DSA · Theory

Recurrence Relation of Merge Sort

← All stacks

Theory

463/810

Recurrence Relation of Merge Sort

Recurrence Relation of Merge Sort sits in the roll list. Rohit’s job is names A→Z. Write that first.

Do Recurrence Relation of Merge Sort once by hand. n log n vs n². Change one input. Say the new result out loud.

Skip Recurrence Relation of Merge Sort and unstable sort when equal keys matter shows up in the roll list.

Use Recurrence Relation of Merge Sort when names A→Z must stay clear. If a simpler DSA step works, use that instead.

If names A→Z breaks under Recurrence Relation of Merge Sort, check unstable sort when equal keys matter first.

Place Recurrence Relation of Merge Sort next to nearby DSA work — n log n vs n² is the link.

Viva for Recurrence Relation of Merge Sort: what it is → n log n vs n² → the mistake (unstable sort when equal keys matter).

Exam tip

For Recurrence Relation of Merge Sort: definition + the roll list + one failure.

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 — Rohit uses it for names A→Z in the roll list.
RuleRecurrence Relation of Merge Sort → n log n vs n².
RememberRecurrence Relation of Merge Sort + a dry-run table (the roll list).
UseRecurrence Relation of Merge Sort in the roll list (names A→Z).
TrapRecurrence Relation of Merge Sort — unstable sort when equal keys matter.
ExRecurrence Relation of Merge Sort → names A→Z.

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