Searching Algorithms in Python

def linear_search(arr, target):
    """
    Perform linear search to find the target value in the given list.

    Parameters:
        arr (list): The list to be searched.
        target: The value to be searched for.

    Returns:
        int: The index of the target value if found, otherwise -1.
    """
    for i in range(len(arr)):
        if arr[i] == target:
            return i
    return -1

# Example usage:
arr = [2, 3, 4, 10, 40]
target = 10
result = linear_search(arr, target)
if result != -1:
    print(f"Linear Search: Element found at index {result}")
else:
    print("Linear Search: Element not found")

def binary_search(arr, target, low, high):
    """
    Perform binary search recursively to find the target value in the given sorted list.

    Parameters:
        arr (list): The sorted list to be searched.
        target: The value to be searched for.
        low (int): The lower index of the search interval.
        high (int): The upper index of the search interval.

    Returns:
        int: The index of the target value if found, otherwise -1.
    """
    if low <= high:
        mid = (low + high) // 2
        if arr[mid] == target:
            return mid
        elif arr[mid] < target:
            return binary_search(arr, target, mid + 1, high)
        else:
            return binary_search(arr, target, low, mid - 1)
    else:
        return -1

# Example usage:
arr = [2, 3, 4, 10, 40]
target = 10
result = binary_search(sorted(arr), target, 0, len(arr) - 1)
if result != -1:
    print(f"Binary Search: Element found at index {result}")
else:
    print("Binary Search: Element not found")

import math

def interpolation_search(arr, target):
    """
    Perform interpolation search to find the target value in the given sorted list.

    Parameters:
        arr (list): The sorted list to be searched.
        target: The value to be searched for.

    Returns:
        int: The index of the target value if found, otherwise -1.
    """
    low = 0
    high = len(arr) - 1
    while low <= high and target >= arr[low] and target <= arr[high]:
        pos = low + ((high - low) // (arr[high] - arr[low])) * (target - arr[low])
        if arr[pos] == target:
            return pos
        elif arr[pos] < target:
            low = pos + 1
        else:
            high = pos - 1
    return -1

# Example usage:
arr = [2, 3, 4, 10, 40]
target = 10
result = interpolation_search(sorted(arr), target)
if result != -1:
    print(f"Interpolation Search: Element found at index {result}")
else:
    print("Interpolation Search: Element not found")

import math

def jump_search(arr, target):
    """
    Perform jump search to find the target value in the given sorted list.

    Parameters:
        arr (list): The sorted list to be searched.
        target: The value to be searched for.

    Returns:
        int: The index of the target value if found, otherwise -1.
    """
    n = len(arr)
    step = int(math.sqrt(n))
    prev = 0
    while arr[min(step, n) - 1] < target:
        prev = step
        step += int(math.sqrt(n))
        if prev >= n:
            return -1
    while arr[prev] < target:
        prev += 1
        if prev == min(step, n):
            return -1
    if arr[prev] == target:
        return prev
    return -1

# Example usage:
arr = [2, 3, 4, 10, 40]
target = 10
result = jump_search(sorted(arr), target)
if result != -1:
    print(f"Jump Search: Element found at index {result}")
else:
    print("Jump Search: Element not found")