removeMax: Remove and return the element whose key has maximum value from the binary heap. In class, we discussed how this operation can be performed in O(log, n) time for a binary heap. Prove, for a binary heap, that any algorithm for the removeMax operation requires N(log, n) operations in the worst case. Hint: Prove the claim via reduction (using contradiction). Is there some problem you could solve faster (than what we know to be impossible) if you could accomplish, obtaining a o(log, n)-time algorithm in the worst case here?

Modify maxHeap.java and heapApplication.java to build a minimum heap and test it. import java.util.*; public class maxHeap{    public int heapSize, capacity;    public int[] Arr;    public maxHeap(int cap)    {        heapSize = 0;        capacity = cap;        Arr = new int[cap];    }     public void heapify(int parent)    {        int Lson, Rson, largest, temp;        Lson = 2 * parent + 1;        Rson = 2 * parent + 2;        /* find the largest among A[parent], A[lson] and A[rson] */        if ( Lson <= heapSize - 1 && Arr[Lson] > Arr[parent] )        {            largest = Lson;        }        else        {            largest = parent;        }        if (Rson <= heapSize - 1 && Arr[Rson] > Arr[largest] )        {            largest = Rson;        }        if (largest != parent)        {            temp = Arr[parent];            Arr[parent] = Arr[largest];            Arr[largest] = temp;            heapify(largest);        }     }     public void…

Python code please thank you!!

For a given heap below: M (K A F H. The array representation of the heap is givep below. 1 2 3 4 Y W M 15 K 11 H. 6. 10 12 F a) Delete the root node, give the resulting heap. 3 1 2 4 6 10 11 12 b) Insert Q into the original heap, give the resulting heap. 3 12 4 16 10 11 12 TTTT Paragraph E- E T Arial 3 (12pt) T T. OS. Mashups HTML CSS O Type here to search