CS99 Fall 2001
Solutions to Prelim2 Sample Problems
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1a. Algorithm
    Spew one box of random size(1 to 5) from chute
    If the amount of carts(8) and amount of boxes(40) is not exhausted:
    + If the current box is not a #5
       -Place the box on the current cart
       -Increment total number of boxes on carts
    + Otherwise
       -Increment the cart count
       -Check if the carts are exhausted
    + If the carts are not exhausted,
       -Place the current box on the new cart
       -Increment total number of boxes on carts
    + Repeat 
    If necesary, adjust the cart count and/or box count to account for 
    whether or not they were incremented too many times
    Report the number of carts used and total boxes taken
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1b. Program 
%Initialize data to test:
MIN=1;             %named constant for minimum box size
MAX=5;             %named constant for maximum box size
maxBoxes=40;       %max # of boxes that the company produces
totalBoxes=12;     %total # of boxes taken so far
cartTotal=8;       %total amount of carts
cartCount=3;       %cart count so far
currentBox=floor(rand*(MAX-MIN+1))+floor(MIN); % random size

%Attempt to place boxes on carts until boxes or carts are used up:
while (cartCount<=cartTotal & totalBoxes+1<=maxBoxes)
   
   if (currentBox~=MAX)             %Stack boxes on old cart
      totalBoxes=totalBoxes+1;
   else						%#5 box starts new cart
      cartCount=cartCount+1;
      if (cartCount<=cartTotal)   %can #5 be stacked?
      totalBoxes=totalBoxes+1;
      end   
   end
   
   currentBox=floor(rand*(MAX-MIN+1))+floor(MIN);
   
end

%Report number of carts used and total number of boxes on all carts:
if (cartCount>cartTotal)
   cartCount=cartCount-1;
   disp(['Final total: ',num2str(totalBoxes)]);
   disp(['Final carts: ',num2str(cartCount)]);
end

% there is a way of compressing the solution even further by changing the
% while condition a bit....
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2.
%  Script file: cable.m
%
%  Purpose: 
%    To calculate the connection point that results in
%    minimum tension on a cable. 
%
%  Record of revisions:
%      Date       Programmer          Description of change
%      ====       ==========          =====================
%    02/18/00    S. J. Chapman        Original code 
%
% Define variables:
%   dist          -- Distance to attachment (ft)
%   lc            -- Cable length (ft)
%   ii            -- index variable
%   lp            -- Pole length (ft)
%   saved_dist    -- Save attachment distance
%   saved_tension -- Saved tension
%   tension       -- Tension on cable
%   weight        -- Weight of object (lbs) 

% Initial values
lc = 8;                 
lp = 8;
weight = 200;
clear dist tension

% Calculate tension at 0.1 ft
dist(1) = 1.0;
tension(1) = weight * lc * lp ...
           / ( dist(1) * sqrt(lp^2 - dist(1)^2) );

% Save these initial values for comparision
saved_dist = dist;
saved_tension = tension;

% Calculate for other values between 1 and 7 ft
for ii = 2:60

   % Calculate tension
   dist(ii) = ii/10 + 1;
   tension(ii) = weight * lc * lp ...
              / ( dist(ii) * sqrt(lp^2 - dist(ii)^2) );
              
   % Find minimum tension point
   if tension(ii) < saved_tension
   
      saved_tension = tension(ii);
      saved_dist = dist(ii);
      
   end
end
 
% Display minimum tension point
disp(['Minimum tension at ' num2str(saved_dist)]);
disp(['Minimum tension = ' num2str(saved_tension)]);

% Plot tension vs distance
figure(1);
plot(dist,tension,'b-','LineWidth',2);
grid on;
title('\bfPlot of tension vs attachment distance');
xlabel('\bfDistance');
ylabel('\bfTension');
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3.
%  Script file: geometric_mean.m
%
%  Purpose: 
%    To calculate the geometric mean of a set of positive
%    numbers.
%
%  Record of revisions:
%      Date       Programmer          Description of change
%      ====       ==========          =====================
%    02/26/00    S. J. Chapman        Original code 
%
% Define variables:
%   x     -- Input values
%   g     -- Geometric mean
%   nvals -- Number of input values
%   prod  -- Product of input values

% Initialize product and nvals
prod = 1;
nvals = 0;

% Read the first number
x = input('Enter first number: ');

% Read the remaining numbers
while x > 0
   prod = prod * x;
   nvals = nvals + 1;
   x = input('Enter next number:  ');
end

% Calculate geometric mean
g = prod ^ (1/nvals);

% Tell user
fprintf('The geometric mean is %.4f\n',g);
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4. 
radius = str2double(input('  Enter a radius: ','s'));
while ~isreal(radius) | isinf(radius) | isnan(radius) | ~isnumeric(radius)
   disp('  Please enter a real, finite number: ');
   radius = str2double(input('  Enter a radius: ','s'));
end

num=1;
for theta=0:(2*pi)/200:(2*pi)
   x(num)=radius*cos(theta);
   y(num)=radius*sin(theta);
   num=num+1;
end
plot(x,y,'-');
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5. 
a=input('Enter a 1-D array: ');
[rows,cols]=size(a)
A=zeros(cols)
rows=cols;
%for each row 
for i=1:rowss
   % for each column
   for j=1:cols
      %1D array on the diagonal
      A(i,i)=a(i);
      %"reverse diagonal"
      A(i,cols-i+1)=a(cols-i+1);
   end
end
A
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