2. Data Structures and Dynamic Arrays

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MIT 6.006 Introduction to Algorithms, Spring 2020
Instructor: Erik Demaine

Data structures are ways to store data with algorithms that support opperations on the data. These collection of osrted operations are interfaces. This class goes over two main interfaces: sequence and set.

License: Creative Commons BY-NC-SA

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This man's enthusiasm for algorithms is what I want in my life.

pantheonCaspian

I've been listening to this guy teaching algorithms for over 10 years seems his age algorithms is super efficient where his age is always constant O(1)

unorandom

0:00 : intro
0:50 : interface vs data-structure
5:50 : static sequences & static arrays
16:50 : dynamic sequences & linked-list
25:20 : static array vs linked-list
34:25 : dynamic arrays (lists in python)
46:27 : amortization

ParthPatel-vjzv

Thanks to the MIT for making this available for free. This is a very selfless move. Amazing

domemvs

This is what passion looks like. I got my CS degrees at the first boom/bust cycle in the 80s. I've enjoyed everything about this career.

georgejetson

I've been programming on and off since high school (class of 2003) and recently decided to catch back up with the MIT OpenCourseWare lectures... 10:05 to 11:17 is the first time I've ever had zero indexing explained in a way that just makes it clear that's why it's being done. Never in my entire life had anyone just said it was an offset in memory and I'm kind of disappointed. That single simple fact of something I thought I knew well just made a whole lot of memory addressing knowledge grok immediately.

RurikLoderr

Shout out to the camera man! For panning to the information he’s referencing that we can’t see!

MrApolloIII

Never got a chance to listen to lectures at IIT. I am lucky enough to learn from even quality lectures. Thanks to MIT.

shankar

In fact I have been watching a lot of tutorials from this channel and this professor is one of my favorites.

yeboahdominic

Awesome lecture! A treat to hear a talk on basics by such an accomplished computer scientist!

dcpugh

I experienced the fact that when you listen to passionate people, you would love to become passionate. This is the ultimate benefit I am taking away right now from this lecture.

shankar

I love the way this guy writes on the board. It's so satisfying.

HulkRemade

Oh, oh, I'm so happy. Years ago I downloaded the old videos and tried watching on metros. I quit at around 1/3. It was too hard for me. Now I'm back. Let me try learning this again.

hanyanglee

This lecture was so brilliant. The concepts are crystal clear.

ssaadhussain

🎯 Key Takeaways for quick navigation:

00:28 🧠 *Today's focus is on data structures, specifically sequences, sets, linked lists, and dynamic arrays.*
01:27 🗂️ *Interface defines what to do; data structure defines how to do it. Data structures involve storing and manipulating data with specified operations.*
02:51 🔄 *Two main interfaces: sets and sequences. Multiple data structures can solve the same problem, each with different advantages.*
05:43 📊 *Static sequence interface includes build, length, iteration, get, and set operations. Focus on static arrays as a natural solution.*
08:34 🧮 *Static array relies on the word RAM model, allowing constant time access. Memory allocation model assumes linear time for array creation.*
17:04 ➕➖ *Dynamic sequence interface adds insert and delete operations. Introduces the concept of insert_at to maintain indexing consistency.*
19:56 ⏮️⏭️ *Special cases like insert_first, insert_last, get_first, set_first, get_last, and set_last are introduced and can be more efficient to solve.*
21:20 🔗 *Linked lists, composed of nodes with item and next fields, are introduced as a data structure to implement dynamic sequences.*
23:17 📚 *Arrays and pointer-based data structures were discussed, highlighting the use of pointers as indices into the memory array.*
25:33 ⏭️ *Dynamic sequence operations were explored on static arrays and linked lists, revealing the challenges of insertion at the beginning for both.*
29:51 🔄 *Linked lists excel in insert and delete operations at the front but struggle with random access, making operations like get and set inefficient.*
33:51 🔄 *The lecture introduces dynamic arrays, aiming to combine the advantages of linked lists and static arrays for efficient operations.*
35:14 🧠 *Dynamic arrays relax the constraint that the array size equals the number of items, allowing for efficient insertions at the end in constant time.*
40:12 📏 *The lecture discusses resizing strategies for dynamic arrays, emphasizing the importance of choosing a constant factor larger than 1 to avoid frequent resizes.*
43:31 ⏱️ *The amortized analysis of resizing dynamic arrays is explained, revealing a geometric series summing to roughly linear time, emphasizing the efficiency of the strategy.*
45:51 🔄 *Geometric series are dominated by the last term, allowing for simplified analysis using theta notation, such as theta of the last term like 2 to the log n, which is theta n.*
46:45 📈 *Amortization is introduced as a way to analyze the average time of operations over a sequence, considering that while some operations may be expensive, they are balanced by cheaper ones, resulting in amortized constant time for certain operations.*
47:42 📊 *Amortization is described as an averaging concept over a sequence of operations, allowing for high-cost operations like resizing to be distributed across the cheaper ones, achieving almost constant time on average.*
49:38 🔄 *Dynamic arrays achieve constant amortized time for operations like insert_last and maintain constant time for get_at and set_at, showcasing a balance between the strengths of arrays and linked lists.*

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