给定一个元素数组，使用最小堆按降序对数组进行排序。
例子：
Input : arr[] = {5, 3, 10, 1}
Output : arr[] = {10, 5, 3, 1}
Input : arr[] = {1, 50, 100, 25}
Output : arr[] = {100, 50, 25, 1}先决条件：使用最小堆进行堆排序。
算法 ：
1.从输入数据构建一个最小堆。
2.此时，最小的项存储在堆的根部。将其替换为堆的最后一项，然后将堆的大小减 1。最后，堆化树的根。
3.当堆的大小大于 1 时，重复上述步骤。
注意：堆排序使用最小堆按降序排序，而最大堆按升序排序
C++
// C++ program for implementation of Heap Sort
#include
using namespace std;
// To heapify a subtree rooted with node i which is
// an index in arr[]. n is size of heap
void heapify(int arr[], int n, int i)
{
int smallest = i; // Initialize smalles as root
int l = 2 * i + 1; // left = 2*i + 1
int r = 2 * i + 2; // right = 2*i + 2
// If left child is smaller than root
if (l < n && arr[l] < arr[smallest])
smallest = l;
// If right child is smaller than smallest so far
if (r < n && arr[r] < arr[smallest])
smallest = r;
// If smallest is not root
if (smallest != i) {
swap(arr[i], arr[smallest]);
// Recursively heapify the affected sub-tree
heapify(arr, n, smallest);
}
}
// main function to do heap sort
void heapSort(int arr[], int n)
{
// Build heap (rearrange array)
for (int i = n / 2 - 1; i >= 0; i--)
heapify(arr, n, i);
// One by one extract an element from heap
for (int i = n - 1; i >= 0; i--) {
// Move current root to end
swap(arr[0], arr[i]);
// call max heapify on the reduced heap
heapify(arr, i, 0);
}
}
/* A utility function to print array of size n */
void printArray(int arr[], int n)
{
for (int i = 0; i < n; ++i)
cout << arr[i] << " ";
cout << "\n";
}
// Driver program
int main()
{
int arr[] = { 4, 6, 3, 2, 9 };
int n = sizeof(arr) / sizeof(arr[0]);
heapSort(arr, n);
cout << "Sorted array is \n";
printArray(arr, n);
} Java
// Java program for implementation of Heap Sort
import java.io.*;
class GFG {
// To heapify a subtree rooted with node i which is
// an index in arr[]. n is size of heap
static void heapify(int arr[], int n, int i)
{
int smallest = i; // Initialize smalles as root
int l = 2 * i + 1; // left = 2*i + 1
int r = 2 * i + 2; // right = 2*i + 2
// If left child is smaller than root
if (l < n && arr[l] < arr[smallest])
smallest = l;
// If right child is smaller than smallest so far
if (r < n && arr[r] < arr[smallest])
smallest = r;
// If smallest is not root
if (smallest != i) {
int temp = arr[i];
arr[i] = arr[smallest];
arr[smallest] = temp;
// Recursively heapify the affected sub-tree
heapify(arr, n, smallest);
}
}
// main function to do heap sort
static void heapSort(int arr[], int n)
{
// Build heap (rearrange array)
for (int i = n / 2 - 1; i >= 0; i--)
heapify(arr, n, i);
// One by one extract an element from heap
for (int i = n - 1; i >= 0; i--) {
// Move current root to end
int temp = arr[0];
arr[0] = arr[i];
arr[i] = temp;
// call max heapify on the reduced heap
heapify(arr, i, 0);
}
}
/* A utility function to print array of size n */
static void printArray(int arr[], int n)
{
for (int i = 0; i < n; ++i)
System.out.print(arr[i] + " ");
System.out.println();
}
// Driver program
public static void main(String[] args)
{
int arr[] = { 4, 6, 3, 2, 9 };
int n = arr.length;
heapSort(arr, n);
System.out.println("Sorted array is ");
printArray(arr, n);
}
}
// This code is contributed by vt_m.Python3
# Python3 program for implementation
# of Heap Sort
# To heapify a subtree rooted with
# node i which is an index in arr[].
# n is size of heap
def heapify(arr, n, i):
smallest = i # Initialize smalles as root
l = 2 * i + 1 # left = 2*i + 1
r = 2 * i + 2 # right = 2*i + 2
# If left child is smaller than root
if l < n and arr[l] < arr[smallest]:
smallest = l
# If right child is smaller than
# smallest so far
if r < n and arr[r] < arr[smallest]:
smallest = r
# If smallest is not root
if smallest != i:
(arr[i],
arr[smallest]) = (arr[smallest],
arr[i])
# Recursively heapify the affected
# sub-tree
heapify(arr, n, smallest)
# main function to do heap sort
def heapSort(arr, n):
# Build heap (rearrange array)
for i in range(int(n / 2) - 1, -1, -1):
heapify(arr, n, i)
# One by one extract an element
# from heap
for i in range(n-1, -1, -1):
# Move current root to end #
arr[0], arr[i] = arr[i], arr[0]
# call max heapify on the reduced heap
heapify(arr, i, 0)
# A utility function to print
# array of size n
def printArray(arr, n):
for i in range(n):
print(arr[i], end = " ")
print()
# Driver Code
if __name__ == '__main__':
arr = [4, 6, 3, 2, 9]
n = len(arr)
heapSort(arr, n)
print("Sorted array is ")
printArray(arr, n)
# This code is contributed by PranchalKC#
// C# program for implementation of Heap Sort
using System;
class GFG {
// To heapify a subtree rooted with
// node i which is an index in arr[],
// n is size of heap
static void heapify(int[] arr, int n, int i)
{
int smallest = i; // Initialize smalles as root
int l = 2 * i + 1; // left = 2*i + 1
int r = 2 * i + 2; // right = 2*i + 2
// If left child is smaller than root
if (l < n && arr[l] < arr[smallest])
smallest = l;
// If right child is smaller than smallest so far
if (r < n && arr[r] < arr[smallest])
smallest = r;
// If smallest is not root
if (smallest != i) {
int temp = arr[i];
arr[i] = arr[smallest];
arr[smallest] = temp;
// Recursively heapify the affected sub-tree
heapify(arr, n, smallest);
}
}
// main function to do heap sort
static void heapSort(int[] arr, int n)
{
// Build heap (rearrange array)
for (int i = n / 2 - 1; i >= 0; i--)
heapify(arr, n, i);
// One by one extract an element from heap
for (int i = n - 1; i >= 0; i--) {
// Move current root to end
int temp = arr[0];
arr[0] = arr[i];
arr[i] = temp;
// call max heapify on the reduced heap
heapify(arr, i, 0);
}
}
/* A utility function to print array of size n */
static void printArray(int[] arr, int n)
{
for (int i = 0; i < n; ++i)
Console.Write(arr[i] + " ");
Console.WriteLine();
}
// Driver program
public static void Main()
{
int[] arr = { 4, 6, 3, 2, 9 };
int n = arr.Length;
heapSort(arr, n);
Console.WriteLine("Sorted array is ");
printArray(arr, n);
}
}
// This code is contributed by vt_m.Javascript
输出：
Sorted array is
9 6 4 3 2时间复杂度： heapify需要O(logn ) ，构造 heap 需要O(n) 。因此，使用最小堆或最大堆的堆排序的总体时间复杂度为O(nlogn)
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