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. TotalValue

% Refer to the Cost-Inventory application in Lecture 13.
% Complete the following function...

function T = totalValue(Inv,Cost)
% T is the total value of all the inventory in all the factories




3. Censoring text
% Refer to Lec 17 on characters and strings and implement this function:

function D = censor(str, A)
% Replace all occurrences of string str in character matrix A, regardless
% of case, with 'X's.
% A is a matrix of characters.
% str is a string.  Assume that str is never split across two lines in A.
% D is A with 'X's replacing the censored string str.
%
% Example:   A = ['Use MATLAB  '; ...
%                 'in that lab.']
%
%   and      str = 'lab'
%
%   Then     D = ['Use MATXXX  '; ...
%                 'in that XXX.']




4. TwoClicks

% Refer to Lecture 13 and the function RandomLinks(n).

A = RandomLinks(1000);

% Note that 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.
% Thus, if A(101,100) = 1 and A(200,101) = 1 then "yes".




5. Transpose

% Refer to Lecture 21 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 '




6. Checking for numbers in a vector/matrix

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




7. 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]




8.  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




9. TopHalf

function C = topHalf(A)
% Refer to Lecture 21.
% 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.

% Obtain a vector of populations...
pop = zeros(50,1);
for k=1:50
   pop(k) = A(k).pop;
end

[y,idx] = sort(pop);
% Note that idx(k) is the index of the kth smallest state.
% Above-the-median states have indices idx(26),..,idx(50).
% Put these indices in a single, length-25 vector

Above = idx(26:50);
% Without the following step the "big" states wont be assembled in alphabetical
% order...

Above = sort(Above);

% This assembles the state names in C...
C = cell(25,1);
for k=1:25
   j = Above(k);
   str = A(j).name;
   C{k} = str;
end



10. BigTriplets
function N = BigTriplets(A)
% Refer to the Lectures 20 and 21.
% 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.




11.  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)




12. Questions from "Insight":
      M7.1.3 
      P8.1.5 (Clarification: y is a row vector that is the left shift of x) 
      P8.1.8
      P9.1.4 (do not use function <tt>deblank</tt>)
      P9.1.7 (do not use built-in functions strfind or find)
      P9.1.9 (count lower case letters only)
      P9.2.5