How to Calculate the Number of Times a Statement is Executed in Nested Loops?

In a given code segment, we have nested loops that iterate over a range of values. How can we determine the total number of times a statement within these loops is executed?

Answer:

To calculate the number of times a statement is executed in a nested loop, we can use summation formulas efficiently. The key is to understand the range of iterations in each loop and set up the appropriate summation.

Understanding Nested Loop Execution:

When dealing with nested loops, it's essential to grasp the relationship between the outer and inner loop variables. The total number of executions of the statement depends on how the loops interact and iterate over values.

Setting up Summation Formulas:

For each loop, we need to analyze the starting and ending points of iteration. The outer loop typically defines the range of the entire process, while the inner loop refines the iterations within that range.

Consider an outer loop from i = 2 to N-1 and an inner loop from j = i to N-1. In this case, we would calculate the total number of times the statement is executed by summing up the iterations of the inner loop for each iteration of the outer loop.

Utilizing Summation Formula:

By using the summation formula, we can simplify the process of calculating the total number of executions. This method allows us to express the iterations in a concise and systematic manner, making it easier to analyze and optimize nested loops.