Why Is Merge Sort O(n * log(n))? The Really Really Long Answer.

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Question: Analyze the total work that Merge Sort performs as an exact function of n, the length of the input list.
My Old MergeSort Video: • Merge Sort - A Step By...
The Infinite Series 1 + 2 + 4 + 8 + ... : en.wikipedia.org/wiki/1_%2B_2...
Logarithm Rules: www.chilimath.com/lessons/adv...
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[@BackToBackSWE]

Table of Contents (If you watch this all, you will know why Merge Sort is upper bounded by O(n * log(n))) What This Video Will Cover 0:00 - 0:40 The Fundamental Subroutines 0:40 - 1:32 The Split Subroutine 1:32 - 8:35 The Split Subroutine In Code 8:35 - 11:05 [ Old Clip ] Merge Sort Execution Trace 11:05 - 14:38 The Merge Subroutine 14:38 - 16:54 The Recurrence Relation 16:54 - 21:45 Investigation: What Work Is Done Per Level? 21:45 - 27:10 Getting Exact: Solving For Total Work Across All Levels 27:10 - 30:50 My Whole Life Has Been A Lie 30:50 - 34:51 Checking Our Work 34:51 - 35:48 Wrap Up 35:48 - 36:30 The code for Merge Sort is in the description, fully commented for understanding.

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For those getting stuck at [29:09], there is a 2^i before the parenthesis, but it might not be visible due to board reflections. Thank you for the video as it helped a lot to understand how its complexity is calculated for the first time.

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First time I ever saw ANYBODY even attempt to explain how we arrive at log n or n log n or all these math conclusions. And I mean even in texts supposedly written to help you understand algorithms. Most times the lecturers/writers just rush to the final result. Way to go brother!!

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You have taken the amount of time for me to understand merge sort from O(n!) to O(n*log(n)), thank you

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this is the stuff i was trying to find about mergesort, not just the how, but also the why, everyone else seems to think teaching splitting and merging functions is enough, but until u realize how the process is unfolding practically u never truely "realize" the essense of mergesort. The thing with recursive algorithms is that they seem very easy and obvious ,until u start thinking how the computer actually handles all the states,calls,order of calls,variables etc, thats probably why everyone tries to talk about recursion on a superficial level. This video is so great btw .Very in-depth.

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i would say you still need to watch few other videos to understand the concept of merge sort and the code as well, however he did great job explaining some concepts in this video, its amazingly helpful

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