CS 99
Summer 2002: Lab 6
Solutions

1. Matrix manipulations

%RandArray.m
M = input('Enter M: ');
N = input('Enter N: ');
A = rand( M, N )
for ii = 1 : M
    for jj = 1 : N
        if A( ii, jj ) < 1/pi
             A( ii, jj ) = 0;
        else
             A( ii, jj ) = 1;
        end
    end
end
A
%Alternate way without for loops:
%A( A < 1/pi ) = 0; A( A > 0 ) = 1;

2. Course scores

%Scores.m
marks = floor( 101*rand( 20, 3 ) );
grade = 0.2*marks(:, 1) + 0.2*marks( :, 2) + 0.6*marks( :, 3 )

3. Dominating permutations

Part A.

%Dominate.m
clear all;
n = input('Enter a size for the array: ');
nums = ceil( rand(1, n )*n );
isDom = 1;
for j = 2 : ( n - 1 )
        if nums( j - 1 ) > nums( j ) & nums( j + 1) > nums( j )
            isDom  = 0;
        end
end

if isDom
    disp( [ num2str( nums ) ' is dominating!' ] );
else
    disp( [ num2str( nums ) ' is not dominating.' ] );
end

Part B.
%DominateFact.m
clear all;
n = input('Enter a value for n: ');
myperms = perms( 1 : n ); %assign to myperms a matrix containing all the permutations of 1:n
count = 0; %number of dominating permutations

for i = 1 : length( myperms )
    nums = myperms( i, : ); %assign nums to current row of perms
    isDom = 1;
    for j = 2 : ( n - 1 )
            if nums( j - 1 ) > nums( j ) & nums( j + 1 ) > nums( j ) %not dominating
                isDom = 0;
            end
    end
    %report results for current row
    if isDom
        count = count + 1;
        disp( [ num2str( nums ) ' is dominating!' ] );
    end
end
disp(['The fraction which are dominating is ' num2str( count/length(myperms) ) ] );
disp(['The theoretical result is is ' num2str( 2^(n-1)/prod(myperms(1, :) )) ] );