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Recurrence Relation of Merge Sort

Theory

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Recurrence Relation of Merge Sort

Recurrence Relation of Merge Sort is a DSA topic. In plain words you use it for names A→Z in the roll list. Don’t start with a slogan — start with that picture.

Smallest example: n log n vs n². Type it, run it, and say what you see. If you can do that from memory, you know Recurrence Relation of Merge Sort.

From the example next to this theory: Recurrence Relation of Merge Sort — merge sort divides the array, sorts halves, then merges — O(n log n).

Trap — unstable sort when equal keys matter. Fix that before you talk about advanced DSA.

Viva — what is Recurrence Relation of Merge Sort? Then show n log n vs n². Then name the trap.

Exam tip

What is Recurrence Relation of Merge Sort? Show this: n log n vs n². Trap: unstable sort when equal keys matter.

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]))

Recurrence Relation of Merge Sort — merge sort divides the array, sorts halves, then merges — O(n log n).

Short notes

DefRecurrence Relation of Merge Sort — names A→Z in the roll list.
Rulen log n vs n²
Trapunstable sort when equal keys matter
Usethe roll list

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]))

Recurrence Relation of Merge Sort

Example

Short notes

Questions

Recurrence Relation of Merge Sort

Example

Short notes

Questions