CS99

Summer 2002

HW6 Solutions

1. Sisyphus, the Snail
clear all;
well_height = input(‘Enter well height: ‘);
up = input(‘Enter distance snail can travel during day while rested: ‘);
down = input(‘Enter distance snail slides down at night: ‘);
fatigue = input(‘Enter the fatigue factor: ‘)/100;
curr_up = up; %current climbing ability
curr_height = 0; %current height of snail
day = 1;
fprintf(‘Calculating …’);
while curr_up >= 0
curr_height = curr_height + curr_up;
%has the snail climbed out of well? is it going to hit bottom later? if so, break
if curr_height > well_height | curr_height < down
break;
end
%at night, snail slides
curr_height = curr_height – down;
%calculate new climbing ability
curr_up = curr_up – fatigue*up;
day = day + 1;
end
%report results
if curr_height >= well_height
fprintf(‘The snail climbs out on day %d.’, day );
else
fprintf(‘The snail is stuck in the well on day %d.’, day);
end

2. Goldbach’s conjecture
Solution 1.
disp(‘Please enter a sequence of even numbers, each greater or equal to 4. ‘);
n = input(‘> ‘);
while mod( n, 2 ) == 0 & n > 4
p = primes( n );
fprintf(‘%d’, n );
pairs = 0;
for k = 1 : length( p )
for m = k : length( p )
if p(k) + p(m) == n
fprintf(‘ = %d + %d’, p(k), p(m));
pairs = pairs + 1;
end
end
end
fprintf(‘. (%d pair’, pairs );
if pairs > 1
fprintf(‘s)\n’);
else
fprintf(‘)\n’);
end
n = input(‘> ‘);
end
disp(‘Bye!’);

Solution 2.
disp(‘Please enter a sequence of even numbers, each greater or equal to 4. ‘);
n = input(‘> ‘);
pairs = 0;
while mod( n, 2 ) == 0 & n >= 4
fprintf(‘%d ‘, n );
for ii = 1 : n/2
if isprime( ii ) & isprime( n – ii )
pairs = pairs + 1;
fprintf(‘ = %d + %d’, ii, n - ii);
end
end
fprintf(‘. (%d pair’, pairs );
if pairs > 1
fprintf(‘s)\n’);
else
fprintf(‘)\n’);
end
n = input(‘> ‘);
end
disp(‘Bye!’);