Review questions for Prelim 3
-----------------------------

1. allInterval

function B = allInterval(x,a,b)
% x is a length-n vector.
% B is assigned the value of 1 (true) if every x-value is in the
%   interval [a,b].
% B is assigned the value of 0 (false) if at least one of the x-values
%   is not in the interval [a,b].
% Your implementation should make effective use of a while-loop.





2. Transpose

% Refer to the 4/8 lecture and the function TheDigits:

C = TheDigits;

% C is a length 10 cell array with the property that C{k} is
% a 7-by-5 bitmap of the digit k (regarding 0 as the "tenth" digit.)
% Produce a length 10 cell array D which houses 5-by-7 bitmaps
% of the "transposed" arrays. Thus, since
%
% C{1} looks like
% 00100
% 01100
% 00100
% 00100
% 00100
% 00100
% 01110
% then D{1} should look like
%
% 0000000
% 0100001
% 1111111
% 0000001
% 0000000
%
% Do not use the transpose operator '





3. TotalValue

% Refer to the Cost-Inventory application in Lecture 15 (3/11).
% Complete the following function...





4. Checking for numbers in a vector/matrix.  Complete the following functions

function B = vecHasNegAndPos(x)
% x is a length-n vector and n>=2
% B is assigned the value of 1 (true) if x has at least one component
%   that is strictly negative and at least one component that is
%   strictly positive.
% Otherise B should be assigned the value of 0.
% Your implementation should make effective use of a while-loop.


function B = matHasNegAndPos(A)
% A is an m-by-n real array with M>=2 and n>=2
% B is assigned the value of 1 (true) if A has at least one component
%   that has a strictly negative value and at least one component that has a
%   strictly positive value.
% Otherise B should be assigned the value of 0.
% Your implemention should make effective use of VecHasNegAndPos




5. TwoClicks

% Refer to Lecture 15 (3/11) and the function RandomLink(n).

A = RandomLink(1000);

% Note that if A(i,j) is one, then there is a link on webpage i
% to webpage j. Write a fragment that prints "yes" if it is
% possible to go from web page #100 to webpage #200 in one or two clicks.
% Thus, if A(100,101) = 1 and A(101,200) = 1 then "yes".




6. TopHalf

function C = topHalf(A)
% Refer to Lecture 20 (4/3).
% Suppose A is a length-50 structure array with two fields
% Assume A(k).name is a string that names a state and A(k).pop
% is an integer whose value is the states population.
% Assume that the states are ordered alphabetically.
% C is a length-25 cell array of strings that names all the
% states whose populations are above the median state population.
% The states should be ordered alphabetically in C.




7. BigTriplets

function N = BigTriplets(A)
% Refer to lectures 19 (4/1) and 20 (4/3).
% Suppose A is a length-50 structure array with two fields.
% Assume A(k).name is a string that names a state and A(k).pop
% is an integer whose value is the states population.
% We say that three different states form a "big triplet" if
% the sum of their populations is greater than 15 million.
% N is the number of big triplets.




8. Reduce

function B = Reduce(A)
% A is an n-by-n array with n odd and at least 3 in value.
% B is obtained by deleting all the even-indexed rows and columns.
% Thus if
% A = [ 1  2  3  4  5 ;...
%       6  7  8  9 10 ;...
%      11 12 13 14 15 ;...
%      16 17 18 19 20 ;...
%      21 22 23 24 25 ]
% then
% B = [ 1  3  5;...
%      11 13 15;...
%      21 23 25]




9. ColorComps

A = imread(’LawSchool.jpg’);
% Matlab assumes that Red pixel values in first layer, e.g., A(:,:,1)
% Matlab assumes that Green pixel values in first layer, e.g., A(:,:,2)
% Matlab assumes that Blue pixel values in first layer, e.g., A(:,:,3)

[m,n,p] = size(A);
% Set up B so image(B) displays the law school but with the rgb values
% permuted. In particular, at each pixel, red is displayed at the
% green intensity level, green is displayed at the blue intensity level,
% and blue is displayed at the red intensity level

B = uint8(zeros(m,n,p));

% Write your code fragment here

image(B)


% Refer to the function Edges from Lecture 17 (3/25).
% We want to display the clock tower with the edge pixels highlighted.
% To that end, modify the array A so that if B(i,j)>20 then pixel
% (i,j) is displayed as white
B = Edges(’Tower.jpg’))

% Modify A
A = imread(’Tower.jpg’)

% Write your code fragment here

image(A)





10.  Longest

function [len, ind] = longest(C)
% Find the longest string(s) in cell array C.
% C is an n-by-1 cell array of strings, n>=1.
% len is the length of the longest string in C.
% ind is a vector, possibly of length one, containing the index number(s) 
% of the string(s) with length len




11.  Shuffle cards

% Given the following cell arrays of strings:
suits= {’Hearts’, ’Clubs’, ’Spades’, ’Diamonds’};
ranks= {’Ace’, ’2’, ’3’, ’4’, ’5’, ’6’, ’7’, ’8’, ’9’, ’10’, ...
        ’Jack’, ’Queen’, ’King’};

% Write a code fragment to create a structure array of cards such 
% that each structure has two fields, suit and rank, that store the
% appropriate strings.  The structure array should be of length 52.
% Do a perfect shuffle of the cards.




12.  Point struct

% Given a structure array Pts where each structure has two fields, x and y,
% sort Pts so that the structures are in the order of 
% increasing distance from (0,0)