Part B: Problem 1: The python function below takes a value and inserts it. into an already sorted array (A): def insert_into_sorted (A, value): return A Answer the following questions: (a) Complete the function using python (or a different language if you prefer). (b) Run your program for several different input values. Does your method appear to work for both standard input and edge cases (e.g. empty arrays, duplicate values, etc...)? Why do you believe this? (c) Describe a loop invariant that will help you prove correctness. (d) Prove that your algorithm is correct by showing that the loop invariant remains true during initialization, maintenance, and termination (e) How does this relate to the correctness of the insertion sort? (Hint: How would you modify insertion sort to use your method?)

Part B: Problem 1: The python function below takes a value and inserts it. into an already sorted array (A): def insert_into_sorted (A, value): return A Answer the following questions: (a) Complete the function using python (or a different language if you prefer). (b) Run your program for several different input values. Does your method appear to work for both standard input and edge cases (e.g. empty arrays, duplicate values, etc...)? Why do you believe this? (c) Describe a loop invariant that will help you prove correctness. (d) Prove that your algorithm is correct by showing that the loop invariant remains true during initialization, maintenance, and termination (e) How does this relate to the correctness of the insertion sort? (Hint: How would you modify insertion sort to use your method?)