Consider the following algorithm. for i ∈ {1,2,3,4,5,6} do beep for j ∈ {1,2,3,4} do beep for k ∈ {1,2,3} do for l ∈ {1,2,3,4,5} do beep for m ∈ {1,2,3,4} do beep How many times does a beep statement get executed?

This is the complete question:

for i ∈ {1,2,3,4,5,6} do  beep  

for j ∈ {1,2,3,4} do  beep  

for k ∈ {1,2,3} do

    for l ∈ {1,2,3,4,5} do beep  

for m ∈ {1,2,3,4} do  beep

Explanation:

I will explain the algorithm line by line.

for i ∈ {1,2,3,4,5,6} do  beep  

This statement has a for loop and i variable that can take the values from 1 to 6. As there are 6 possible values for i so the beep statement gets executed 6 times in this for loop.

for j ∈ {1,2,3,4} do  beep  

This statement has a for loop and j variable that can take the values from 1 to 4. As there are 4 possible values for j so the beep statement gets executed 4 times in this for loop.

for k ∈ {1,2,3} do

    for l ∈ {1,2,3,4,5} do beep  

There are two statements here. The above statement has a for loop and k variable that can take the values from 1 to 3. As there are 3 possible values for k so the beep statement gets executed 3 times in this for loop. The below statement has a for loop and l variable that can take the values from 1 to 5. As there are 5 possible values for l so the beep statement gets executed 5 times in this for loop. However these statement work like an inner and outer loop where the outer loop is k and inner one is l which means 1 gets executed for each combination of values of k and l. As there are three values for k and 5 possible values for l so the combinations of values of k and l is 15 because 3 * 5 = 15. Hence the beep statement gets executed 15 times.

for m ∈ {1,2,3,4} do  beep

This statement has a for loop and m variable that can take the values from 1 to 4. As there are 4 possible values for m so the beep statement gets executed 4 times in this for loop.

Now lets take the sum of all the above computed beeps.

for i = 6 beeps

for j = 4 beeps

for k and l possible combinations = 15 beeps

for m = 4 beeps

total beeps = 6 + 4 + 15 + 4 = 29 beeps