java 堆排序

复杂度最坏： nlgn  代码中有标注

和top n 问题关系：用的堆模型，和top n 问题用的模型相同

http://blog.youkuaiyun.com/nx188/article/details/51218846

createHeap    从1开始遍历堆去令每个节点做child, 用child 去找parent, 

adjustHeap    parent 一直是0, 用parent 去和lChild 和rChild 去比较, 这个是log N,  每个节点都置换一次最小值, 就是O(n), 所以是nlogN

代码：

package AlgorithmTopK;

public class Heapsort {
	
	//建立小根堆  super.createHeap(int input[], int K);
	public int[] createHeap(int input[]) {  //创建小根堆
		int heap[] = new int[input.length];
		for(int i=0;i<input.length;i++)
			heap[i] = input[i];
		for(int i = 1;i < heap.length;i++) {   //这个复杂度是 n
			int child = i;
			int parent = (child-1) / 2;
			while(parent >= 0 && child!=0 && heap[parent] > heap[child]) {  //这个复杂度最坏是lgn
				int temp = heap[child];
				heap[child] = heap[parent];
				heap[parent] = temp;
				child = parent;
				parent = (parent - 1) / 2;
			}
		}
		return heap;
	}
	
	//循环根和最后一个换，再调整堆   根和倒数第二个换，再调整堆  直到根和左儿子交换后，不用再调整堆
	public void adjustHeap(int[] heap, int last) {
		//先把根和heap[last]交换，
		int temp = heap[0];
		heap[0] = heap[last];
		heap[last] = temp;	
		//再调整堆
		if(last > 1) {
			int parent = 0;
			while(parent < last-1) {   //这个循环复杂度最坏是  lgn
				int lchild = parent*2 + 1;
				int rchild = parent*2 + 2;
				int minIndex = parent;  //指向左右儿子中最小的
				if(lchild < last-1 && heap[lchild] < heap[parent])
					minIndex = lchild;
				if(rchild < last-1 && heap[rchild] < heap[minIndex])
					minIndex = rchild;
				if(minIndex == parent) {
					break;
				}
				else {
					temp = heap[minIndex];
					heap[minIndex] = heap[parent];
					heap[parent] = temp;
					parent = minIndex;
				}
			}
		} 
	}
	
	//打印结果数组
	public int[] heapSort(int[] input) {
		int[] smallRootHeap = createHeap(input);   //复杂度最坏是nlgn
		for(int i=smallRootHeap.length-1;i>0;i--)  //复杂度最坏是nlgn
			adjustHeap(smallRootHeap, i);
		return smallRootHeap;
	}
			
	public static void main(String[] args) {
		int a[] = {5,4,1,2,6,7,9,10,2,3};
		int result[] = new Heapsort().heapSort(a);
		for(int resultItem : result) {
			System.out.print(resultItem + " ");
		}
	}

}

结果：

10 9 7 6 5 4 3 2 2 1