AI Big-O Analyzer | Python

Binary Search Algorithm Efficiency

Analysis of time and space complexities of the binary search algorithm, showcasing its logarithmic time complexity and constant space complexity. Illustration of average-case scenario for better understanding.


Empty image or helper icon

Prompt

def binary_search(arr, x):
    low = 0
    high = len(arr) - 1
    mid = 0
 
    while low <= high:
 
        mid = (high + low) // 2
 
        if arr[mid] < x:
            low = mid + 1
 
        elif arr[mid] > x:
            high = mid - 1
 
        else:
            return mid
 
    return -1

arr = [2, 3, 4, 10, 40]
x = 10

result = binary_search(arr, x)
print(result)

Answer

Code Inspection

The provided code snippet implements the binary search algorithm to find the index of a given element in a sorted array.

Complexity Analysis

  • Time Complexity:

    • Best Case: O(1) - When the element to be found is at the middle index in the first comparison.
    • Worst Case: O(log n) - When the element is not present in the array and all elements need to be considered.
    • Average Case: O(log n) - Considering the element has an equal probability of being in any part of the array.

  • Space Complexity:

    • The algorithm has a space complexity of O(1) as it uses a constant amount of extra space regardless of the size of the input array.

  • Comments:

    • The while loop executes log n times, making the time complexity logarithmic.
    • The algorithm efficiently halves the search space in each iteration, leading to the logarithmic time complexity.

Average-Case Scenario Illustration

For an array of size 1000, where the target element is located in the middle of the array, the binary search algorithm would exhibit average-case behavior. In this scenario, the algorithm would take approximately log₂(1000) = 10 iterations to find the element. Therefore, the expected runtime complexity in this typical scenario would be O(log n). The space complexity remains constant at O(1).

Create your Thread using our flexible tools, share it with friends and colleagues.

Your current query will become the main foundation for the thread, which you can expand with other tools presented on our platform. We will help you choose tools so that your thread is structured and logically built.

Description

Analysis of time and space complexities of the binary search algorithm, showcasing its logarithmic time complexity and constant space complexity. Illustration of average-case scenario for better understanding.

More AI Big-O Analyzers
Apache Flink AI Big-O AnalyzerApache Pig AI Big-O AnalyzerAzure Data Factory AI Big-O AnalyzerC/C++ AI Big-O AnalyzerCouchDB AI Big-O AnalyzerDAX AI Big-O AnalyzerExcel AI Big-O AnalyzerFirebase AI Big-O AnalyzerGoogle BigQuery AI Big-O AnalyzerGoogle Sheets AI Big-O AnalyzerGraphQL AI Big-O AnalyzerHive AI Big-O AnalyzerJava AI Big-O AnalyzerJavaScript AI Big-O AnalyzerJulia AI Big-O AnalyzerLua AI Big-O AnalyzerM (Power Query) AI Big-O AnalyzerMATLAB AI Big-O AnalyzerMongoDB AI Big-O AnalyzerOracle AI Big-O AnalyzerPostgreSQL AI Big-O AnalyzerPower BI AI Big-O AnalyzerPython AI Big-O AnalyzerR AI Big-O AnalyzerRedis AI Big-O AnalyzerRegex AI Big-O AnalyzerRuby AI Big-O AnalyzerSAS AI Big-O AnalyzerScala AI Big-O AnalyzerShell AI Big-O AnalyzerSPSS AI Big-O AnalyzerSQL AI Big-O AnalyzerSQLite AI Big-O AnalyzerStata AI Big-O AnalyzerTableau AI Big-O AnalyzerVBA AI Big-O Analyzer