DSA · Theory

Merge Sort Tree for Range Order Statistics

Theory

390/810

Merge Sort Tree for Range Order Statistics

Merge Sort Tree for Range Order Statistics is a DSA topic. In plain words you use it for folder on disk in a file explorer. Don’t start with a slogan — start with that picture.

Smallest example: left < root < right. Type it, run it, and say what you see. If you can do that from memory, you know Merge Sort Tree for Range Order Statistics.

From the example next to this theory: Merge Sort Tree for Range Order Statistics — merge sort divides the array, sorts halves, then merges — O(n log n).

Trap — unbalanced BST becoming a list. Fix that before you talk about advanced DSA.

Viva — what is Merge Sort Tree for Range Order Statistics? Then show left < root < right. Then name the trap.

Exam tip

What is Merge Sort Tree for Range Order Statistics? Show this: left < root < right. Trap: unbalanced BST becoming a list.

Example

def merge_sort(arr):
    if len(arr) <= 1:
        return arr
    mid = len(arr) // 2
    left = merge_sort(arr[:mid])
    right = merge_sort(arr[mid:])
    out, i, j = [], 0, 0
    while i < len(left) and j < len(right):
        if left[i] <= right[j]:
            out.append(left[i]); i += 1
        else:
            out.append(right[j]); j += 1
    return out + left[i:] + right[j:]

print(merge_sort([5, 1, 4, 2]))

Merge Sort Tree for Range Order Statistics — merge sort divides the array, sorts halves, then merges — O(n log n).

Short notes

DefMerge Sort Tree for Range Order Statistics — folder on disk in a file explorer.
Ruleleft < root < right
Trapunbalanced BST becoming a list
Usea file explorer

def merge_sort(arr): if len(arr) <= 1: return arr mid = len(arr) // 2 left = merge_sort(arr[:mid]) right = merge_sort(arr[mid:]) out, i, j = [], 0, 0 while i < len(left) and j < len(right): if left[i] <= right[j]: out.append(left[i]); i += 1 else: out.append(right[j]); j += 1 return out + left[i:] + right[j:] print(merge_sort([5, 1, 4, 2]))

Merge Sort Tree for Range Order Statistics

Example

Short notes

Questions

Merge Sort Tree for Range Order Statistics

Example

Short notes

Questions