Strategi Algoritma #7 : Decrease & Conquer

Summary

This script discusses the Divide and Conquer algorithm strategy, illustrating its concept with examples such as binary search and the counterfeit coin problem. It explains how problems are divided into smaller sub-problems, recursively processed, and eventually solved by combining the solutions. The script also touches on the three variations of the Divide and Conquer approach: constant reduction, exponential reduction, and linear reduction, providing insights into their applications in solving complex problems.

Takeaways

• 😀 Divide and Conquer is a popular algorithmic strategy that breaks down problems into smaller, more manageable sub-problems.
• 📚 The concept is similar to Divide and Conquer but differs in the approach of handling sub-problems and combining their solutions.
• 🔍 In Divide and Conquer, each sub-problem is solved and then combined, whereas in the discussed strategy, only the solvable sub-problems are processed.
• 💡 The strategy is exemplified by searching for a value in an array, where the problem is divided and only the relevant parts are processed, eliminating the need to search through all elements.
• 🔎 The method is illustrated with a binary search example, where the array is repeatedly divided, and the search space is narrowed down until the target value is found.
• 🧐 The strategy is also applicable to the problem of identifying a counterfeit coin among a set of identical-looking coins by using a balance scale and dividing the set in half repeatedly.
• 🔑 The script discusses three variations of the strategy: constant reduction, exponential reduction, and linear reduction, each with different ways of reducing the problem size.
• 🌐 The constant reduction approach reduces the problem size by a fixed constant at each step, such as reducing a problem of 100 to 99 and so on.
• 🌟 The exponential reduction method halves the problem size at each iteration, like reducing 100 to 50, then 50 to 25, and so on.
• 📉 The linear reduction variant varies the reduction at each step, such as reducing 70 to 33, then 33 to 20, and continuing with different reductions at each step.

Q & A

What is the main topic discussed in the script?

The main topic discussed in the script is the Divide and Conquer algorithmic strategy, with a focus on its application in solving problems by breaking them down into smaller sub-problems.

How does the Divide and Conquer strategy differ from other problem-solving approaches?

The Divide and Conquer strategy differs by reducing a problem into smaller sub-problems, solving only one of them, and then combining the solutions to solve the original problem. It contrasts with other approaches that might solve all sub-problems before combining their solutions.

What is an example of a problem-solving approach using the Divide and Conquer method mentioned in the script?

An example given is searching for a specific value in a sorted array, where the array is divided into halves, and the search continues in the relevant half based on the value's position relative to a pivot.

How does the Divide and Conquer strategy apply to the problem of finding a counterfeit coin among a set of identical-looking coins?

The strategy applies by dividing the set of coins into two equal parts and weighing them against each other. The lighter side indicates the presence of the counterfeit coin, which is then further divided and weighed until the counterfeit is isolated.

What are the three variations of the Divide and Conquer strategy mentioned in the script?

The three variations mentioned are: 1) Regular Divide and Conquer, where problems are reduced by a constant amount each iteration. 2) Divide and Conquer with a constant factor, where problems are reduced by a constant factor (usually two) each iteration. 3) Divide and Conquer with varying factors, where the reduction varies with each iteration.

What is the significance of reducing problems to the smallest possible sub-problems in the Divide and Conquer approach?

Reducing problems to the smallest possible sub-problems allows for more manageable and efficient solutions, as it simplifies the complexity and makes it easier to find solutions that can be combined to solve the original problem.

How does the script illustrate the process of elimination in the Divide and Conquer strategy?

The script illustrates the process of elimination by showing how, after dividing the problem, certain parts can be disregarded based on comparisons (e.g., if a value is greater than the target, the left side can be eliminated), thus narrowing down the search space.

What is the role of recursion in the Divide and Conquer strategy as described in the script?

Recursion plays a crucial role in the Divide and Conquer strategy by allowing the algorithm to repeatedly apply the divide and conquer process to smaller sub-problems until a base case is reached.

Can you provide an example from the script that demonstrates the efficiency of the Divide and Conquer strategy?

An example from the script is the binary search algorithm, which efficiently finds a target value in a sorted array by repeatedly dividing the search space in half, showcasing the strategy's efficiency in reducing the problem size.

What is the final step in the Divide and Conquer strategy after dividing and solving sub-problems?

The final step in the Divide and Conquer strategy is to combine the solutions of the sub-problems to form the solution to the original problem.