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Author: nitishtw

Competitive Coding/Sorting/Heap Sort/HeapSort.cpp

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+#include<bits/stdc++.h>
+using namespace std;
+#define rep(i,a,b,c) for(i=a;i<b;i+=c)
+#define repp(i,a,b,c) for(i=a;i>b;i+=c)
+
+//--------------------------------------Heapify 
+void max_heapify(int *a, int i, int n)
+{
+    int l=2*i+1;
+     int r=2*i+2;
+     int largest=0;
+     if(l<=n and a[l]>a[i])
+     	 largest=l;
+     else
+         largest=i;
+     if(r<=n and a[r]>a[largest])
+         largest=r;
+     if(largest!=i)
+        {
+        	swap(a[largest],a[i]);
+        	max_heapify(a,largest,n);
+        }
+}
+//---------------------------------Build max Heap
+void build_maxheap(int *a, int n)
+{
+	int i;
+     repp(i,n/2,-1,-1)
+    {
+    	max_heapify(a,i,n);
+    }
+}
+
+//-----------------------------------HeapSort
+void heapsort(int *a, int n)
+{
+	 int i;
+    build_maxheap(a,n);
+    repp(i,n,-1,-1)
+       {
+       	   swap(a[0],a[i]);
+       	   n--;
+       	   max_heapify(a,0,n);
+       }
+}
+
+int main()
+{
+    int n, i, x;
+    cout<<"Enter no of elements of array\n";
+    cin>>n;
+    
+    //Dynamic Memory Allocation
+    int *dynamic;
+    dynamic = new int[n];
+	
+	//Input Of Elements
+	cout<<"Enter the elements of array :\n";
+    rep(i,0,n,1)
+       cin>>dynamic[i];
+    
+    heapsort(dynamic,n-1);  
+    //Sorted Array using heap sort
+    cout<< "Sorted Sequence is : " ;
+	
+	rep(i,0,n,1)
+      cout<< dynamic[i]<<"\t";
+    delete []dynamic;
+}

Competitive Coding/Sorting/Heap Sort/Readme.md

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+# Heap sort is a comparison based sorting technique based on Binary Heap data structure.
+# Heapsort is an in-place algorithm, but it is not a stable sort.
+# Heap Sort is one of the best sorting methods being in-place and with no quadratic worst-case scenarios.
+# In max-heaps, maximum element will always be at the root. Heap Sort uses this property of heap to sort the array.
+
+Heap sort algorithm is divided into two basic parts :
+(1) Creating a Heap of the unsorted list.
+(2) Then a sorted array is created by repeatedly removing the largest/smallest element from the heap, and inserting it into the array. 
+{3) The heap is reconstructed after each removal.
+
+Time Complexity: Time complexity of heapify is O(logn). 
+Time complexity of BUILD-MAX-HEAP(A) is O(n) 
+and we run max_heapify N−1 times in heap_sort function,
+therefore complexity of heap_sort function in each case (Best, worst and average) is O(nlogn)
+
+Space Complexity: O(1)