Linear Search and Binary Search With example

Linear search is the simplest search algorithm—it just checks each element one by one until it finds the desired value. It works well for small or unsorted lists.

Example: Finding '7' in a list

Let’s say we have this list:
[3, 8, 5, 7, 6]

1. Check the first number (3) → not 7
2. Check the second number (8) → not 7
3. Check the third number (5) → not 7
4. Check the fourth number (7) → Found it! ✅

Linear search is simple but slow for large lists because it may have to check every single element.

def linear_search(arr, target):
    for i in range(len(arr)):
        if arr[i] == target:
            return i  # Return index if found
    return -1  # Return -1 if not found

# Example usage
arr = [3, 8, 5, 7, 6]
target = 7
result = linear_search(arr, target)
print("Element found at index:", result)  # Output: 3

Binary Search

Binary search is much faster but requires a sorted list. It works by repeatedly dividing the list in half and checking the middle element.

Example: Finding '7' in a sorted list

Let’s say we have this sorted list:
[1, 3, 5, 7, 9, 11]

1. Look at the middle number (5) → is 7 greater? Yes! So, ignore the left half.
   New search area: [7, 9, 11]
2. Look at the middle number (9) → is 7 smaller? Yes! So, ignore the right half.
   New search area: [7]
3. Found 7 ✅!

Binary search is very fast because it cuts down the search space with each step, making it much more efficient than linear search.

Would you like a Python implementation for both? 🚀

def binary_search(arr, target):
    left, right = 0, len(arr) - 1
    while left <= right:
        mid = (left + right) // 2
        if arr[mid] == target:
            return mid  # Return index if found
        elif arr[mid] < target:
            left = mid + 1  # Ignore left half
        else:
            right = mid - 1  # Ignore right half
    return -1  # Return -1 if not found

# Example usage
arr = [1, 3, 5, 7, 9, 11]  # Sorted list
target = 7
result = binary_search(arr, target)
print("Element found at index:", result)  # Output: 3