Binary Search Algorithm - Python Example & Code
# Understanding Binary Search: A Step-by-Step Guide
## Introduction to Binary Search
Welcome back to another discussion on algorithms! In today's video, we delve into the binary search algorithm, building on our previous exploration of linear search. While linear search is straightforward, binary search offers significant advantages in efficiency, especially with larger datasets.
## How Binary Search Works
Binary search operates by repeatedly dividing the search interval in half. Here’s a detailed breakdown using an example list: `[1, 2, 3, 4, 5]`, where we're searching for the number `1`.
1. **Initial Setup**: The algorithm starts by identifying the middle index of the list. For our example with five elements, the middle index is at position `2` (element `3`).
2. **Comparison**:
- If the target (`1`) is greater than the middle element (`3`), continue searching in the higher half.
- If the target is less (`1 < 3`), narrow down to the lower half.
3. **Iteration**: Repeat the process on the narrowed-down section until the target is found or the section becomes empty.
## Binary Search Code Explanation
Here’s a Python function implementing binary search:
```python
def binary_search(lst, target):
top = 0
bottom = len(lst) - 1
while top <= bottom:
mid = (top + bottom) // 2
if lst[mid] == target:
return f"Found at index {mid}"
elif lst[mid] > target:
bottom = mid - 1
else:
top = mid + 1
return "Not found"
# Example usage
sorted_list = [1, 2, 3, 4, 5]
target = 1
print(binary_search(sorted_list, target))
```
**Explanation**:
- **Initialization**: `top` starts at `0`, and `bottom` is the last index of the list.
- **Loop**: Continues until `top` exceeds `bottom`.
- **Mid Calculation**: Uses integer division to find the midpoint.
- **Comparison**: Adjusts `top` or `bottom` based on whether the target is less than or greater than the middle element.
This code efficiently narrows down the search space, making it much faster than linear search.
## Efficiency of Binary Search
Binary search operates in O(log n) time complexity, where `n` is the number of elements. This logarithmic efficiency means the algorithm becomes exponentially faster as the dataset grows:
- **Example**: Searching through 1 million elements takes about 20 steps, compared to potentially a million steps with linear search.
## Comparison with Linear Search
While binary search is highly efficient for large datasets and sorted lists, it has trade-offs:
- **Sorting Requirement**: The list must be sorted beforehand.
- **Use Case**: Ideal for scenarios where data is static and frequently accessed (e.g., databases).
Linear search, while less efficient, is simpler and doesn't require sorting, making it suitable for small datasets or dynamic data.
## Conclusion
Binary search is a powerful algorithm offering significant efficiency gains over linear search, especially with large datasets. Its ability to halve the search space each iteration makes it indispensable in many applications. Understanding and implementing binary search can greatly enhance the performance of your programs.
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