Merge Sort divides the array in half, recursively sorts each half, then merges the two sorted halves into one sorted array.
- Base case: If the array has 0 or 1 elements, it's already sorted — return it.
- Find the middle index.
- Recursively sort the left half and the right half.
- Merge the two sorted halves using a two-pointer merge technique.
- Time Complexity: O(N log N).
- Space Complexity: O(N).
def merge_sort(arr):
if len(arr) <= 1:
return arr
mid = len(arr) // 2
left = merge_sort(arr[:mid])
right = merge_sort(arr[mid:])
return merge(left, right)
def merge(left, right):
result = []
i = j = 0
while i < len(left) and j < len(right):
if left[i] <= right[j]:
result.append(left[i])
i += 1
else:
result.append(right[j])
j += 1
result.extend(left[i:])
result.extend(right[j:])
return result