Final answer:
To calculate the number of times the beep statement is executed, multiply the number of iterations of each loop together: 4 (i) * 3 (j) * 4 (k) * 5 (l) * 6 (m), for a total of 1440 beeps.
Step-by-step explanation:
The question requires us to determine the total number of times the beep statement is executed in the given nested loop algorithm. To solve this, we can treat each loop as a multiplier of possibilities for the inner loops. Let's break it down step by step:
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- The outermost loop runs for i in {1, 2, 3, 4}, so it executes 4 times.
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- The next loop for j in {1, 2, 3} runs 3 times for each iteration of the outer loop.
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- The third loop for k in {1, 2, 3, 4} runs 4 times for each iteration of the second loop.
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- The fourth loop for l in {1, 2, 3, 4, 5} runs 5 times for each iteration of the third loop.
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- The innermost loop for m in {1, 2, 3, 4, 5, 6} runs 6 times for each iteration of the fourth loop, and this is where the beep occurs.
So, the beep occurs 6 times in the innermost loop, which itself is run 5 times by the loop containing it, and so on up the chain. The total number of beeps is therefore 4 (for i) * 3 (for j) * 4 (for k) * 5 (for l) * 6 (for m) = 1440 times.
This is also known as calculating the Cartesian product of the sets from which the loop indices are drawn, or calculating the number of outcomes in a compound event in probability theory.