent 

5) Insert() : Inserts an item.
    Frequency: Least frequent

6) Delete() : Deletes an item. 
    Frequency: Least frequent.
simple solution is to maintain a sorted array where smallest element is at first position and largest element is at last. The time complexity of findMin(), findMAx() and deleteMax() is O(1). But time complexities of deleteMin(), insert() and delete() will be O(n).
Can we do the most frequent two operations in O(1) and other operations in O(Logn) time?.
The idea is to use two binary heaps (one max and one min heap):t we have used doubly linked list as a mutual data structure. The doubly linked list contains all input items and indexes of corresponding min and max heap nodes. The nodes of min and max heaps store addresses of nodes of doubly linked list. The root node of min heap stores the address of minimum item in doubly linked list. Similarly, root of max heap stores address of maximum item in doubly linked list. Following are the details of operations.

struct LNode
{
    int data;
    int minHeapIndex;
    int maxHeapIndex;
    struct LNode *next, *prev;
};
 
// Structure for a doubly linked list
struct List
{
    struct LNode *head;
};
 
// Structure for min heap
struct MinHeap
{
    int size;
    int capacity;
    struct LNode* *array;
};
 
// Structure for max heap
struct MaxHeap
{
    int size;
    int capacity;
    struct LNode* *array;
};
 
// The required data structure
struct MyDS
{
    struct MinHeap* minHeap;
    struct MaxHeap* maxHeap;
    struct List* list;
};
// Function to delete an item from List. The function also
// removes item from min and max heaps
void Delete(struct MyDS* myDS, int item)
{
    MinHeap *minHeap = myDS->minHeap;
    MaxHeap *maxHeap = myDS->maxHeap;
 
    if (isListEmpty(myDS->list))
        return;
 
    // search the node in List
    struct LNode* temp = myDS->list->head;
    while (temp && temp->data != item)
        temp = temp->next;
 
    // if item not found
    if (!temp || temp && temp->data != item)
        return;
 
    // remove item from min heap
    minHeap->array[temp->minHeapIndex] = minHeap->array[minHeap->size - 1];
    --minHeap->size;
    minHeap->array[temp->minHeapIndex]->minHeapIndex = temp->minHeapIndex;
    minHeapify(minHeap, temp->minHeapIndex);
 
    // remove item from max heap
    maxHeap->array[temp->maxHeapIndex] = maxHeap->array[maxHeap->size - 1];
    --maxHeap->size;
    maxHeap->array[temp->maxHeapIndex]->maxHeapIndex = temp->maxHeapIndex;
    maxHeapify(maxHeap, temp->maxHeapIndex);
 
    // remove node from List
    removeLNode(myDS->list, &temp);
}
 
// insert operation for main data structure
void Insert(struct MyDS* myDS, int data)
{
    struct LNode* temp = newLNode(data);
 
    // insert the item in List
    insertAtHead(myDS->list, temp);
 
    // insert the item in min heap
    insertMinHeap(myDS->minHeap, temp);
 
    // insert the item in max heap
    insertMaxHeap(myDS->maxHeap, temp);
}
// Function to delete maximum value stored in the main data structure
void deleteMax(struct MyDS* myDS)
{
    MinHeap *minHeap = myDS->minHeap;
    MaxHeap *maxHeap = myDS->maxHeap;
 
    if (isMaxHeapEmpty(maxHeap))
        return;
    struct LNode* temp = maxHeap->array[0];
 
    // delete the maximum item from maxHeap
    maxHeap->array[0] =
        maxHeap->array[maxHeap->size - 1];
    --maxHeap->size;
    maxHeap->array[0]->maxHeapIndex = 0;
    maxHeapify(maxHeap, 0);
 
    // remove the item from minHeap
    minHeap->array[temp->minHeapIndex] = minHeap->array[minHeap->size - 1];
    --minHeap->size;
    minHeap->array[temp->minHeapIndex]->minHeapIndex = temp->minHeapIndex;
    minHeapify(minHeap, temp->minHeapIndex);
 
    // remove the node from List
    removeLNode(myDS->list, &temp);
}
 
// Function to delete minimum value stored in the main data structure
void deleteMin(struct MyDS* myDS)
{
    MinHeap *minHeap = myDS->minHeap;
    MaxHeap *maxHeap = myDS->maxHeap;
 
    if (isMinHeapEmpty(minHeap))
        return;
    struct LNode* temp = minHeap->array[0];
 
    // delete the minimum item from minHeap
    minHeap->array[0] = minHeap->array[minHeap->size - 1];
    --minHeap->size;
    minHeap->array[0]->minHeapIndex = 0;
    minHeapify(minHeap, 0);
 
    // remove the item from maxHeap
    maxHeap->array[temp->maxHeapIndex] = maxHeap->array[maxHeap->size - 1];
    --maxHeap->size;
    maxHeap->array[temp->maxHeapIndex]->maxHeapIndex = temp->maxHeapIndex;
    maxHeapify(maxHeap, temp->maxHeapIndex);
 
    // remove the node from List
    removeLNode(myDS->list, &temp);
}
// Function to find minimum value stored in the main data structure
int findMin(struct MyDS* myDS)
{
    if (isMinHeapEmpty(myDS->minHeap))
        return INT_MAX;
 
    return myDS->minHeap->array[0]->data;
}
 
// Function to find maximum value stored in the main data structure
int findMax(struct MyDS* myDS)
{
    if (isMaxHeapEmpty(myDS->maxHeap))
        return INT_MIN;
 
    return myDS->maxHeap->array[0]->data;
}
 
// A utility function to remove an item from linked list
void removeLNode(struct List* list, struct LNode** temp)
{
    if (hasOnlyOneLNode(list))
        list->head = NULL;
 
    else if (!(*temp)->prev) // first node
    {
        list->head = (*temp)->next;
        (*temp)->next->prev = NULL;
    }
    // any other node including last
    else
    {
        (*temp)->prev->next = (*temp)->next;
        // last node
        if ((*temp)->next)
            (*temp)->next->prev = (*temp)->prev;
    }
    free(*temp);
    *temp = NULL;
}
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