Question 4 - Algorithm DesignImagine you are a treasure hunter standing at one side of the river. There are n (a positiveinteger) stones on the river. They are aligned on a straight line and at the nth stone, there istreasure waiting for you. Your target is to reach the nth stone. For each move, you have thechoice of either walking (move one stone ahead) or leaping (move two stones ahead). Also, youare 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 thealgorithm and demonstrate the correctness of the algorithm with a complete proof.Here is an example. For n =15, there are 8 ways:Method 1: walk → walk → walk → walk → walkMethod 2: walk → walk → walk → leapMethod 3: walk → walk → leap → walkMethod 4: walk → leap → walk →walkwalkMethod 5: leap → walk → walk →Method 6: leap → leap walkMethod 7: leap → walk → leapMethod 8: walk → leap leap

The subject of dynamic programming is a powerful problem-solving technique used in computer science…

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