Review questions

Review the prelims as well as the review questions for the prelims!

  1. Point class and sorting algorithm

    % Given an array of Point objects Pts where each object has two properties,
% x and y, sort Pts so that the objects are in the order of
% increasing distance from (0,0)
% Write two different scripts to solve this problem:
%  (a) Make effective use of built-in function sort.
%  (b) Use the INSERTION SORT algorithm; do not use built-in function sort.

  2. Lecture 27

    Consider the following function:

    function y = mergeSort(x)
% x is a column n-vector.
% y is a column n-vector consisting of the values in x sorted
%   from smallest to largest.

n = length(x);
if n==1
   y = x;
else
   m = floor(n/2);
   % Sort the first half..
   yL = mergeSort(x(1:m));
   % Sort the second half...
   yR = mergeSort(x(m+1:n));
   % merge...
   disp('Call merge')
   y = merge(yL,yR);
end

    How many lines of output are produced by the call y = mergeSort(rand(7,1))?

  3. Lecture 26

    Consider the function

    function MeshTriangle(x,y,L)
% x and y are 3-vectors.  L is a nonnegative integer.
% Adds to the current figure window a level-L partitioning of the
%    triangle whose vertices are specified by the 3-vectors x and y.
% Assumes that hold is on.

if L==0
   % No subdivision required...
   fill(x,y,'y','linewidth',1.5)
else
   % A subdivision is called for...
   % Determine the side midpoints (a(1),b(1)), (a(2),b(2)), and (a(3),b(3))
   a = [(x(1)+x(2))/2 (x(2)+x(3))/2 (x(3)+x(1))/2];
   b = [(y(1)+y(2))/2 (y(2)+y(3))/2 (y(3)+y(1))/2];
   % Color the interior triangle magenta...
   fill(a,b,'m','linewidth',1.5)
   % Apply the process to the three "outer" triangles...
   MeshTriangle([x(1) a(1) a(3)],[y(1) b(1) b(3)],L-1)
   MeshTriangle([x(2) a(2) a(1)],[y(2) b(2) b(1)],L-1)
   MeshTriangle([x(3) a(3) a(2)],[y(3) b(3) b(2)],L-1)
end

    Assume that the length-3 vectors x and y define an equilateral triangle and that MeshTriangle(x,y,2) is executed. What fraction of the original triangle is displayed yellow?

  4. Lab 13

    Suppose z = MyF(x) is a function that accepts a real value x and returns a real value y. Assume that MyF() is very expensive to evaluate. Write a script that sets up an n-by-n array Z with the property that Z(i,j) is assigned the value of MyF(1+abs(i-j)). Assume that n is initialized.

  5. Lecture 26/27

    Assume that insertSort(x) is faster than mergeSort(x) if the length of the input vector is less than 500. How would you modify the mergeSort() function to make it more efficient?

  6. Matrix

    % Let A be a connectivity matrix, i.e.,
% if A(i,j) is one, then there is a link on webpage j
% to webpage i. Write a fragment that prints "yes" if it is
% possible to go from web page #100 to webpage #200 in one or two clicks.
% Assume that the number of webpages is >=200.
% Thus, if A(101,100) = 1 and A(200,101) = 1 then "yes".

  7. OOP

    Refer to class Interval from Lecture 22. Implement the following function:

    function idxs = greatestOverlap(iArray)
% Find the biggest pairwise overlap between Intervals in iArray.
% iArray is an array of Interval references.  iArray has a length greater than 1.
% idxs is a vector of length 2 storing the indices of the two Intervals in
%   iArray that overlap the most.  If there is not a pair of overlapping
%   Intervals in iArray, idxs is the empty vector.
% Write efficient code:  avoid unnecessary iteration.

  8. OOP

    Implement the following class as specified:

    classdef LengthUnit < handle
% A LengthUnit represents a length (distance) in imperial units: feet and
% inches.  The values are non-negative and inches must be less than 12.

    properties
       feet    % a non-negative integer value
       inches  % a non-negative value
    end

    methods

        function L = LengthUnit(ft, in)
        % Constructor: Create a LengthUnit object with ft feet and in inches.
        % If one or both parameters are negative, halt the program and
        % display an error message.

          %--Write your code here

        end

        function ft = inFeet(self)
        % self references a LengthUnit.  ft is self represented in feet.

          %--Write your code here

        end

        function L = add(self, other)
        % self and other reference LengthUnits.  L references a new
        % LengthUnit that is the sum of self and other.

          %--Write your code here

        end

        function yesno = isLongerThan(self, other)
        % self and other reference LengthUnits.  yesno is true (1) if
        % self is longer than other; otherwise yesno is false (0).
        % For full credit, make effective use of method inFeet.

          %--Write your code here

        end

    end %methods

end %classdef

  9. OOP

    Write a script that

    1. generates 10 values, each uniformly random in (0,50). Let these random values be lengths in inches and use an array of LengthUnit objects to store these lengths.
    2. determines which LengthUnits are shorter than or equal in length to the first LengthUnit in the array; display their indices and their lengths in feet. Make efficient use of available methods in class LengthUnit.

  10. Questions from Insight

    Errata: P14.1.3 part (b) should read “... then the reverse of s is the concatenation of the reverse of s(2:n) and s(1) in that order.” The subvector was incorrectly specified as s(1:n-1).

    Please see the Insight Errata link for the full errata list.