Lecture

Merge Sort: Divide, Conquer, Combine

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In course

CS-250: Algorithms I

The students learn the theory and practice of basic concepts and techniques in algorithms. The course covers mathematical induction, techniques for analyzing algorithms, elementary data structures, major algorithmic paradigms such as dynamic programming, s ...

Description

This lecture covers the concept of Merge Sort, which applies the divide-and-conquer strategy to sorting. The instructor explains the process of dividing an array into two subarrays, recursively sorting them, and then merging them back together. The lecture delves into the implementation details of the merging algorithm, the linear-time merging idea, and the analysis of Merge Sort's time complexity. By analyzing the recurrence relation for Merge Sort, it is shown to run in O(nlog n) time, making it significantly faster than Insertion Sort for large instances.

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Instructors (3)

Mikhail Kapralov

Teaching & PhD PhD Students Weronika Wrzos-Kaminska, Guy Weissenberg, Davide Mazzali, Ekaterina Kochetkova, Kshiteej Jitesh Sheth Past EPFL PhD Students Amir Zandieh, Aidasadat Mousavifar, Navid Nouri, Jakab Tardos, Grzegorz Adam Gluch, Makarov Mikhail Past EPFL PhD Students as codirector Paritosh Garg Courses Algorithms II CS-450 The students learn the theory and practice of basic concepts and techniques in algorithms. The course covers mathematical induction, techniques for analyzing alg

Ola Nils Anders Svensson

Alessandro Chiesa

Alessandro Chiesa is a faculty member in computer science. He conducts research in complexity theory, cryptography, and security, with a focus on the theoretical foundations and practical implementations of cryptographic proofs that are short and easy to verify. He is a co-author of several zkSNARK libraries, and is a co-inventor of the Zerocash protocol. He has co-founded Zcash and StarkWare Industries. He is a recipient of a Sloan Research Fellowship (2021), an Okawa Foundation Research Grant (2020), and Google Faculty Research Awards (2018 and 2017). He was included in MIT Technology Review's "35 Innovators Under 35" list in 2018.

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Related concepts (32)

External sorting

External sorting is a class of sorting algorithms that can handle massive amounts of data. External sorting is required when the data being sorted do not fit into the main memory of a computing device (usually RAM) and instead they must reside in the slower external memory, usually a disk drive. Thus, external sorting algorithms are external memory algorithms and thus applicable in the external memory model of computation. External sorting algorithms generally fall into two types, distribution sorting, which resembles quicksort, and external merge sort, which resembles merge sort.

Bubble sort

Bubble sort, sometimes referred to as sinking sort, is a simple sorting algorithm that repeatedly steps through the input list element by element, comparing the current element with the one after it, swapping their values if needed. These passes through the list are repeated until no swaps had to be performed during a pass, meaning that the list has become fully sorted. The algorithm, which is a comparison sort, is named for the way the larger elements "bubble" up to the top of the list.

Bucket sort

Bucket sort, or bin sort, is a sorting algorithm that works by distributing the elements of an array into a number of buckets. Each bucket is then sorted individually, either using a different sorting algorithm, or by recursively applying the bucket sorting algorithm. It is a distribution sort, a generalization of pigeonhole sort that allows multiple keys per bucket, and is a cousin of radix sort in the most-to-least significant digit flavor. Bucket sort can be implemented with comparisons and therefore can also be considered a comparison sort algorithm.

Complexity class

In computational complexity theory, a complexity class is a set of computational problems "of related resource-based complexity". The two most commonly analyzed resources are time and memory. In general, a complexity class is defined in terms of a type of computational problem, a model of computation, and a bounded resource like time or memory. In particular, most complexity classes consist of decision problems that are solvable with a Turing machine, and are differentiated by their time or space (memory) requirements.

P (complexity)

In computational complexity theory, P, also known as PTIME or DTIME(nO(1)), is a fundamental complexity class. It contains all decision problems that can be solved by a deterministic Turing machine using a polynomial amount of computation time, or polynomial time. Cobham's thesis holds that P is the class of computational problems that are "efficiently solvable" or "tractable". This is inexact: in practice, some problems not known to be in P have practical solutions, and some that are in P do not, but this is a useful rule of thumb.

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