• Introduction
• Step-by-Step Guide
• Code Example
• Additional Notes
• Summary
• Conclusion

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The input list must be sorted for binary search to work. Binary search is an efficient algorithm for finding a target value within a sorted list. It works by repeatedly dividing the search interval in half. At each step, the algorithm compares the middle element of the current interval with the target value. If the middle element is equal to the target value, the search is successful, and the index of the middle element is returned. If the target value is less than the middle element, the search continues in the left half of the interval. Otherwise, the search continues in the right half. This process is repeated until the target value is found or the interval becomes empty. def binary_search(list, target): """ Performs binary search on a sorted list.

Args: list: The sorted list to search. target: The value to search for.

Returns: The index of the target value if found, -1 otherwise. """ left = 0 right = len(list) - 1 while left <= right: mid = (left + right) // 2 if list[mid] == target: return mid elif target < list[mid]: right = mid - 1 else: left = mid + 1 return -1

numbers = [2, 5, 7, 8, 11, 12] target = 11 index = binary_search(numbers, target) if index != -1: print(f"Found {target} at index {index}") else: print(f"{target} not found in list") This code defines a function called binary_search that takes a sorted list and a target value as input. It returns the index of the target value if found in the list, otherwise -1. The example then demonstrates how to use this function to search for the value 11 in the list numbers. The output of the example would be: Found 11 at index 4. This indicates that the target value 11 was found at index 4 in the list.

Please create a step-by-step explanation on how to implement a binary search algorithm in Python. Use these resources:

• Concept Explanation: https://en.wikipedia.org/wiki/Binary_search_algorithm
• Python Implementation Guidance: https://www.geeksforgeeks.org/binary-search-in-python/

Focus on these aspects:

1. Preconditions: What needs to be true about the input list for binary search to work correctly?
2. The Algorithm: Explain each step of the algorithm in detail.
3. Python Code: Provide a well-commented Python function that implements binary search.
4. Example Usage: Show an example of how to call the function and interpret its output.

1. Preconditions:

• Emphasize Importance: Strongly emphasize that binary search only works on sorted lists. Unsorted input will lead to incorrect results.
• Visual Aid: Consider adding a visual example of a sorted vs. unsorted list to highlight this point.

2. The Algorithm:

• Iteration: Clearly state that binary search is an iterative algorithm, meaning it repeats steps until a condition is met (finding the target or exhausting the search space).
• "Divide and Conquer": Mention that binary search is an example of the "divide and conquer" algorithmic paradigm, which can make it easier to grasp for learners familiar with this concept.
• Step-by-step Breakdown: Break down the algorithm into smaller, numbered steps for better readability. For example:
  1. Initialize: Set left to 0 and right to the last index of the list.
  2. Calculate Middle: Find the middle index mid using integer division: mid = (left + right) // 2.
  3. Compare: Compare the value at list[mid] with the target:
     • Match: If they are equal, the target is found, return mid.
     • Target Smaller: If target < list[mid], search the left half: update right = mid - 1.
     • Target Larger: If target > list[mid], search the right half: update left = mid + 1.
  4. Repeat: Continue steps 2-3 until left > right (target not found).
• Visualizations: Consider adding diagrams or illustrations to visually represent how the search interval is halved in each step.

3. Python Code:

• Docstring: The provided docstring is good, but you could add an example to make it even clearer.
• Variable Names: The variable names are clear, but you could consider more descriptive names like start_index and end_index instead of left and right.
• Floor Division: Explain why floor division // is used when calculating mid.

4. Example Usage:

• Different Cases: Include examples where:
  • The target is found at the beginning, middle, and end of the list.
  • The target is not present in the list.
• Real-world Application: Briefly mention a real-world scenario where binary search is used (e.g., searching for a word in a dictionary, searching for a specific record in a sorted database).

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Binary search is a highly efficient algorithm for finding a target value within a sorted list. Its core principle involves repeatedly dividing the search interval in half, comparing the target value with the middle element of the current interval. If the middle element matches the target, the search is successful. If the target is smaller, the search continues in the left half; otherwise, it proceeds in the right half. This process repeats until the target is found or the search interval is empty. Remember, binary search only works on sorted lists. If the list is not sorted, the results will be incorrect. The provided Python code effectively implements this algorithm, offering a clear and reusable function for performing binary search. The example usage demonstrates how to utilize this function and interpret its output. By understanding the preconditions, the step-by-step process, and the code implementation, you can effectively leverage the power of binary search in your own programs.