Question

#!/usr/bin/php <?php $A = array( 1, 2, 3, 4 ); $B = array( 1, 2, 3, 4); foreach($A as $i) { foreach ($B as $j) { print ("Foo\n"); 11 foreach($A as $i) { foreach($B as $j) { if ($i < $j) print ("Bar\n"); } F (a) How many times will the script output foo? (Hint: See example 9.2.5 in your textbook.) (b) How many times will the script output bar? (Hint: Make a chart to see the pattern.) (c) Suppose the arrays A and B both contained the numbers 1 through n. How many times would the script output bar? (Formula, not number.)

Answer 1

(a) A and B both the array contain elements from 1 to 4 . For each element of A the script prints foo 4 times. Since there are 4 elements in array A. Thus the number of foo output is 4X4=16

(b) When $i is 1, bar will be printed 3 times when $j is 2,3,4

When $i is 2, bar will be printed 2 times when $j is 3,4

When $i is 3, bar will be printed 1 times when $j is 4

When $i is 4, bar will be printed 0 times

Thus number of times of bar output is (3+2+1) = 6

(c) Following the same logic as (b)

When $i is k, bar will be printed (n - k) times where k can take value in 1,2,...,n

Thus total number of "bar" output is

(n-1 ) + (n-2) + (n - 3) + ... + 1

= (n-1)n/2 [sum of first (n-1) natural numbers]

= $\frac{n(n-1)}{2}$