Menerapkan Konsep Rekursi - Berpikir Komputasional - Rekursi

Summary

This video focuses on computational thinking and recursion strategies in algorithmic programming. It presents two problems: the first involves determining how many ways tiles can be arranged on a 2xN floor using recursion. For N = 8, there are 34 ways, following a Fibonacci-like sequence. The second problem discusses stacking pancakes of varying sizes and moving them between plates according to specific rules. The recursive solution finds the minimal steps required to move six pancakes, resulting in 63 moves. The video demonstrates these concepts through step-by-step examples.

Takeaways

• 🧱 The problem involves placing tiles on a 2xN floor using 1x2 tiles, which can be placed either horizontally or vertically.
• 🔢 For N=8, the number of ways to place the tiles can be calculated using a recursive relation.
• 🔄 The recursive formula is based on the two previous terms: K(n) = K(n-1) + K(n-2).
• 📊 Example calculations: K(1) = 1, K(2) = 2, K(3) = 3, K(4) = 5, K(5) = 8, K(6) = 13, K(7) = 21, K(8) = 34.
• 🎯 The final answer for N=8 is 34 ways to arrange the tiles.
• 🥞 The second problem involves moving a stack of pancakes from one plate to another, following a size-order rule.
• 💡 The pancake problem is similar to the Tower of Hanoi problem, requiring a helper plate to transfer pancakes while maintaining the size-order.
• ⏳ The minimum steps to transfer pancakes follow a recursive pattern: P(n) = 2 * P(n-1) + 1.
• 📈 For example, 1 pancake takes 1 step, 2 pancakes take 3 steps, 3 pancakes take 7 steps, and 6 pancakes require 63 steps.
• 🚀 Both problems showcase the power of recursive thinking in solving algorithmic challenges.

Q & A

What is the first problem described in the script?

The first problem is about tiling a 2xN floor with N tiles, where each tile is of size 1x2. The tiles can be placed either horizontally or vertically, and the task is to determine how many different ways the tiles can be arranged on the floor for N=8.

How does the script explain the solution to the tile placement problem?

The script explains that for N=1, there is 1 way to place the tile (vertically), and for N=2, there are 2 ways (either both vertical or both horizontal). For higher values of N, the number of ways is calculated using a recursive relation: K(n) = K(n-1) + K(n-2), where K(n) represents the number of ways to tile the floor. This relation is similar to the Fibonacci sequence.

What is the recursive formula provided to solve the tile placement problem?

The recursive formula is K(n) = K(n-1) + K(n-2), with base cases K(1) = 1 and K(2) = 2. This allows for calculating the number of ways to place tiles for any value of N.

How many ways can the tiles be arranged for N=8?

For N=8, the number of ways to arrange the tiles is 34, as calculated by the recursive formula using the previously computed values for smaller N.

What is the second problem described in the script?

The second problem is about moving a stack of pancakes from one plate to another. The largest pancake must always be at the bottom, and only one pancake can be moved at a time. Budi, the person in the problem, wants to know the minimum number of steps required to move 6 pancakes while following these rules.

What is the minimum number of steps required to move 6 pancakes?

The minimum number of steps required to move 6 pancakes is 63, as derived from a recursive relation similar to the Tower of Hanoi problem.

How does the recursive relation for the pancake problem work?

The recursive relation is P(n) = 2 * P(n-1) + 1, where P(n) is the minimum number of steps required to move n pancakes. The base case is P(1) = 1.

How many steps are required to move 3 pancakes?

To move 3 pancakes, the minimum number of steps required is 7, following the recursive process described in the script.

What is the general strategy for solving the pancake problem?

The strategy is to move the smallest pancake first, then progressively move larger pancakes while using an auxiliary plate to temporarily hold pancakes during the process. The recursive solution builds on smaller subproblems, similar to the Tower of Hanoi.

What are the key concepts covered in the script related to recursion?

The key concepts covered include recursive problem-solving techniques, the use of base cases, and recursive relations. The tile placement problem uses a Fibonacci-like sequence, while the pancake problem uses a Tower of Hanoi-like approach.