The Algorithms logo
The Algorithms
AboutDonate

Linear Search

A
J
E
L
E
and 45 more contributors
"""
This is pure Python implementation of linear search algorithm

For doctests run following command:
python3 -m doctest -v linear_search.py

For manual testing run:
python3 linear_search.py
"""


def linear_search(sequence: list, target: int) -> int:
    """A pure Python implementation of a linear search algorithm

    :param sequence: a collection with comparable items (as sorted items not required
        in Linear Search)
    :param target: item value to search
    :return: index of found item or None if item is not found

    Examples:
    >>> linear_search([0, 5, 7, 10, 15], 0)
    0
    >>> linear_search([0, 5, 7, 10, 15], 15)
    4
    >>> linear_search([0, 5, 7, 10, 15], 5)
    1
    >>> linear_search([0, 5, 7, 10, 15], 6)
    -1
    """
    for index, item in enumerate(sequence):
        if item == target:
            return index
    return -1


def rec_linear_search(sequence: list, low: int, high: int, target: int) -> int:
    """
    A pure Python implementation of a recursive linear search algorithm

    :param sequence: a collection with comparable items (as sorted items not required
        in Linear Search)
    :param low: Lower bound of the array
    :param high: Higher bound of the array
    :param target: The element to be found
    :return: Index of the key or -1 if key not found

    Examples:
    >>> rec_linear_search([0, 30, 500, 100, 700], 0, 4, 0)
    0
    >>> rec_linear_search([0, 30, 500, 100, 700], 0, 4, 700)
    4
    >>> rec_linear_search([0, 30, 500, 100, 700], 0, 4, 30)
    1
    >>> rec_linear_search([0, 30, 500, 100, 700], 0, 4, -6)
    -1
    """
    if not (0 <= high < len(sequence) and 0 <= low < len(sequence)):
        raise Exception("Invalid upper or lower bound!")
    if high < low:
        return -1
    if sequence[low] == target:
        return low
    if sequence[high] == target:
        return high
    return rec_linear_search(sequence, low + 1, high - 1, target)


if __name__ == "__main__":
    user_input = input("Enter numbers separated by comma:\n").strip()
    sequence = [int(item.strip()) for item in user_input.split(",")]

    target = int(input("Enter a single number to be found in the list:\n").strip())
    result = linear_search(sequence, target)
    if result != -1:
        print(f"linear_search({sequence}, {target}) = {result}")
    else:
        print(f"{target} was not found in {sequence}")
About this Algorithm

Problem Statement

Given an array of n elements, write a function to search for the index of a given element (target)

Approach

  • Start iterating with the first element in the array.
  • Compare it with the target element
  • If it is equal to the target element then return the index
  • Else continue iterating
  • Return -1 if target element is not found in the array

Time Complexity

O(n) Worse Case
O(1) Best Case (If first element of array is the target element)

Space Complexity

O(1)

Example

arr = [1, 3, 9, 5, 0, 2]  

target = 5
Linear Search should return index 3 as 5 is on index 3     

target = 6           
Linear Search should return -1 as 6 is not present in the array

Code Implementation Links

Video Explanation

A CS50 video explaining the Linear Search Algorithm

Animation Explanation