Solutions to some old exam questions
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%Question 1

  function p = pascalVector(lev)
  % p is the vector corresponding to level lev of Pascal's triangle
  %
  % (Mostly) Non-vectorized version

  p= 1;   % values in level 0 of Pascal's triangle
  for currentLevel= 1:lev
      % Temporary vec (q) for current level is one cell longer than prev level
      q= ones(1,currentLevel+1);

      % Use the general formula for INTERNAL entries
      for i= 2:length(p)         
          q(i)= p(i-1) + p(i);   
      end

      p= q;  % Update p
  end

  % p=q is actually vectorized. Truly non-vectorized code is:
  %     for i= length(q):-1:1
  %        p(i)= q(i);
  %     end

  ----------------------------------

  function p = pascalVector(lev)
  % p is the vector corresponding to level lev of Pascal's triangle
  %
  % First build a Pascal's MATRIX, then extract the row

  m= ones(lev+1, lev+1);
  for currentLevel= 1:lev
     for c= 2:currentLevel  % "interior" entries only
        m(currentLevel+1, c) = m(currentLevel, c-1) + m(currentLevel, c);
     end
  end
  p= m(lev+1, :);  % p is just the last row of pascal matrix


  ----------------------------------

  function p = pascalVector(lev)
  % p is the vector corresponding to level lev of Pascal's triangle
  %
  % Vectorized version

  p= [1];  % values in level 0 of Pascal's triangle
  for currentLevel= 1:lev
      p = [p 0] + [0 p];     % each level is one cell longer, so shift and add
  end


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%Question 2

  function MyHistogram(v)
  % Draw a histogram for the data in v using asterisks in the COMMAND WINDOW.
  % v is a vector of non-negative values.
  % The histogram is scaled so that the largest data value is represented by 
  %   ten asterisks.  Round as necessary in order to draw whole asterisks.
  % Example:  v = [12  4.1  0.5  9.2  20]
  % Output in Command Window:
  %    ******
  %    **
  %    
  %    *****
  %    **********

  multiplier= 10/max(v);
  scaledV= round(multiplier*v);

  for r= 1:length(v)
      astr= ' ';
      for c= 1:scaledV(r)
          astr= [astr '*'];
      end
      disp(astr)
  end


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%Question 3

  function alfa = isIn(x, v)
  % alfa is 1 if value x is in vector v.  Otherwise alfa is 0.
  % x is an integer.  v is a vector of integers, possibly of length 0. 
  % If v has length 0 (v is the empty vector), then alfa is 0.

  alfa= 0;
  k= 1;
  while  k<=length(v) && alfa==0
    alfa= x==v(k);
    k= k+1;
  end

  function s = intersectionSet(a,b)
  % a and b are vectors of integers.  a and b are not empty.
  % Vector s contains only the values that are in both vectors a and b.
  % Vector s contains distinct values.  s may be empty.

  s= [];
  for k= 1:length(a)
    if ~isIn(a(k),s) && isIn(a(k),b)
        s= [s a(k)];
    end
  end


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%Question 4

  function z = overlap(diskA, diskB)
  % z is 1 (true) if diskA and diskB overlap; otherwise z is 0 (false).
  % diskA and diskB are each a disk structure with the following fields:
  %   x: x-coordinate of center of disk
  %   y: y-coordinate of center of disk
  %   radius: radius of disk

  dis = sqrt((diskA.x - diskB.x)^2 + (diskA.y - diskB.y)^2);

  if dis < diskA.radius + diskB.radius

      z = 1;
  else
      z = 0;
  end


  function idx = diskTriplets(D)
  % D is a 1-d array of disk structures; each structure has fields as defined in 
  %   part (a). Assume D has a length greater than 3.
  % idx is a vector of indices indicating all triplet overlap combinations. For example,
  %   if disks 2, 4, and 5 form a triplet and disks 3, 4, and 6 form a triplet, idx
  %   should be the vector [2 4 5 3 4 6].  Other orderings of triplets are acceptable,
  %   however each triplet should only appear once.

  n = length(D);

  idx = [];

  for i = 1:n - 2

      for j = i + 1:n - 1

          for k = j + 1:n

              if overlap(D(i), D(j)) && ... 
                 overlap(D(j), D(k)) && overlap(D(i), D(k))

                  idx = [idx, i, j, k];
              end
          end
      end
  end