二叉堆的Java实现及应用举例

二叉堆实现

import java.util.Arrays;

//二叉堆
public class BinaryHeap {

	private static final int DEFAULT_CAPACITY = 10;
	private int currentSize;
	private int[] arr;

	public BinaryHeap() {
		this(DEFAULT_CAPACITY);
	}

	public BinaryHeap(int defaultCapacity) {
		currentSize = 0;
		arr = new int[defaultCapacity];
	}

	public BinaryHeap insert(int x) {
		if (currentSize == arr.length - 1) {
			throw new RuntimeException("溢出...");
		}

		// 首先假设，将待插节点放在叶子节点的末端处
		int pos = ++currentSize;

		// 如果根节点还没有下滤过，并且待插节点小于pos的父节点
		while (pos > 1 && x < arr[pos / 2]) {
			// 父节点下滤
			arr[pos] = arr[pos / 2];
			// pos上移
			pos /= 2;
		}

		arr[pos] = x;

		return this;
	}

	public int delete() {
		if (currentSize == 0) {
			throw new RuntimeException("堆空...");
		}

		int min = arr[1];

		int temp = arr[currentSize--];
		int pos = 1;
		int child = pos * 2;

		// 当pos位置还不是叶子节点时
		while (pos * 2 <= currentSize) {
			// 找到pos的孩子节点
			child = pos * 2;
			// 当pos不是只有左孩子，并且右孩子小于左孩子
			if (child != currentSize && arr[child + 1] < arr[child]) {
				child++;
			}

			// 如果最小的孩子小于temp
			if (arr[child] < temp) {
				// 孩子节点上滤
				arr[pos] = arr[child];
			} else {
				// pos的最小孩子比temp大，此时应跳出循环，将temp赋给pos位置
				break;
			}

			pos = child;
		}
		arr[pos] = temp;

		return min;
	}

	public int size() {
		return currentSize;
	}

	public String toString() {
		return Arrays.toString(arr);
	}

	public static void main(String[] args) {
		BinaryHeap heap = new BinaryHeap();

		heap.insert(1).insert(2).insert(3).insert(4).insert(6);
		System.out.println(heap.toString());

		System.out.println(heap.delete());
		System.out.println(heap.toString());

		heap.insert(5).insert(6);
		System.out.println(heap.toString());

	}
}

应用举例 （Fence Repair）

import java.util.Scanner;

public class Main {

	public static void main(String[] args) {

		Scanner input = new Scanner(System.in);
		BinaryHeap heap = new BinaryHeap();

		int n = input.nextInt();
		int[] arr = new int[n];
		for (int i = 0; i < n; i++) {
			arr[i] = input.nextInt();
			heap.insert(arr[i]);
		}

		int result = 0;
		while (heap.size() > 1) {
			// 取出最短和次短的木板
			int min1 = heap.delete();
			int min2 = heap.delete();

			result += min1 + min2;
			
			
			heap.insert(min1 + min2);
		}

		System.out.println(result);
	}

}