import java.util.Arrays;
import java.util.NoSuchElementException;
public class BinaryHeap {
private static final int d = 2;
private int[] heap;
private int heapSize;
/**
* This will initialize our heap with default size.
*/
public BinaryHeap(int capacity) {
heapSize = 0;
heap = new int[capacity + 1];
Arrays.fill(heap, -1);
}
public boolean isEmpty() {
return heapSize == 0;
}
public boolean isFull() {
return heapSize == heap.length;
}
private int parent(int i) {
return (i - 1) / d;
}
private int kthChild(int i, int k) {
return d * i + k;
}
/**
* Inserts new element in to heap
* Complexity: O(log N)
* As worst case scenario, we need to traverse till the root
*/
public void insert(int x) {
if (isFull()) {
throw new NoSuchElementException("Heap is full, No space to insert new element");
}
heap[heapSize] = x;
heapSize ++;
heapifyUp(heapSize - 1);
}
/**
* Deletes element at index x
* Complexity: O(log N)
*/
public int delete(int x) {
if (isEmpty()) {
throw new NoSuchElementException("Heap is empty, No element to delete");
}
int maxElement = heap[x];
heap[x] = heap[heapSize - 1];
heapSize--;
heapifyDown(x);
return maxElement;
}
/**
* Maintains the heap property while inserting an element.
*/
private void heapifyUp(int i) {
int insertValue = heap[i];
while (i > 0 && insertValue > heap[parent(i)]) {
heap[i] = heap[parent(i)];
i = parent(i);
}
heap[i] = insertValue;
}
/**
* Maintains the heap property while deleting an element.
*/
private void heapifyDown(int i) {
int child;
int temp = heap[i];
while (kthChild(i, 1) < heapSize) {
child = maxChild(i);
if (temp >= heap[child]) {
break;
}
heap[i] = heap[child];
i = child;
}
heap[i] = temp;
}
private int maxChild(int i) {
int leftChild = kthChild(i, 1);
int rightChild = kthChild(i, 2);
return heap[leftChild] > heap[rightChild] ? leftChild : rightChild;
}
/**
* Prints all elements of the heap
*/
public void printHeap() {
System.out.print("nHeap = ");
for (int i = 0; i < heapSize; i++)
System.out.print(heap[i] + " ");
System.out.println();
}
/**
* This method returns the max element of the heap.
* complexity: O(1)
*/
public int findMax() {
if (isEmpty())
throw new NoSuchElementException("Heap is empty.");
return heap[0];
}
public static void main(String[] args) {
BinaryHeap maxHeap = new BinaryHeap(10);
maxHeap.insert(10);
maxHeap.insert(4);
maxHeap.insert(9);
maxHeap.insert(1);
maxHeap.insert(7);
maxHeap.insert(5);
maxHeap.insert(3);
maxHeap.printHeap();
maxHeap.delete(5);
maxHeap.printHeap();
maxHeap.delete(2);
maxHeap.printHeap();
}
}
堆的實現代碼
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