Logic Visualizer | Python

Simplified Binary Search Algorithm Overview

A breakdown of the binary search algorithm showcasing pseudocode and a flowchart for a clearer understanding of its recursive nature and efficiency in finding elements in sorted arrays.


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Prompt

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

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

result = binary_search(arr, 0, len(arr)-1, x)

Answer

Visual Representation of Binary Search Algorithm

Pseudocode:

function binary_search(arr, low, high, x):
    if high >= low:
        mid = low + (high - low) // 2
        
        if arr[mid] == x:
            return mid
        else if arr[mid] > x:
            return binary_search(arr, low, mid - 1, x)
        else:
            return binary_search(arr, mid + 1, high, x)
    else:
        return -1

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

result = binary_search(arr, 0, len(arr)-1, x)

Flowchart Description:

  • The algorithm starts by checking if the high index is greater than or equal to the low index.
  • It then calculates the mid index to divide the array into two parts.
  • If the element at the mid index is equal to x, the algorithm returns the index of x.
  • If the element at the mid index is greater than x, it recursively calls binary_search on the left subarray.
  • If the element at the mid index is less than x, it recursively calls binary_search on the right subarray.
  • This process continues until the element is found or the subarray size becomes zero.
  • If the element is not found, the algorithm returns -1.

Annotations:

  • The algorithm divides the array in each step based on comparing the middle element with the target value x.
  • It efficiently narrows down the search space by half in each recursive call.
  • The base case is when the search space is empty, meaning the element is not in the array.
  • The algorithm exploits the sorted nature of the array to perform efficient search operations.

This representation simplifies the binary search algorithm, making it easier to understand the recursive nature and the logic behind efficiently finding an element in a sorted array.

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Description

A breakdown of the binary search algorithm showcasing pseudocode and a flowchart for a clearer understanding of its recursive nature and efficiency in finding elements in sorted arrays.

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