Suppose you are the security officer for the Bank of Peterborough. One day, a box full of n bank cards lands on your desk. Your task is to determine if more than n/2 of these cards belong to the same account. To help in your task, you use a special machine called the Equivalator. It reads the magnetic strips of two cards and then returns true if the two cards belong to the same account; false otherwise. This is only information the Equivalator provides. 1. (14 marks) Design, implement, and test a divide-and-conquer algorithm that solves your task. You can mimic the Equivalator by ensuring that two bank cards can only be compared for equality. So, no sorting is allowed. 2. (4 marks) State the time complexity T(n) of your algorithm as a recurrence relation and determine its exact order of complexity using the Master Theorem. Suppose you are the security officer for the Bank of Peterborough. One day, a box full of n bank cards lands on your desk. Your task is to determine if more than n/2 of these cards belong to the same account. To help in your task, you use a special machine called the Equivalator. It reads the magnetic strips of two cards and then returns true if the two cards belong to the same account; false otherwise. This is only information the Equivalator provides. 1. (14 marks) Design, implement, and test a divide-and-conquer algorithm that solves your task. You can mimic the Equivalator by ensuring that two bank cards can only be compared for equality. So, no sorting is allowed. 2. (4 marks) State the time complexity T(n) of your algorithm as a recurrence relation and determine its exact order of complexity using the Master Theorem