Question

Assume a ≤ b and c ≤ d. For i := a to b, for j := c to d [statements in the body of the inner loop. None contain branching statements that lead outside the loop.] Next j, Next i.

Answer 1

The student's question is about a nested iteration structure in programming, with the inner loop statements set to execute for each combination of i and j values within the specified ranges. The execution count is the product of the number of iterations in each loop.

Step-by-step explanation:

The question refers to a nested iteration structure in a programming context, where i is the iterator variable for the outer loop ranging from a to b, and j is the iterator for the inner loop ranging from c to d. There are no branching statements inside the body of the loops that would cause an exit from the loops. As such, the loops will execute the body of the inner loop for each value of j from c to d, for each value of i from a to b.

To understand how many times the statements within the inner loop will execute, you would calculate the product of the number of iterations of each loop. If a is less than or equal to b, and c is less than or equal to d, then the outer loop will run for (b - a + 1) times, and the inner loop will run (d - c + 1) times for each iteration of the outer loop. Therefore, the inner loop statements will execute a total of (b - a + 1) * (d - c + 1) times.