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Question 1: (10 points)
Part (a): (4 points)
What will be displayed at the end of each fragment below? If there is an error write the word “error” in the box.
w = [2 3]; x = w(w(1))
z = [2 3 1]; for k = 1:length(z) z(k+1) = z(k); end disp(z)
Part (b): (6 points)
What will be printed when the following script is executed?
Script Function Output a=2; b=6; c=3; d= zoo(c,b); fprintf('a is %d\n', a); fprintf('b is %d\n', b); fprintf('d is %d\n', d);
function a = zoo(b,c) b= b/c; a= b; fprintf('c is %d\n', c);
c is 6 a is 2 b is 6 d is 0.
Output
Output x = 3
Question 2: (20 points)
Complete each of the functions below according to the specifications. Do not use function find.
Part (a): (10 points)
function h = histData(yr, maj) % h is the data for drawing a bar graph showing the number of UNDERGRADUATE % students in each of the 90 majors at Cornell. % yr and maj are vectors of the same length. For a valid index k: % yr(k) is the year code of student k. Possible values are integers % in [1..13]; values 1,2,3,4 indicate undergraduate. % maj(k) is the major code of student k; possible values are integers % in [1..90]. % Assume that the length of yr (and maj) is greater than 1. h= zeros(1,90); % h(i) will be the number of undergrads in major i
for k= 1:length(yr)
if yr(k)<
h(maj(k)) = h(maj(k)) + 1; end end
bar(1:90, h) title(‘Number of UNDERGRADUATE students in each major’)
Part (b): (10 points)
function s = smoothVec(v) % Smooth vector v by averaging each "interior" value with its left and right % neighbors. s is the smoothed vector and is two components shorter than v. % Example: If v=[-2 5 3 4 8] then s=[2 4 5] % Assume that the length of v is greater than 2.
for k= 2:length(v)-
s(k-1) = (v(k-1)+v(k)+v(k+1))/3; end
Question 4: (25 points)
Write the function header for the function below. The function name is checkLengths. It has two input parameters, a and b, and returns two vectors, shortV and longV.
function [shortV, longV] = checkLengths(a,b) % a and b are vectors with length>1; assume their lengths are different. % shortV is the shorter vector between a and b. % longV is the longer vector between a and b.
if length(a)<length(b) shortV= a; longV= b; else shortV= b; longV= a; end
Complete the function below to interleave two vectors. You must use function checkLengths from Part (a) above as part of your solution. Do not use vectorized code!
function v = interleave(a,b) % Interleave the values from vectors a and b to form vector v. % a and b are vectors with length > 1; assume their lengths are different. % The first value in v comes from the longer vector of a and b. % The "leftover" values from the longer vector are copied to the end of v. % For example, if a=[10 90 30] and b=[8 4 5 2 4] % then v=[8 10 4 90 5 30 2 4] % NO VECTORIZED CODE!
[S, L]= checkLengths(a,b); % S is shorter than L
nS= length(S); nL= length(L); v= zeros(1,nS+nL); % not necessary to pre-allocate v iv= 1; % next index position of vector v
% Interleave up to length of short vector for k= 1:nS v(iv)= L(k); iv= iv+1; v(iv)= S(k); iv= iv+1; end
% Copy over leftovers from long vector for k= nS+1:nL v(iv)= L(k); iv= iv+1; end
Question 5: (25 points)
Complete the function below to draw a set of grayscale disks arranged in a triangle. Read the specifications in the function comment. An example figure is shown on the right with n=6, s=0.5. Assume the availability of function DrawDisk and recall that you can specify a color in Matlab using a vector of length 3:
colr = [1 1 1]; %white DrawDisk(5,0,1, colr )
draws a white disk with radius 1 centered at (5,0). The grid lines and “color values” are shown on the diagram on the right for your convenience; you do not have to draw them.
function grayness(n,s) % Draw a triangle of disks; there are n disks on each side of the triangle. % The disk in row 1 is black [0 0 0]; the disks in row n are white [1 1 1]; % the rows in between vary uniformly in grayness. % The disks have unit radius and are spaced s units apart. % The center of the lower left disk is at (0,0).
close all; figure; axis equal; hold on
d= 2+s; % distance from center to center g= 1/(n-1); % "distance" between grayness
for r= n:-1:
y= (n-r)*d;
colr= (r-1)*g; % color for this row
for c= 1:r
x= (c-1)*d;
DrawDisk(x,y,1,colr*ones(1,3))
end end
hold off
-2 0 2 4 6 8 10 12 14
0
2
4
6
8
10
12
[1.0 1.0 1.0]
[0.8 0.8 0.8]
[0.6 0.6 0.6]
[0.4 0.4 0.4]
[0.2 0.2 0.2]
[0.0 0.0 0.0]
