Perhitungan Manual Algoritma Binary Search

Summary

This video script delves into the manual calculation aspect of the binary search algorithm, contrasting it with sequential search. It explains the binary search's efficiency in locating a target value by repeatedly dividing the search interval in half. The presenter, despite limited resources, provides a step-by-step guide on how to perform binary search, emphasizing the importance of a sorted dataset. An example is used to illustrate the process, from calculating the middle index to adjusting the search boundaries until the target value is found, aiming to simplify the concept for future coding implementations.

Takeaways

• 📚 The script is a lecture on the binary search algorithm, a manual calculation method used in data searching scenarios.
• 🔍 Binary search is differentiated from sequential search by its method of finding the target value, which involves checking the middle element and then narrowing down the search range based on comparisons.
• 🔢 The fundamental principle of binary search is to repeatedly divide the search interval in half by calculating the middle value until the target value is found or the interval is empty.
• ➗ The formula for calculating the middle value is the average of the lower and upper bounds, expressed as (lower_bound + upper_bound) / 2.
• 📉 If the middle value is less than the target, the search continues in the upper half by recalculating the lower bound to be one index after the middle value.
• 📈 Conversely, if the middle value is greater than the target, the search continues in the lower half by recalculating the upper bound to be one index before the middle value.
• 📝 An important note is that for binary search to work, the data must be sorted in ascending order; it cannot be in a random order.
• 📊 The script provides an example of searching for the number 9 in an array of numbers from 1 to 10, demonstrating the step-by-step process of binary search.
• 👉 The index notation starts from zero, which is a common practice in programming, but the script also mentions that some tutorials may start from one, emphasizing the importance of consistency.
• 🔄 The process involves iteratively updating the bounds based on comparisons with the middle value until the target value is located or the search space is exhausted.
• 📚 The lecture aims to make the manual calculation and application of formulas easier for future implementation in coding.

Q & A

What is the main topic discussed in the video script?

The main topic discussed in the video script is the manual calculation within the binary search algorithm.

What is the difference between sequential search and binary search as mentioned in the script?

The difference is that sequential search checks each index one by one to find the data, while binary search finds the middle value and compares it with the value being searched for, then adjusts the search range based on whether the middle value is less than or greater than the target value.

What is the fundamental principle of the binary search algorithm?

The fundamental principle of the binary search algorithm is to find the middle value of a sorted array and compare it with the target value, then adjust the search range accordingly until the target value is found or the range is exhausted.

How is the middle value calculated in binary search?

The middle value is calculated using the formula: (lower bound + upper bound) / 2. The result is then rounded down to the nearest whole number to get the middle index.

What is the condition for the data in binary search?

The data must be sorted in ascending order for binary search to work correctly.

What happens if the middle value is not equal to the value being searched for?

If the middle value is not equal to the value being searched for, the algorithm compares it with the target value to determine if it is smaller or larger, then updates the search range by adjusting the lower or upper bound accordingly.

How is the lower bound updated when the middle value is less than the target value?

The lower bound is updated by setting it to the position of the middle value plus one: lower bound = middle position + 1.

How is the upper bound updated when the middle value is greater than the target value?

The upper bound is updated by setting it to the position of the middle value minus one: upper bound = middle position - 1.

What is the significance of the term 'binary' in 'binary search'?

The term 'binary' signifies that the search space is repeatedly divided into two halves, which is how the algorithm narrows down the location of the target value.

Can you provide an example of how the binary search algorithm works with the numbers 1 to 10?

In the script, an example is given where the algorithm starts with a sorted array of numbers 1 to 10. It calculates the middle index (4 in this case), checks if the value at that index (5) is the target value (9), and then updates the search range based on the comparison, continuing this process until the target value is found or the range is exhausted.

What is the importance of consistency when starting the index in binary search?

Consistency in starting the index, whether from 0 or 1, is important to ensure that the final index or the count of elements matches the actual number of elements in the array, which is crucial for the correct implementation of the binary search algorithm.