Table of Contents The Problem Introduction 0:00 - 0:51 A Way To Think About Number Bases 0:51 - 3:56 Back To The Problem At Hand 3:56 - 4:16 Let's Add Some Numbers (Decimal, Base 10) 4:16 - 4:59 Let's Add Some Numbers (Binary, Base 2) 4:59 - 7:40 Bit Shifting Operators: The 'AND' -> '&' 7:40 - 9:41 Bit Shifting Operators: The 'XOR' -> '^' 9:41 - 11:36 Bit Shifting Operators: The 'Left Shift' -> '
What do you mean? It also works on negative numbers (great explanation of the whole process btw :) ). I used this algorithm on leetcode in C++ (and it has to work with negative numbers as well). The only catch is that I had to convert the carry to unsigned when doing the left bitshift (which wraps the bits around with 1111....11 (32 bits)) int getSum(int a, int b) { while(b) { int carry = a & b; // get all carry bits (all 1&1s) a = a^b; // sum of disjoint bits (everything except what needs to be carried)
// shift carry by one, as this is how a regular sum operation works // the carry is moved to the next position b = (unsigned)carry
dude, you need to come back and teach us. the world needs more people like you, blackpenredpen, the organic chemistry teacher, 3blue1brown, nick white, tech with tim, jenny it and many more.
I took compsci and learned this but could never explain to my friend who couldn’t grasp it. She struggled the whole time. This is such a great explanation and you are an excellent teacher.
Hey man I just wanted to say I think these videos are immensely helpful. The way you explain your thought process on these complex but tiny subjects rashly helps a person change the way they think about code, not to mention learning the lingo of a SWE. Also please don't ever lose the awkward endings and outtakes.
I have spent literal years glossing over bitshifting because no explanation could come close to me understanding it. I now have at least a basic knowledge and a starting place. Thank you!
Faced this problem in an interview with Qualcomm ... I wish I could see this video earlier to come up with bit manipulation solution :( Thanks a lot for clear explaination!
Thanks for your vids. I found some inconsistencies with your explanation. At 11:48 you say that when we do shift, '1 gets shifted out'. However, it doesn't. As an example, take 0101 (5) and 1101(13) When shifting, we add 0 on the right side and if carry started with 1, it will grow as well. We can't loose the first 1 because just like other 1s in the carry, it specify an index where we need to carry over. In the provided github code, line 134, it says "1 got shifted out". Again, if we shift it, we will loose part of our answer. The reason why, at some point, 'carry' becomes 0 and we brake out of the loop, because on 3rd iteration after increasing the carry by one more digit, we will be performing '&' operation between 4 digit (0010) and 5 digit (10000). The result of it will be 00000. Result of the '^' operation will be 10010 (which, again, won't be possible if we lost that left most '1'. 'carry
My Brother, since college back in 1999, I haven't had to use it. But, you have refreshed my way of thinking. Thanks and continue to progress forward!!!!
To begin with, here is an intuitive approach for this question. This is not optimal, but its easier to understand and present to your interviewer(at the beginning) def addTwoNumbersWithoutPlus(a, b): arr = [] carry = 0 while a > 0 or b > 0: # get the least significant digit of a x = 0 if a > 0: x = a & 1 a >>= 1 # get the least significant digit of b y = 0 if b > 0: y = b & 1 b >>= 1 # add them by using a naive hard-coded table num, carry = add(x, y, carry) arr.append(num) # append the carry if it exists if carry > 0: arr.append(1) # binary to int res = 0 for i in range(len(arr)): res += arr[i] * 2**i return res def add(a, b, carry): m = { (0, 0, 0): (0, 0), (0, 1, 0): (1, 0), (1, 0, 0): (1, 0), (1, 1, 0): (0, 1), (0, 0, 1): (1, 0), (0, 1, 1): (0, 1), (1, 0, 1): (0, 1), (1, 1, 1): (1, 1), } return m[(a, b, carry)]
You are extremely talented at teaching this stuff, I have struggled with bitwise operations for a while now, however after watching your explanation I was able to implement this myself, which is a major break through. Thank you for this video!
Watched on C computer Opened UA-cam on phone just to like the video Then thought you are really good so suscribed also And and and ... (redundant) I understand why these kind of stuffs are generally not well explained or no one does some hard work on it because everyone thinks that other DS&A are more important and they mostly form important questions but this concept was required in a programming question where looking to solve at the problem from this perspective seemed improbable. But normal bitwise loop operation would exceed the time limit. The only way was to understand thoroughly how the shifting works and then solve the question in a completely different way and then it passed within time limits. Keep posting concepts like these because they form really difficult questions.
I am always impressed with your videos. How do you choose the questions? It seems like you have a set of question that you plan to cover and I can feel that those questions are more relevant to actual skills that we need for interviews (not like brain teasers). Also, what's your plan after to cover all planned questions?
I built a list of like 300 when I started this channel. But at some point I just started doing the most burning questions that I felt that I just HAD to try to cover. And as for plans after I have many questions covered...eh, I don't know. Here is my rough plan for this project: backtobackswe.com/plans I don't think any human can ever cover all questions. But they can cover all topics and concepts. This channel is far from the latter.
Happy Halloween 🎃 Thank you for your kind words, Siddhant! Let us know other topics we could cover! We'd love to offer you 50% Off our exclusive lifetime membership use the code SPOOKY50 - backtobackswe.com/checkout?plan=lifetime-legacy&discount_code=SPOOKY50
5 steps: 1. base 10 to base 2 2. while carry > 0 3. carry = a & b 4. b = a ^ b 5. a = carry k = x * (1/2)^k, note that right shift will cut off the decimal part, e.g. 20 >> 3 => 20 * 1/8 => 2.5 = 2
Table of Contents
The Problem Introduction 0:00 - 0:51
A Way To Think About Number Bases 0:51 - 3:56
Back To The Problem At Hand 3:56 - 4:16
Let's Add Some Numbers (Decimal, Base 10) 4:16 - 4:59
Let's Add Some Numbers (Binary, Base 2) 4:59 - 7:40
Bit Shifting Operators: The 'AND' -> '&' 7:40 - 9:41
Bit Shifting Operators: The 'XOR' -> '^' 9:41 - 11:36
Bit Shifting Operators: The 'Left Shift' -> '
What do you mean? It also works on negative numbers (great explanation of the whole process btw :) ). I used this algorithm on leetcode in C++ (and it has to work with negative numbers as well). The only catch is that I had to convert the carry to unsigned when doing the left bitshift (which wraps the bits around with 1111....11 (32 bits))
int getSum(int a, int b) {
while(b)
{
int carry = a & b; // get all carry bits (all 1&1s)
a = a^b; // sum of disjoint bits (everything except what needs to be carried)
// shift carry by one, as this is how a regular sum operation works
// the carry is moved to the next position
b = (unsigned)carry
yeah
Hey !! This explanation is excellent! But I can't see the code for this problem in the description! Is it moved?
Arun Prakash same here
Thank you for these videos. However, I dont see the code in the description in any of your videos. Am I missing something?
dude, you need to come back and teach us.
the world needs more people like you, blackpenredpen, the organic chemistry teacher, 3blue1brown, nick white, tech with tim, jenny it and many more.
is he working at FAANG now?
@@albertjtyeh53 Back To Back SWE is at twitter!
Corey Schafer and Sentdex are great too
your explanation really helps people who were totally lost, like me.
nah, ur good
I took compsci and learned this but could never explain to my friend who couldn’t grasp it. She struggled the whole time.
This is such a great explanation and you are an excellent teacher.
Whenever I get stuck on a problem and see if your video is there, I'm relieved! Thank you man!
Nice sure
u r a good teacher bro!
Actually i came here because of your comment in leetcode lol :)
nice
@@BackToBackSWE I do agree you should make comments on all leet code questions you've solved! That's how I landed on B2B SWE!
@@angelanayiga4060 hey
@@angelanayiga4060 Now because of your comment I landed on B2B which I didn't even know.
Harsha G I’m really glad you landed on it and I hope it helps you the way it helped me 🤗🙏🏾
Now I understand a lot of techniques that I wasn't able to understand before by following your channel, keep it up!
nice
Hey man I just wanted to say I think these videos are immensely helpful. The way you explain your thought process on these complex but tiny subjects rashly helps a person change the way they think about code, not to mention learning the lingo of a SWE.
Also please don't ever lose the awkward endings and outtakes.
Explanation is so good that we won't need to write code for this in interview - just a dry-run with example would do.
ye
The best teaching that I have seen in my life till now is yours .
thanks
This is the ultimate guide to this hell of bits manipulation. Thank you so much.
You are such a good teacher! Thanks for breaking down the basics and emphasizing the details!
I have spent literal years glossing over bitshifting because no explanation could come close to me understanding it. I now have at least a basic knowledge and a starting place. Thank you!
Dude keep it up, i've learned more from you then my attempt at graduate school lol
ha nice
Likewise!
Faced this problem in an interview with Qualcomm ... I wish I could see this video earlier to come up with bit manipulation solution :( Thanks a lot for clear explaination!
nice
This is a stupid interview question to ask.. honestly, they don't deserve you.
@@prithazz maybe they wanted to check low level understanding
Thanks for your vids. I found some inconsistencies with your explanation. At 11:48 you say that when we do shift, '1 gets shifted out'. However, it doesn't.
As an example, take 0101 (5) and 1101(13)
When shifting, we add 0 on the right side and if carry started with 1, it will grow as well. We can't loose the first 1 because just like other 1s in the carry, it specify an index where we need to carry over.
In the provided github code, line 134, it says "1 got shifted out". Again, if we shift it, we will loose part of our answer.
The reason why, at some point, 'carry' becomes 0 and we brake out of the loop, because on 3rd iteration after increasing the carry by one more digit, we will be performing '&' operation between 4 digit (0010) and 5 digit (10000). The result of it will be 00000.
Result of the '^' operation will be 10010 (which, again, won't be possible if we lost that left most '1'.
'carry
Woah, a lot to parse, will need to jog my memory on this one. And nice, hey, I'm in Maryland rn so oof
Ive learnt alot today. Ive been struggling these days and i was almost burn out because of the amount of unfinished projects i had. Thank you
Happy to help
A short video like this about Two's complement would be great.
ok
very well explained solution!
i think it’s worth noting that this only really works with positive integers
Yeah, true, I'll add that to the notes.
Love you man. I'm in Graduate school & your videos have helped me so much.
My Brother, since college back in 1999, I haven't had to use it. But, you have refreshed my way of thinking. Thanks and continue to progress forward!!!!
Genuinely explained. Excellent, keep doing your work. You`re a great teacher.
thanks.
Using that ad to cover the redundant statement was brilliant lmao. I would've never noticed it was repeated if you didn't point it out honestly.
Your explanations are always so clear and engaging.
This is the best explanation I've ever seen! Thanks a lot!!!
sure
Totally understood from zero background. Thumbs up!
nice
Bro...u r a genius.... thanks for making me prepared.
nice! good luck
To begin with, here is an intuitive approach for this question. This is not optimal, but its easier to understand and present to your interviewer(at the beginning)
def addTwoNumbersWithoutPlus(a, b):
arr = []
carry = 0
while a > 0 or b > 0:
# get the least significant digit of a
x = 0
if a > 0:
x = a & 1
a >>= 1
# get the least significant digit of b
y = 0
if b > 0:
y = b & 1
b >>= 1
# add them by using a naive hard-coded table
num, carry = add(x, y, carry)
arr.append(num)
# append the carry if it exists
if carry > 0:
arr.append(1)
# binary to int
res = 0
for i in range(len(arr)):
res += arr[i] * 2**i
return res
def add(a, b, carry):
m = {
(0, 0, 0): (0, 0),
(0, 1, 0): (1, 0),
(1, 0, 0): (1, 0),
(1, 1, 0): (0, 1),
(0, 0, 1): (1, 0),
(0, 1, 1): (0, 1),
(1, 0, 1): (0, 1),
(1, 1, 1): (1, 1),
}
return m[(a, b, carry)]
nice
Great video. Speaking the entire process through like the computer solidified it for me.
Wow finally found someone who can explain things on youtube. Thanks.
sure
@@BackToBackSWE youtube needs someone who can explain system design questions as well.
@@skullTRTR Gaurav sen
You are extremely talented at teaching this stuff, I have struggled with bitwise operations for a while now, however after watching your explanation I was able to implement this myself, which is a major break through.
Thank you for this video!
Glad to know we could help!
You just explained how computers add on a fundamental level. Well done
Haven't seen a better explanation. Kudos.
thanks
This guy was born to teach!
yis he wuz
Loved the way you explained even the basics. Thank you.
sure
wow...it did take me a lot of rewinding to understand, but thanks to God I finally could get the whole picture of how it works.
nice
Never saw a better explanation than this👏👏👏
thanks
Very helpful but the code examples are missing from the description, were they removed?
That's a pretty intuitive explanation here!
Wow. You made it so simple. Thank you sir.
This was super helpful !! You're amazing at teaching !
thanks - glad it helped
Oh wow! Cool, this was a nice refresher. Great video
You are awesome! Your presentation is so clear and easy to understand!
love this channel!
thanks buddy! try our 5 day free mini course for some awesome content - backtobackswe.com/
I start so well, then I just get lost. I have to find a way to get this concepts in my head permanently.
You did such a great job at explaining this tedious problem. Please make a video on Dynamic programming concepts as well. :-)
ok
Watched on C computer
Opened UA-cam on phone just to like the video
Then thought you are really good so suscribed also
And and and ... (redundant)
I understand why these kind of stuffs are generally not well explained or no one does some hard work on it because everyone thinks that other DS&A are more important and they mostly form important questions but this concept was required in a programming question where looking to solve at the problem from this perspective seemed improbable. But normal bitwise loop operation would exceed the time limit. The only way was to understand thoroughly how the shifting works and then solve the question in a completely different way and then it passed within time limits. Keep posting concepts like these because they form really difficult questions.
Thx and ok
I am always impressed with your videos. How do you choose the questions? It seems like you have a set of question that you plan to cover and I can feel that those questions are more relevant to actual skills that we need for interviews (not like brain teasers). Also, what's your plan after to cover all planned questions?
I built a list of like 300 when I started this channel. But at some point I just started doing the most burning questions that I felt that I just HAD to try to cover.
And as for plans after I have many questions covered...eh, I don't know. Here is my rough plan for this project: backtobackswe.com/plans
I don't think any human can ever cover all questions. But they can cover all topics and concepts.
This channel is far from the latter.
This couldn't have been explained any better.
eh maybe it could've
I just started to study this stuff and my mind is like seeing the light
You are my go to when comes to all questions!
ye
Glad I found this channel. Truly amazing 🎉
Happy Halloween 🎃 Thank you for your kind words, Siddhant! Let us know other topics we could cover! We'd love to offer you 50% Off our exclusive lifetime membership use the code SPOOKY50 - backtobackswe.com/checkout?plan=lifetime-legacy&discount_code=SPOOKY50
Back To Back SWE + Leetcode + Cracking the Coding Interview = Total Interview prep package
Thanks for explaining this so clearly
sure!
This was a real cool and intuitive explanation! Thanks!
Thank You, Glad you liked it.
Do check out backtobackswe.com/platform/content
and please recommend us to your family and friends :)
This is great! but I wish you put the code in your video rather than in the description.
yeah got it
Awesome explanation covering from basics 🔥
thx
What an explanation man! thank you ton!!
sure
Awesome explanation.. By the way once again thank you for ...
best explanation, subbed
thanks
This was a fantastic explanation!!
thanks
"A problem well stated is a problem half solved" -Charles F. Kettering
i need to remember this...
ye
Thank you for the explanation!!
You are awesome!!!
Excellent teacher. Excellent!!
Never thought about this logic 😯😯.... Amazing 😍😍
sure
Man, that's been interesting and fun to listen to you! Thanks! I got topic)
nice
the best video on this question
Thanks
Awesome bro love all your videos
thank you.
much better than the technique taught in my grad class
Great vid! Why isn't it enough to do the following?
int whereCarry = (a & b)
I haven't replied to this for a bit, replying to close this out in my "unresponded to comments" feed.
Because when you use | it does not add two numbers. If it adds, then we would use a|b directly.
Thank you for the superb explanation!
Not able to find the code in the description! Can some let me know if I'm missing something?
Great video man ✊🏾
Excellent, you have put in lot of effort in explaining it, thanks appreciate it!! :)
sure
Best explanation, so thank you, man!
you really helped with just simple concepts
leetcode brings me here :) Thanks sir you are a good teacher :)
ya
U R an excellent teacher 👍🏼thanks a lot ✔️
Thanks sure - parents....
Thanks a lot.Ur explaination really cleared my doubt....
Explanation is awesome bro
Thank you so much for the clear explanation. Could you please upload video on Division as well
yes
You helped a lot , thank you for making such kind of videos.....
sure
The video is super helpful as usual... BTW, what's the name of the outro music??
OMG came from Geeksforgeeks. Thank you so much sir.
sure
Thank you so much, this solve my wondering for years as not an engineer
That's simply Great. I appreciate your work. Thanks for the explanation ♥️♥️
Nicely explained!
Very nice explanation!
wow. teaching in so simple way. Amazing!
Thank you, glad you liked it 😀
Do check out backtobackswe.com/platform/content
and please recommend us to your family and friends 😀
Clearly explained, Thanks
sure
Well explained buddy
thx
brilliant explanation~!
5 steps:
1. base 10 to base 2
2. while carry > 0
3. carry = a & b
4. b = a ^ b
5. a = carry k = x * (1/2)^k, note that right shift will cut off the decimal part, e.g. 20 >> 3 => 20 * 1/8 => 2.5 = 2
Thank you very much. Finally, I got the concept!
Best explanation I've seen. It helped me implement my C# program!
Could you do a similar video for substraction without using arithmetic operators?
Hey, thanks for the video! You're the best. Can you make more videos on bit manipulation please?
thx - thx - sure
Thank you, I'm learning so much from your lectures!
great
So clearly explained, i can't thank enough. 👍
Excellent video.
thx
Man!!! This is so helpful!!!
sure