QUESTION 9A Verify thаt {} is аn оrthоgоnаl set and then find the orthogonal projection of y onto Span {}
Prоgrаmming: Stаcks, Lists, Generics Linked lists аre a very typical data structure used in ADTs like stacks, оr queues. Fоr this question, implement the list operation shown below: deleteKth. The first element is K=0 like an array. This method will search for the Kth element in a doubly linked list, delete it, and return the head of the modified list. Assume that the list will always be long enough to find the Kth element. Although the list is doubly linked, you only have a reference to it's head (not tail). The DoubleNode class may be used, but you may not import any packages. public class DoubleNode { private DoubleNode next; private DoubleNode prev; public T element; //shouldn't be needed! public DoubleNode(T elem) { next = prev = null; element = elem; } public DoubleNode getNext() { return next; } public void setNext(DoubleNode node) { next = node; } public DoubleNode getPrev() { return prev; } public void setPrev(DoubleNode node) { prev = node; } } //Given the head of a doubly linked list, removes the node at the Kth position in the //list. Assume that the list will always be long enough to find the Kth element. (This //implies the list is non-empty.) Returns head of modified list. //EXAMPLES: deleteKth([A, B, C], 0) returns [B, C] // deleteKth([A, B, C], 1) returns [A, C] // deleteKth([A], 0) returns an empty list // where brackets show the contents of the list at a high level (the actual // value will be head of that list) and the left most node is the head. public static DoubleNode deleteKth(DoubleNode head, int K)
Prоgrаmming (Repаir): Dаta Abstractiоn Fоr this question, you will debug a method from the Matrix you were assigned for homework. In the homework, you were asked to implement an immutable Matrix ADT. Below we give a partial implementation of CompletedMatrix. Unfortunately, the provided equals() method has incorrect behavior. All other methods have a correct implementation and may not be changed. Based on the interface description for equals(), fix the method so it gives the correct behavior. The other (correct) methods have been provided to give you additional context and help you to understand the overall solution. You may not import any packages. The equals() method has three different bugs: for each bug, describe the issue conceptually and then explain how it may be fixed (e.g., give the corrected code). You should assume that the code provided already compiles and no compilation bugs must be fixed, only logical bugs. package edu.ser222.m01_02; public class CompletedMatrix implements Matrix { private final int[][] data; public CompletedMatrix(int[][] matrix) { if(matrix == null) throw new IllegalArgumentException(); data = new int[matrix.length][]; for(int y = 0; y < data.length; y++) data[y] = matrix[y].clone(); } public int getElement(int y, int x) { return data[y][x]; } public int getRows() { return data.length; } public int getColumns() { if(getRows() == 0) return 0; else return data[0].length; } public Matrix plus(Matrix other) { if(other == null) throw new IllegalArgumentException(); if(getRows() != other.getRows() || getColumns() != other.getColumns()) throw new RuntimeException("Incompatible matrix dimensions."); int[][] result = new int[getRows()][getColumns()]; for(int y = 0; y < getRows(); y ++) for (int x = 0; x < getColumns(); x++) result[y][x] = data[y][x] + other.getElement(y, x); return new CompletedMatrix(result); } //omitted: scale(), minus(), mutiply() /** * Returns true if this matrix matches another matrix. * @param other another matrix * @return equality */ @Override public boolean equals(Object other) { //TODO: the following method implemenation is buggy! if (other == null) return false; if (other.getClass() == this.getClass()) return true; if(getRows() != other.getRows() && getColumns() != other.getColumns()) return false; for(int y = 0; y < getRows(); y++) for (int x = y; x < getColumns(); x++) if(data[y][x] != ((CompletedMatrix)other).getElement(y, x)) return false; return true; } }