Update 堆排序.cpp

堆排序.cpp

@@ -1,5 +1,19 @@
-#include <stdio.h>
+5.堆排序
+
+5.1 描述
+（1）将初始待排序关键字序列(R1,R2….Rn)构建成大顶堆，此堆为初始的无序区；
+（2）将堆顶元素R[1]与最后一个元素R[n]交换，此时得到新的无序区(R1,R2,……Rn-1)和新的有序区(Rn),
+     且满足R[1,2…n-1]<=R[n]；
+（3）由于交换后新的堆顶R[1]可能违反堆的性质，因此需要对当前无序区(R1,R2,……Rn-1)调整为新堆，
+然后再次将R[1]与无序区最后一个元素交换，得到新的无序区(R1,R2….Rn-2)和新的有序区(Rn-1,Rn)。
+不断重复此过程直到有序区的元素个数为n-1，则整个排序过程完成 
 
+5.2 复杂程度
+时间复杂度O(nlog2n)                 
+空间复杂度O(1)
+
+5.3 代码
+#include <stdio.h>
 void swap(int arr[], int a, int b)
 {
 	int tmp;
@@ -14,21 +28,21 @@ void heapify(int tree[], int n, int i)
 	{
 		return;
 	}
-	int max = i;//<EFBFBD><EFBFBD><EFBFBD>踸<EFBFBD>ڵ<EFBFBD>Ϊ<EFBFBD><EFBFBD><EFBFBD>ֵ
+	int max = i;//假设父节点为最大值
 	int c1 = 2 * i + 1;
-	int c2 = 2 * i + 2; //<EFBFBD><EFBFBD><EFBFBD>ӽ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>±<EFBFBD>Ϊ2i + 1, <20>Һ<EFBFBD><D2BA>ӽ<EFBFBD><D3BD><EFBFBD><EFBFBD>±<EFBFBD>Ϊ2i + 2
+	int c2 = 2 * i + 2; //左孩子结点的下标为2i + 1, 右孩子结点的下标为2i + 2
 	if (c1 < n && tree[c1] > tree[max])
-	{//<EFBFBD><EFBFBD><EFBFBD>ӵ<EFBFBD><EFBFBD>±<EFBFBD>ҪС<EFBFBD><EFBFBD><EFBFBD>ܽ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>
+	{//左孩子的下标要小于总结点数
-		max = c1;//<EFBFBD><EFBFBD><EFBFBD>ϴ<EFBFBD>ֵ<EFBFBD>Ľ<EFBFBD><EFBFBD><EFBFBD>±<EFBFBD><EFBFBD>¼<EFBFBD><EFBFBD><EFBFBD><EFBFBD>
+		max = c1;//将较大值的结点下标记录下来
 	}
 	if (c2 < n && tree[c2] > tree[max])
 	{
-		max = c2;//<EFBFBD><EFBFBD><EFBFBD>ϴ<EFBFBD>ֵ<EFBFBD>Ľ<EFBFBD><EFBFBD><EFBFBD>±<EFBFBD><EFBFBD>¼<EFBFBD><EFBFBD><EFBFBD><EFBFBD>
+		max = c2;//将较大值的结点下标记录下来
 	}
 	if (max != i)
-	{//<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ֵ<EFBFBD><EFBFBD><EFBFBD>Ǹ<EFBFBD><EFBFBD>ڵ<EFBFBD>
+	{//如果最大值不是根节点
-		swap(tree, max, i);//<EFBFBD><EFBFBD><EFBFBD><EFBFBD>tree[max]<5D><>tree[i]<5D><>ֵ
+		swap(tree, max, i);//交换tree[max]和tree[i]的值
-		heapify(tree, n, max);//max<EFBFBD><EFBFBD><EFBFBD>Ǻ<EFBFBD><EFBFBD>ӽ<EFBFBD><EFBFBD><EFBFBD>±<EFBFBD>
+		heapify(tree, n, max);//max就是孩子结点下标
 	}
 }
 
@@ -48,7 +62,7 @@ void heapify_sort(int tree[], int n)
 	build_heapify(tree, n);
 	int tmp = tree[0];
 	for (int i = n - 1; i >= 0; i--)
-	{//<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>һ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>㿪ʼ
+	{//从最后一个结点开始
 		swap(tree, i, 0);
 		heapify(tree, i, 0);
 	}
@@ -57,14 +71,14 @@ void heapify_sort(int tree[], int n)
 int main(){
 	int tree[] = { 22, 34, 3, 32, 82, 55, 89, 50, 37, 5, 64, 35, 9, 70 };
 	int n = 14;
-	printf("ԭ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ϊ:");
+	printf("原数组为:");
 	for (int i = 0; i < n; i++)
 	{
 		printf("%d ", tree[i]);
 	}
 	printf("\n");
 	heapify_sort(tree, n);
-	printf("<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ϊ<EFBFBD><EFBFBD>");
+	printf("经过堆排序后的数组为：");
 	for (int i = 0; i < n; i++)
 	{
 		printf("%d ", tree[i]);
@@ -73,3 +87,5 @@ int main(){
 	return 0;
 }
 
+5.4 运行时间
+0.02498s