Changed the .md file accordingly!!!

Author: blackeye735

Heapsort.md

@@ -163,7 +163,7 @@ The code below shows the operation.
          heapify(arr, i, 0);
        }
 
-Performance
+Performance:-
 
 Heap Sort has O(nlogn) time complexities for all the cases ( best case, average case and worst case).
 
@@ -185,169 +185,6 @@ Application of Heap Sort
 Systems concerned with security and embedded system such as Linux Kernel uses Heap Sort because of the O(n log n) upper bound on Heapsort's running time and constant O(1) upper bound on its auxiliary storage.
 
 Although Heap Sort has O(n log n) time complexity even for worst case, it doesn’t have more applications ( compared to other sorting algorithms like Quick Sort, Merge Sort ). However, its underlying data structure, heap, can be efficiently used if we want to extract smallest (or largest) from the list of items without the overhead of keeping the remaining items in the sorted order. For e.g Priority Queues.
-Heap Sort Implementation in different Programming Languages
-C++ Implementation
-
-    // C++ program for implementation of Heap Sort
-    #include <iostream>
-    using namespace std;
-    void heapify(int arr[], int n, int i)
-    {
-       // Find largest among root, left child and right child
-       int largest = i;
-       int l = 2*i + 1;
-       int r = 2*i + 2;
-       if (l < n && arr[l] > arr[largest])
-         largest = l;
-       if (right < n && arr[r] > arr[largest])
-         largest = r;
-       // Swap and continue heapifying if root is not largest
-       if (largest != i)
-       {
-         swap(arr[i], arr[largest]);
-         heapify(arr, n, largest);
-       }
-    }
-    // main function to do heap sort
-    void heapSort(int arr[], int n)
-    {
-       // Build max heap
-       for (int i = n / 2 - 1; i >= 0; i--)
-         heapify(arr, n, i);
-       // Heap sort
-       for (int i=n-1; i>=0; i--)
-       {
-         swap(arr[0], arr[i]);
-         
-         // Heapify root element to get highest element at root again
-         heapify(arr, i, 0);
-       }
-    }
-    void printArray(int arr[], int n)
-    {
-       for (int i=0; i<n; ++i)
-         cout << arr[i] << " ";
-       cout << "\n";
-    }
-    int main()
-    {
-       int arr[] = {1,12,9,5,6,10};
-       int n = sizeof(arr)/sizeof(arr[0]);
-       heapSort(arr, n);
-       cout << "Sorted array is \n";
-       printArray(arr, n);
-    }
-
-Java program for implementation of Heap Sort
-
-    // Java program for implementation of Heap Sort
-    public class HeapSort
-    {	
-      
-        public void sort(int arr[])
-        {
-            int n = arr.length;
-     
-          	// Build max heap
-            for (int i = n / 2 - 1; i >= 0; i--) {
-              heapify(arr, n, i);
-            }
-                
-     
-    		// Heap sort
-            for (int i=n-1; i>=0; i--)
-            {
-                int temp = arr[0];
-                arr[0] = arr[i];
-                arr[i] = temp;
-     
-              	// Heapify root element
-                heapify(arr, i, 0);
-            }
-        }
-     
-        void heapify(int arr[], int n, int i)
-        {
-          	// Find largest among root, left child and right child
-            int largest = i; 
-            int l = 2*i + 1; 
-            int r = 2*i + 2;  
-     
-            if (l < n && arr[l] > arr[largest])
-                largest = l;
-     
-            if (r < n && arr[r] > arr[largest])
-                largest = r;
-     
-          	// Swap and continue heapifying if root is not largest
-            if (largest != i)
-            {
-                int swap = arr[i];
-                arr[i] = arr[largest];
-                arr[largest] = swap;
-     
-                heapify(arr, n, largest);
-            }
-        }
-     
-        static void printArray(int arr[])
-        {
-            int n = arr.length;
-            for (int i=0; i < n; ++i)
-                System.out.print(arr[i]+" ");
-            System.out.println();
-        }
-     
-        public static void main(String args[])
-        {
-            int arr[] = {1,12,9,5,6,10};
-            HeapSort hs = new HeapSort();
-            hs.sort(arr);
-     
-            System.out.println("Sorted array is");
-            printArray(arr);
-        }
-    }
-
-Python program for implementation of heap sort (Python 3)
-
-    def heapify(arr, n, i):
-        # Find largest among root and children
-        largest = i
-        l = 2 * i + 1
-        r = 2 * i + 2 
-     
-        if l < n and arr[i] < arr[l]:
-            largest = l
-     
-        if r < n and arr[largest] < arr[r]:
-            largest = r
-     
-        # If root is not largest, swap with largest and continue heapifying
-        if largest != i:
-            arr[i],arr[largest] = arr[largest],arr[i]
-            heapify(arr, n, largest)
-     
-    def heapSort(arr):
-        n = len(arr)
-     
-        # Build max heap
-        for i in range(n, 0, -1):
-            heapify(arr, n, i)
-     
-        
-        for i in range(n-1, 0, -1):
-            # swap
-            arr[i], arr[0] = arr[0], arr[i]  
-            
-            #heapify root element
-            heapify(arr, i, 0)
-     
-    arr = [ 12, 11, 13, 5, 6, 7]
-    heapSort(arr)
-    n = len(arr)
-
-    print ("Sorted array is")
-    for i in range(n):
-        print ("%d" %arr[i])
 
+#The above algorithm for Heap Sort i.e. the Heap Sorting Algorithm is proposed by Argho Chakraborty!!!
+#Have a great fun.Love Coding,CHEERS!!!!