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