Consider the following function written in Python 3 (recalling that range(x, y), in Python, refers to...

  

Transcribed Image Text:

Consider the following function written in Python 3 (recalling that range(x, y), in Python, refers to the sequence of values starting at x, counting up by 1s, and stopping at y-1. for a in range (1, n+1): foo () for bin range (1, n+1): bar () for c in range (1, a+1): bar () bar () for d in range (0, c): foo () If n has a value of 2000, how many times will the function foo () be called and how many times will the function bar () be called? You must solve this problem using Sigma notation (i.e., you must derive an expression that uses Sigma notation to specify how many times each of these functions will be called, and then you must find a closed form for this expression and evaluate for n = 2000). You must show all your work. Consider the following function written in Python 3 (recalling that range(x, y), in Python, refers to the sequence of values starting at x, counting up by 1s, and stopping at y-1. for a in range (1, n+1): foo () for bin range (1, n+1): bar () for c in range (1, a+1): bar () bar () for d in range (0, c): foo () If n has a value of 2000, how many times will the function foo () be called and how many times will the function bar () be called? You must solve this problem using Sigma notation (i.e., you must derive an expression that uses Sigma notation to specify how many times each of these functions will be called, and then you must find a closed form for this expression and evaluate for n = 2000). You must show all your work.