最大最小堆
一个堆同时具有最大堆和最小堆的操作属性。
// C program for efficient data structure #include <stdio.h> #include <stdlib.h> #include <limits.h> // A node of doubly linked list 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 swap two integers void swapData(int* a, int* b) { int t = *a; *a = *b; *b = t; } // Function to swap two List nodes void swapLNode(struct LNode** a, struct LNode** b) { struct LNode* t = *a; *a = *b; *b = t; } // A utility function to create a new List node struct LNode* newLNode(int data) { struct LNode* node = (struct LNode*) malloc(sizeof(struct LNode)); node->minHeapIndex = node->maxHeapIndex = -1; node->data = data; node->prev = node->next = NULL; return node; } // Utility function to create a max heap of given capacity struct MaxHeap* createMaxHeap(int capacity) { struct MaxHeap* maxHeap = (struct MaxHeap*) malloc(sizeof(struct MaxHeap)); maxHeap->size = 0; maxHeap->capacity = capacity; maxHeap->array = (struct LNode**) malloc(maxHeap->capacity * sizeof(struct LNode*)); return maxHeap; } // Utility function to create a min heap of given capacity struct MinHeap* createMinHeap(int capacity) { struct MinHeap* minHeap = (struct MinHeap*) malloc(sizeof(struct MinHeap)); minHeap->size = 0; minHeap->capacity = capacity; minHeap->array = (struct LNode**) malloc(minHeap->capacity * sizeof(struct LNode*)); return minHeap; } // Utility function to create a List struct List* createList() { struct List* list = (struct List*) malloc(sizeof(struct List)); list->head = NULL; return list; } // Utility function to create the main data structure // with given capacity struct MyDS* createMyDS(int capacity) { struct MyDS* myDS = (struct MyDS*) malloc(sizeof(struct MyDS)); myDS->minHeap = createMinHeap(capacity); myDS->maxHeap = createMaxHeap(capacity); myDS->list = createList(); return myDS; } // Some basic operations for heaps and List int isMaxHeapEmpty(struct MaxHeap* heap) { return (heap->size == 0); } int isMinHeapEmpty(struct MinHeap* heap) { return heap->size == 0; } int isMaxHeapFull(struct MaxHeap* heap) { return heap->size == heap->capacity; } int isMinHeapFull(struct MinHeap* heap) { return heap->size == heap->capacity; } int isListEmpty(struct List* list) { return !list->head; } int hasOnlyOneLNode(struct List* list) { return !list->head->next && !list->head->prev; } // The standard minheapify function. The only thing it does extra // is swapping indexes of heaps inside the List void minHeapify(struct MinHeap* minHeap, int index) { int smallest, left, right; smallest = index; left = 2 * index + 1; right = 2 * index + 2; if ( minHeap->array[left] && left < minHeap->size && minHeap->array[left]->data < minHeap->array[smallest]->data ) smallest = left; if ( minHeap->array[right] && right < minHeap->size && minHeap->array[right]->data < minHeap->array[smallest]->data ) smallest = right; if (smallest != index) { // First swap indexes inside the List using address // of List nodes swapData(&(minHeap->array[smallest]->minHeapIndex), &(minHeap->array[index]->minHeapIndex)); // Now swap pointers to List nodes swapLNode(&minHeap->array[smallest], &minHeap->array[index]); // Fix the heap downward minHeapify(minHeap, smallest); } } // The standard maxHeapify function. The only thing it does extra // is swapping indexes of heaps inside the List void maxHeapify(struct MaxHeap* maxHeap, int index) { int largest, left, right; largest = index; left = 2 * index + 1; right = 2 * index + 2; if ( maxHeap->array[left] && left < maxHeap->size && maxHeap->array[left]->data > maxHeap->array[largest]->data ) largest = left; if ( maxHeap->array[right] && right < maxHeap->size && maxHeap->array[right]->data > maxHeap->array[largest]->data ) largest = right; if (largest != index) { // First swap indexes inside the List using address // of List nodes swapData(&maxHeap->array[largest]->maxHeapIndex, &maxHeap->array[index]->maxHeapIndex); // Now swap pointers to List nodes swapLNode(&maxHeap->array[largest], &maxHeap->array[index]); // Fix the heap downward maxHeapify(maxHeap, largest); } } // Standard function to insert an item in Min Heap void insertMinHeap(struct MinHeap* minHeap, struct LNode* temp) { if (isMinHeapFull(minHeap)) return; ++minHeap->size; int i = minHeap->size - 1; while (i && temp->data < minHeap->array[(i - 1) / 2]->data ) { minHeap->array[i] = minHeap->array[(i - 1) / 2]; minHeap->array[i]->minHeapIndex = i; i = (i - 1) / 2; } minHeap->array[i] = temp; minHeap->array[i]->minHeapIndex = i; } // Standard function to insert an item in Max Heap void insertMaxHeap(struct MaxHeap* maxHeap, struct LNode* temp) { if (isMaxHeapFull(maxHeap)) return; ++maxHeap->size; int i = maxHeap->size - 1; while (i && temp->data > maxHeap->array[(i - 1) / 2]->data ) { maxHeap->array[i] = maxHeap->array[(i - 1) / 2]; maxHeap->array[i]->maxHeapIndex = i; i = (i - 1) / 2; } maxHeap->array[i] = temp; maxHeap->array[i]->maxHeapIndex = i; } // 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; } // 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 enList an item to List void insertAtHead(struct List* list, struct LNode* temp) { if (isListEmpty(list)) list->head = temp; else { temp->next = list->head; list->head->prev = temp; list->head = temp; } } // 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); } // Driver program to test above functions int main() { struct MyDS *myDS = createMyDS(10); // Test Case #1 /*Insert(myDS, 10); Insert(myDS, 2); Insert(myDS, 32); Insert(myDS, 40); Insert(myDS, 5);*/ // Test Case #2 Insert(myDS, 10); Insert(myDS, 20); Insert(myDS, 30); Insert(myDS, 40); Insert(myDS, 50); printf("Maximum = %d \n", findMax(myDS)); printf("Minimum = %d \n\n", findMin(myDS)); deleteMax(myDS); // 50 is deleted printf("After deleteMax()\n"); printf("Maximum = %d \n", findMax(myDS)); printf("Minimum = %d \n\n", findMin(myDS)); deleteMin(myDS); // 10 is deleted printf("After deleteMin()\n"); printf("Maximum = %d \n", findMax(myDS)); printf("Minimum = %d \n\n", findMin(myDS)); Delete(myDS, 40); // 40 is deleted printf("After Delete()\n"); printf("Maximum = %d \n", findMax(myDS)); printf("Minimum = %d \n", findMin(myDS)); getchar(); return 0; }
