What are some examples of space complexity in algorithms?

What are some examples of space complexity in algorithms?

Space complexity refers to the amount of memory an algorithm uses relative to the input size. Examples include:

1. Bubble Sort: O(1) - uses a constant amount of space.
2. Merge Sort: O(n) - requires additional space for merging.
3. Dynamic Programming: O(n) - often uses arrays to store intermediate results.

Can you explain why Merge Sort has O(n) space complexity?

Sure! Merge Sort divides the array into halves, sorts them, and then merges them back together. The merging process requires additional space proportional to the size of the input array, hence O(n) space complexity.

What about Quick Sort? Does it have a space complexity?

Yes, Quick Sort has an average space complexity of O(log n) due to the recursive stack space used during the sorting process. However, in the worst case, it can go up to O(n) if the pivot selection is poor.

Are there algorithms with constant space complexity?

Yes, algorithms like Insertion Sort and certain iterative algorithms can achieve O(1) space complexity, as they only require a fixed amount of additional space regardless of input size.