Question 4 - Algorithm Design Imagine you are a treasure hunter standing at one side of the river. There are n (a positive integer) stones on the river. They are aligned on a straight line and at the nth stone, there is treasure waiting for you. Your target is to reach the nth stone. For each move, you have the choice of either walking (move one stone ahead) or leaping (move two stones ahead). Also, you are not allowed to travel backwards. Design an algorithm that calculates the number of ways (sequences of walks/leaps) that get you to the treasure stone. You should clearly explain the algorithm and demonstrate the correctness of the algorithm with a complete proof. 1

Question 4 - Algorithm Design Imagine you are a treasure hunter standing at one side of the river. There are n (a positive integer) stones on the river. They are aligned on a straight line and at the nth stone, there is treasure waiting for you. Your target is to reach the nth stone. For each move, you have the choice of either walking (move one stone ahead) or leaping (move two stones ahead). Also, you are not allowed to travel backwards. Design an algorithm that calculates the number of ways (sequences of walks/leaps) that get you to the treasure stone. You should clearly explain the algorithm and demonstrate the correctness of the algorithm with a complete proof. 1