3. String Manipulation, Guess and Check, Approximations, Bisection 

Dr. Bell really does deserve an applause. Nice to see that the students actually did that in the end of the lecture. An amazing lecture with such articulate explanation of concepts. Thank to MIT OCW and also to the course staff!

0:01:54​ Strings 0:03:32 Strings indexing 0:05:34 (Coding) 0:06:49 Strings slicing 0:08:37 Strings slicing example 0:10:05 Strings slice inversly 0:11:18 ​Strings was fixed in memory 0:13:20​ For loops recap 0:16:31 Coding example : robot cheer leaders 0:18:00 Coding example : robot cheer leaders(Coding) 0:20:36 Coding example : robot cheer leaders 0:22:00 Coding example : robot cheer leaders 0:23:37 ​Guess and check cube root1.0 0:26:00 Guess and check cube root2.0 0:28:30​ Linear Search for cube root approximation 0:31:22 Linear Search for cube root approximation examples 0:32:53 Linear Search for cube root approximation of 10000 0:34:33 ​Linear Search preventing going to far 0:36:48 Bisection Search ​ 0:38:00​ Bisection Search @3rd iteration 0:39:52 Bisection Search summary 0:42:47 O(n) (Complexity)

I love Dr. Bell's enthusiasm for this. Makes learning it so much more fun!

Cannot exaggerate how helpful this content is. Thank you MIT OCW. I know hindsight is 20/20, but I wish I would’ve watched these videos (and the Walter Lewis videos) when I was in high school. I would’ve been so much more motivated to work hard and try to get into MIT.

This series of lectures and this lecturer are both so insightful that I often have to take long breaks between views because of the amount of complex and hidden/misunderstood information they make so accessible can make life overwhelmingly easy to understand Thank you Dr. Ana Bell, MIT and everyone involved with all of this! You are all amazing! (no angry text here :)

Im watching these lectures and practicing the course works from the website (the assignments and problem sets, also playing around with each thing I've learned). I've learned more in 3 days watching these than I have with a month of watching how-to tutorials (which is not surprising at all, just what I was trying before) and I am so glad I found this. I've made a very simple calculator that can add 2 numbers together that the user inputs! Very simple, but it's a victory to me! I'm starting college soon and majoring in computer science, so I can't wait to look back and see how far I've come. Really thanks to these kind people and this great teacher, I am understanding concepts that were constantly foreign to me no matter how much I tried to understand on my own. Although I haven't attended a class, I'll remember Dr. Bell as one of my favorite teachers because I have learned so much.

It was very useful. HUGE THANKS TO MIT.

cube = float(input("Enter a no whose cube root is to be calculated: ")) epsilon = 0.01 num_guesses = 0 if cube > 1: low = 0 high = cube guess = (low + high)/2.0 while abs(guess**3 - cube) >= epsilon: if guess**3 < cube: low = guess else: high = guess guess = (low + high)/2.0 num_guesses += 1 elif 0 < cube < 1: low = cube high = 1 guess = (low + high)/2.0 while abs(guess**3 - cube) >= epsilon: if guess**3 < cube: low = guess else: high = guess guess = (low + high)/2.0 num_guesses += 1 elif -1 < cube < 0: low = cube high = 1 guess = (abs(low) + high)/2.0 while abs(guess**3 - abs(cube)) >= epsilon: if guess**3 < abs(cube): low = guess else: high = guess guess = (low + high)/2.0 num_guesses += 1 else: low = cube high = 0 guess = (abs(low) + high)/2.0 while abs(guess**3 - abs(cube)) >= epsilon: if guess**3 < abs(cube): low = guess else: high = guess guess = (low + high)/2.0 num_guesses += 1 print('num_guesses = ', num_guesses) if cube < 0 : guess = -guess print(guess, "is close to the cube root of", cube) I guess this covers all possible cases?

Thank you for these videos MIT and Professor Bell, I've learned so much from watching these videos and this has accelerated the career change I'm beginning now at 27. Much love, -Sam :)

She is an amazing teacher! Explain it so clearly and fun. Thank you so much!

Hi guys. I'm going to thank the MIT team. Thank you, for these awsome courses.

Ana Bell you’re the best 🙏🏽

first sorry about my miserable English. All I want to say is thank you very very much You gave me a new start and a new goal in my life with python.

In Metrology, the Approximate solution or Guess and check is analogous to Linear search and the bi-sectIon search that Dr. Bell used is called Binary search. We use it comprehensively to find the levels and timing parameters of an integrated circuit.

Thank you for these courses. I took programming 17 years ago and wanted to brush up and learn Python. Since that seems to be the go to language now. I learned on VB. I've written a couple programs in VB for my current employer to connect to, manipulate, and retrieve data from a database. Mainly to make my job easier. LOL... I thought I would try and learn to do it in a more current language. Granted I have to get through this 6.0001 course first so I can get to 6.0002 where I need to be for database programming. I'm just hoping to learn something I didn't know. So far it's just refresher, which is fine. I already know pretty much everything being discussed. It's just slightly different syntax such as the double =, that's not a thing in VB. Or the single quote vs double quote. Yeah that's not a thing in VB either double quote only for strings.

Wow! They clapped at the end. Can't remember ever being so much into the class that I end up clapping.

This video literally answered all of my remaining questions

prof. Anna Bel your lectures are very helpful thanks

Love it. Dr. Bell, I hope you're still at this: you do it *really* well, and as I've watched from the first lecture, you're losing (or taming?) what seems to be a little stage-fright. I've never lost mine, but I did tame it enough to teach by interactive lectures way back when. Good onya. :-) One question: the "bisection" method seems just like (electronics engineering technology 35 years ago) what we called "successive approximation by halves"... and we did it with logic-gate constructs and not code... but is that the same idea?

this was a good lecture. I hope I watch them all.

college drop out learning python for free from MIT, who would have ever thought...

Code at 35:33 does not work for negative cubes. Here some changes in order to let it work also for negative numbers. Hope it will be useful :). ___________________________________________________________________________________ cube = 27 epsilon = 0.01 guess = 0.0 increment = 0.0001 num_guesses = 0 while abs(guess**3 - cube) >= epsilon and abs(guess**3) = epsilon: print('Failed on cube root of', cube) else: print(guess, 'is close to the cube root of', cube)

thnks alot prof Ana Bell ,,its very helpful for me

I really love this course and had to donate! Between MIT OCW & Free Code Camp, I'm definitely learning a lot of valuable information! Thank you! You guys are absolutely amazing!

The final algorithm that she explained is actually called Successive Approximation which there is also circuits for that which is called Successive Approximation Register (SAR) Analog to Digital Converter (ADC). Looking at these algorithms being in both computer science and electronic engineering is so cool.

Amazing content. Thank you MIT.❤

Thanks for sharing knowledge in free Actually Approximations were a headache for me which u guys solved.

I absolutely love these courses! Learning so much! Both lecturers I've seen are outstanding, and much appreciation to everyone involved in this amazing gift to mankind! I do have one, small suggestion, though. It would be great to leave the camera on the slides for longer periods of time. In a classroom, as I'm taking notes, I am focused more on the slides and what the teacher is saying, than on how they look (even though these teachers are very pleasant to watch). Because there is so much video of the instructors, it leads to a lot of pausing on slides and interrupting their wonderful lectures. :(

Excellent videos!! Thanks MIT

Great session! Thank you for contributing to the coding community.

Absolutely well done and definitely keep it up!!! 👍👍👍👍👍

What a helpful and interesting class!

thank you ,mit

Great lecture, thank you!

picking up python, I know absolutely nothing but I am 3 lectures in. Anybody else actually following along with the whole series and doing the problems the course gives ?

bisection,very insightful

thanks a lot Dr. Ana Bell

13:00 On for loops #pre 14:20 #14:39 It seems that you don't need to use the word range() when u are binding characters to the iteration variable 16:27 more complicated example of assigning characters to iteration variable #pre 19:32 explanation of 'in' keyword 19:50 20:14

21:58 Start of Basic Algorithms

nice work by DR. ANNA BELL and MIT as well..

43:51 She meant to say it only works for cubes greater than or equal to 1

13:21 loop variable that iterates over a collection, not a set?

nice lecture

Her Voice is Good and the Explaining is perfect ! thanks M-I-T the game of guess was Fun :D .

Great. I was hoping she would use Newton-Raphson or secant method for the cube root calculation.

# cube root calc cube = input("Please input a number: ") cube = int(cube) for guess in range(abs(cube) + 1): if guess**3 == abs(cube): if cube > 0: print("The cube root of", cube, "is", guess) break elif cube < 0: guess = -guess print("The cube root of", cube, "is", guess) break if guess**3 > abs(cube): print("Not a perfect cube")

38:00 the fact Sophie chosed 76 makes me wonder if she had an inkling as to what the teacher was aiming at. I mean a middle guess +1 is the hardest to find in a bisectional search. So either Sophie was lucky, or she's a sly fox >:)

Very useful

Correct me if I'm wrong but in 43:50 when the professor says the code works only for positive cubes, she makes an example of 0.5 not working, but that is the positive cube of 0.79... So I guess the correct statement to make is that this algorithm works only for positive cubes "bigger or equal to 1".

I am sending a packet of thanks to mit for this clear explanation And sorry I can't afford a Google product so only thank you

this is very helpful

# This might be of help to someone as I had trouble following along due to this misconception # Assign the string "MIT" to variable "i" i = 'MIT' # Print the elements of variable "i" starting from index 0 and ending at index 3 but not including index 3 - "[0:3]" print(i[0:3]) # When working with an index remember that it starts at 0 "[0:]" # when specifying where you would like to end the index "[:3]" it's up to the index value 3 but not including it # So in this example - "M" is located at index 0 # "I" is located at index 1 # "T" is located at index 2 # >>> MIT # If we were to print the elements of variable "i" at index "[0:2]" it would be print(i[0:2]) # >>> MI # "M" is located at index 0 # "I" is located at index 1 # "T" is located at index 2 # Rember it's up to the index value 2 but not including it

Are there any recommended videos to watch on RU-vid following this course to build more upon Python knowledge? Thanks!

Dammnnn what an experience should be studying at MIT!!!

I love her.

Nice tutorial and lesson. Just a small note, IMHO, on ~35:00 Anna made a small "mistake" when added "and guess

can''t believe sophie didn't pick 69

The idea of creating something to cheer oneself up is just funny

0:34:43 I would add 'and abs(guess**3)

I’ve watched this twice, and it’s still hard as hell for me to grasp

Why aren't we getting cube root of 27 and 8120601 in form of x.xx as we always increment guess by second decimal place.

God bless you.

Thanks

Who edited this? Every time she's pointing and talking about something on the board the camera is on her for some reason. Really bad practice.

Here's what I have for bisection search that accounts for negative numbers and abs (numbers) < 1: cube = -0.027 epsilon = 0.0001 num_guesses = 0 if cube >= 1: low = 0 high = cube elif cube >= 0 and cube < 1: low = cube high = 1 elif cube < 0 and cube > -1: low = -1 high = cube else: low = cube high = 0 if abs(cube) == 1: guess = cube else: guess = (high + low) / 2.0 while abs(guess**3 - cube) >= epsilon: if guess**3 < cube: low = guess else: high = guess guess = (high + low) / 2.0 num_guesses += 1 print('num_guess is', num_guesses) print(guess, 'is close to cube root of', cube)

37:00 that's exactly how one should play the clock game on the price is right.

thanks!

What I get from the approximation algorithm is that it will only give you an answer if the difference between guess**3 and cube is equal to epsilon, if it manages to jump above epsilon, guess will increase in value until it is

What does she mean with we can use for loops to iterate ANY SEQUENCE OF VALUES?? Im learning coding from scratch and some terms and concepts are quite sneaky to comprenhend, dont be to harsh pleas, and thanks

Very helpful resources 💙

my teacher is beautyfull

Thanks, now i can learn python in high school

At 10:05, a typo in screen slides ...evaluates to "hgfedbca", should be "hgfedcba".

when should we start doing those given assissgnment

Is there a typo at 6:56? s[: : -1] -> "hgfed'BC'a" doesn't make sense, unless it's supposed to be "...cba"

MIT one and only!👍🇷🇸

18:00 nice example

What is the answer of cube = 27 on the exercise. I rewrote the code on the IDE but the execution never ended, why? Help, please

My teacher in INDIA taught me in same way, iam studing in class 11th feeling too good after watching this, that i have same access to learning as any other brilliant student have 💛💛😇😇🇮🇳🇺🇸

Are these videos outdated or are they still a good place to start learning Python?

@21:20 Clean and peaceful

38:50 why was my first thought before she even explained the method to choose e as my number

Could you please tell me which programming environment python do you use in the lecture?

Guess & Check: cube = -27 # only guess the first natural number for which guess**3 >= cube for guess in range(abs(cube)+1): if guess**3 >= abs(cube): break # return perfect cube, if exists if guess**3 == abs(cube): if cube < 0: print("Cube root of " + str(cube) + " is " + str(-guess)) else: print("Cube root of " + str(cube) + " is " + str(guess)) # if there exists no perfect cube else: print(str(cube) + " is not a perfect cube")

In the approximate way of finding cube root codes: the guesses is increasing by guess += increment. I may think the output of guess should be multiply of increment, why the final output is something like .999999999998

An "all possible inputs" approach for cheer loop (Eric taught me 😐): an_letters = "aefhilmnorsxAEFHILMNORSX" word = input("I will cheer for you!. Enter a word: ") times = int(input("Enthusiasm level (1 - 10): ")) if times > 10: while times > 10: times = int(input("Please ensure an enthusiasm level between 1-10 ")) for char in word: if char == ' ': continue if char in an_letters: print("Give me an " + char + "! " + char) else: print("Give me a " + char + "! " + char) print("What does that spell?") print((word + "!!! ")*times)

when the robots are cheering, can you index word[1,3] in the for loop? for char in word[1,3]:

How do you do a bisection search for a cuberoot when x is a decimal? I can’t be find an answer anywhere.

The professor mentioned that a previously assigned string stays in memory after the variable is reassigned. Does this mean the programmer has to free memory allocates to the string manually?

I wonder what test are like in these programming courses at mit

27:39 what if the cube is not perfect and negative? ,

when I try to run the code at 32:07, my cell just says In[*] instead if In[a number] and the cell doesn't even run. Anyone know what's going on? Note: the rest of my notebook until this point is running perfectly.

Cube root simple guess. Why does that code keeps running?

Can someone help me out - surely the code at 29:55 is wrong? The While loop should not run because the condition is not true i.e. guess**3 - cube is NOT greater than or equal to 0.1. Rather 0x0x0 - 27 is LESS than 0.1? So surely the While loop would not run in the first place?

Am I stupid? In Approximations code we set guess=0.0 and increment=0.01. How can our answer be different than increment times number of guesses??

and guess**3

39:37 bisection search code

How to get the notes which mam is showing on board?

Assignment 2.3 Bisectional Search: salary = [] def optimal_savings_rate(): current_savings = 0.00 semi_annual_salary_raise = 7.00 down_payment = 250000.00 epsilon = 100 high = 1.00 low = 0.00 count = 0 portion_saved = (high + low) / 2 annual_salary = float(input("What is your annual salary?")) salary.append(annual_salary) """Lets's check for sufficiency of the person's annual salary.""" """Take portion saved as %100. Would it be enough to save for down payment?""" """With a for loop we save each semi years salary to salary list.""" """Then check if sum of them is enough to pay down payment.""" for i in range(6): annual_salary += (annual_salary * semi_annual_salary_raise * 0.01) salary.append(annual_salary) if (salary[1] + salary[2] + salary[3]+ salary[4] + salary[5] + salary[6]) / 2 < down_payment: print("Not enough income to have a saving equivalent to down payment in three years") return "Sorry." """After being sure about the sufficiency of the annual salary, we can begin to make a research bisectionally.""" while abs(current_savings - down_payment) > epsilon: current_savings = 0 annual_salary = salary[0] for i in range(0, 36): """Raise the salary each six month. Don't take first month.""" if i % 6 == 0 and i != 0: annual_salary += (annual_salary * semi_annual_salary_raise * 0.01) monthly_salary = annual_salary / 12 monthly_savings_income = current_savings * 0.04 / 12 monthly_savings = (monthly_salary * portion_saved) + monthly_savings_income current_savings += monthly_savings if current_savings < down_payment: low = portion_saved if current_savings > down_payment: high = portion_saved portion_saved = (high + low) / 2 count += 1 print("The proper saving portion would be really close to {}.Binary " "step count = {}".format(round(portion_saved,4), count)) optimal_savings_rate()

10:10, single line to reverse a string !! :)