N pancakes, all of distinct sizes, are piled in a stack. Your task is to sort th

Question

N pancakes, all of distinct sizes, are piled in a stack. Your task is to sort them by size, with the largest pancake at the bottom and the smallest one on top. The only operation you are allowed to perform is to stick a spatula anywhere in the stack and flip the pancakes above the spatula. That is, in one operation you can flip the top k pancakes, where k is any number of your choice between 1 and N. An example is shown below. Describe a recursive strategy to sort any stack using a sequence of allowed operations. Give a detailed proof to show that your strategy correctly sorts every stack. Do not omit any details. Write a recurrence relation S(N) for the maximum number of operations that suffice to sort a stack of N pancakes. Show that S(N) lessthanorequalto 2N - 3. for all N greaterthanorequalto 1.

Explanation / Answer

N is the answer for all the questions. Because the logic is very simple. Its N>1

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.