BS-16. Kth Missing Positive Number | Maths + Binary Search

Problem Link: bit.ly/3p30UBg
Notes/C++/Java/Python codes:
We have solved the problem, and we have gone from brute force and ended with the most optimal solution. Every approach's code has been written in the video itself. Also, we have covered the algorithm with intuition.
Full Course: bit.ly/tufA2ZYt
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Linkedin/Instagram/Telegram: linktr.ee/takeUforward
0:00 Introduction of Course

[@sauravchandra10]

Is it only me or the brute force was difficult to understand?

[@bhalulal5947]

Same here bro I was frst shocked 😅

[@tarunprajapati7642]

For me also

[@kiranmoura2974]

Yes it is difficult

[@elizabethr5161]

even I feel difficult.

[@dhruv412]

same

[@rounaq_khandelwal]

Correction, @striver, at 2:45 the answer for arr=[5,7,10,12] and k=6 is 8 and not 7. Thanks for these series

[@Bharat_Rider]

😂😂 this correction helped me so much🤣

[@sidharthjain2129]

TBH it did help understand the brute force. Thanks mate.

[@rounaq_khandelwal]

@@sidharthjain2129 welcome!

[@Anony.musk01]

correction: 21:18 time complexity should be O(logN)* . Great explanation though

[@kirannagulakonda3443]

Happy to solve without watching solution , took 4hrs to figure out approach and code it . Yeah happy me🙂

[@aryansinha1818]

No doubt you explain nicely, everything gets crystal clear after going through your lecture video, but I wonder how do you come up with this type of solution on your own. It's like scientist making some mind boggling discoveries.

[@cinime]

Understood! Super fantastic explanation as always, thank you so so much for your effort!!

[@karanhaldar755]

I have never seen anything fantastic than this , I already enrolled in paid DSA course but trust me guys if I found out this channel and dsa sheet before that i have never taken the paid dsa course this is just awesome

[@alessandrocamilleri1239]

Thank you for the explanation. Two edge cases that should improve running time: if (k < vec[low]) return k; if (k > vec[high] - n) return k + n;

[@Dev-x3b]

💯

[@prathamsharma4802]

you are far better than any of the comedians and so called celebrities . Thanks!

[@swayamsharma7614]

in what sense you are comparing ?

[@bhaskararya9112]

Awesome explanation man, after some self dry run of few examples, I completely got the concept. Thanks!

[@dayashankarlakhotia4943]

Very beautiful explained. With logic

[@varunpalsingh3822]

Optimal one is just out of the box kind of thing ❤

[@shreyxnsh.14]

yeah, you can only solve this question in the interview if you have solved it before

[@Ayush37262]

​@@shreyxnsh.14 Thanks bhai, Solve nhi ho rha tha aur easy tag dekh kar depressed feel ho rha tha...

[@saswatrath4646]

@@Ayush37262 Many easy problems are actually hard so don't be demotivated if you can't solve an easy rated problem, it's because it's not easy at all.

[@sagarsrivastava1236]

Pure Genius Explanation....

[@adityamaurya6646]

This guy's just incredibleee!

[@sayakghosh5104]

For [4,7,9] and k = 3, answer will be simple that is 3, bcz k < arr[0] for all these cases we can directly return k. And at the end we can use arr[high] like:- " int diff = (arr[high] - high + 1); int miss = k - diff; return arr[high] + miss; "

[@takeUforward]

Yes you can do this as well

[@003_baneshubhamvijay3]

int diff = arr[high] - (high + 1); int miss = k - diff; return arr[high] + miss; A small correction in parenthesis**

[@sukhii0220]

how does this works ? where we would write this after when high cross low ?

[@sukhii0220]

@@003_baneshubhamvijay3 how does it working ? it gives 6 if we apply in [4, 7,9] and k=3

[@abhishekshinde5375]

brute force assume you have an empty array and we have some k value, say k = 4the missing number, so in this case the missing value would be 4 Case 1:- where the value at a index in the array < k now just consider the empty array again and we added a number smaller than k to it, say 2, so now when we again try to find the 4th missing number we would get it as 5 ( as 1 3 4 5 , as 2 already present in the array, hence the missing value shifts by one position ahead and 5 is the 4th missing value), hence whenever we get a number in the array smaller than k, the kth missing value shifts by position ahead Case2 :- where value at a index in array > k now consider empty array again and we added a number greater than k, assume k = 4 and we added 7 to it, here the kth missing element will be 4 itself, as even though seven was added - it indicated that the array might or might not contain the first 6 numbers and as the k = 4 value is lesser than 7, so this kth value would also come under missing value, and as 7 > k, so no effect on k occur. So k is the missing element

[@harrisjutt5021]

Thank you very much man 💜💜

[@user-ti3bd8mp1w]

understood Thank you striver for such an amazing explanation

[@dipanshuraj7868]

Literally, I spent one day trying to solve the brute force but when I saw the brute force in the video I was shocked how is it possible?😐😐

[@ipshitatandon5134]

Crazy derivation sir! thank youu for the series

[@Josuke217]

Nice question, learned a new concept.

[@purushottam108]

simple problem koo completed or comopleted problem koo simple, bana koi aap sai sikhai, you are master of dsa🤩🤩🤩🤩❤❤❤❤❤❤❤❤

[@girikgarg8]

Great explanation !

[@lostcyrus8578]

Bhaiya you are doing a great work ❤

[@rushilvyas9869]

Loved the explanation.

[@santhosh7042]

🤯 didn't thought for the binary search approach

[@AnmolGupta-oj4lm]

Understood Very Well!

[@lokeshnegi5051]

awesome explanation

[@user-or5oz1pk2x]

Thanks a lot Bhaiya . Crystal Clear

[@yoMisterWhyte]

The subtlety in the algorithm is not considering (arr[mid] - (mid+1) == k) coz if we hit that we have no way to figure out the answer(take k=1 as example and your arr[mid]-(mid+1) matches with k, that is why there is no condition for equals k. Idea is to move high to the index where the missing numbers are lesser than k, that way we get the low end and all we got to do is add the remaining. would have been good if this point was insisted coz if you forget the algorithm and try to write from scratch thinking oh it's binary search, you're gonna get stuck in an interview.

[@harshitpandey8304]

I agree

[@saswatrath4646]

great observation, it will help me memorize this algorithm better, thanks!

[@ayushmanpaul3931]

great explanation for low+k.

[@ReD4eva94]

Brilliant. Thanks!

[@mittal_aaditya]

For brute force in the array 5,7,10,12 k=6. For 5 -> k=7, 7 -> k=8, 10 exceeds the value hence k becomes 8 and 8 should be returned. Hope this helps!

[@seekingsoul871]

Best explanation

[@immrhrr]

thankfully I was able to do it by my own. I was able to think this approach myself

[@mikedelta658]

Fantastic. Thank you.

[@jaganmohan2198]

nicely explained bro ....thanks

[@thedon713]

you are the best brother

[@playwithlinux]

Nice explanation Sir ❤❤❤

[@pulkitjain5159]

amazing solution , maja agya

[@Gaurav_Tripathi_]

Understood Bhaiya ..!!

[@NazeerBashaShaik]

Understood, thank you.

[@_SahilShah]

letsss goooo!! Understood

[@mzia1210]

Helped a lot 🙂🙂😌

[@sarangkumarsingh7901]

Awesome Sir......

[@YourCodeVerse]

Understood✅🔥🔥

[@happyteen7195]

how beautifully u explained the brute force. top level intuition👑.

[@Shunya_Advait]

Understood Sir.

[@shamanthhegde2820]

Thank you so much!! this is one of the trickiest binary search problem which I was able to figure out on my own. class Solution { public int findKthPositive(int[] arr, int k) { if(k < arr[0]) { return k; } int low = 0; int high = arr.length-1; while(low

[@sukhii0220]

this existingdifff is the difference between the range we find out ?

[@ShahNawaz-cx3pi]

******** ONE OBSERVATION ********* what if the number of missing elements = k , i.e. int missing = arr[mid]-(mid+1); missing == k can we write this: if(missing

[@tridibeshmisra9426]

good question .. maza aya karke

[@rahulkarki6857]

Totally dependent on you bro ❤

[@harshdiwase1941]

I coudln't think this way !! best solution

[@md.imrankhan6912]

Legendary Boss

[@culeforever5408]

understood 😇

[@K_EN_VisheshSaini]

An easier brute force code:- int missingK(vector < int > vec, int n, int k) { // Write your code here. int i=0,j=1,missing=0; while(missing!=k){ if(vec[i]!=j){ missing++; j++; } else{ i++, j++; } } j--; //We did this because j moved 1 forward because of the if statement. So to get our answer, we need to move j backward by 1. return j; }

[@thedon713]

we learn here how to implement binary search not only how to solve in this specific problem.

[@rishabh_pant]

its perfect

[@shrinikclub8883]

there is a potential issue in your code. The j-- statement before returning the result might cause incorrect results. If the loop exits because missing equals k, then j should already represent the k-th missing positive number. Decrementing it before returning could lead to incorrect results.

[@user-xe2jt5vl5g]

i knew there was better algo than quick select thanks

[@Blissfulvibes3401]

thank you so much sir

[@Amine-yq7jg]

understood!

[@samreenimam8608]

bar bar dekho... hazaar bar dekho or practice kro is the key here

[@lucario404]

@takeUforward maybe you can update the time complexity in description for binary search as O(log2N)

[@senseiAree]

Understood ❤

[@user-tk2vg5jt3l]

Thank you Bhaiya

[@harshitjaiswal9439]

Understooooooood!

[@user-is6ky7pp2n]

Understood !! 😎😎

[@saketjaiswal9381]

21:23 error time complexity will be o(log base 2 n) that is o(log n)

[@Kaushik846]

Understood!!

[@PeeyushSharma-pc8fc]

the optimal solution definitely does not fit in the easy category striver 😂 btw amazing lecture🙏🏻♥

[@dank7044]

the brute force solution is beautiful.\

[@nayankhuman1043]

Understood :)

[@Akhilkumar0024]

this question scared the living daylights out of me, couldn't solve it even brute force was this really an easy question

[@pihus3498]

understoood :)

[@her_soulmate]

Understand 🎉

[@ankitgupta7467]

Hey Bhagwan , The BS intuition great

[@prakharsahu5778]

when are you planning to complete this series ?

[@anonymousits]

understood

[@dreamyme543]

Understood🙃

[@dogwoofwoof8154]

after a good brainstorming session it's time to see the video :)

[@Ayush37262]

Did you solved the question before watching solution??

[@dogwoofwoof8154]

@@Ayush37262 yep

[@Ayush37262]

@@dogwoofwoof8154 You are Batman!

[@parth2439]

Understood

[@U2011-n7w]

why this question is tagged easy on leetcode

[@VivekYadav-uy9ts]

Bacause of the contraints, there the array size is given between 1 to 1000 only, so you can just simply traverse the whole array and can find k'th missing element!

[@AS-gf3ci]

Both the solutions are difficult to grasp at first go. It needs another revisit for sure

[@shreyxnsh.14]

faxx, how is your dsa prep now btw?

[@bhanusingh4351]

at 21:17 , time complexity would be O(logn) [ just a human error]

[@sujalgupta6100]

GodLike!

[@nousad-ali-0]

After Watching 3 time I Finally understand

[@dhamotz4737]

can you explain why are we using missing=arr[I]-[I+1] , for finding the missing numbers ? cause this formulae is setting in the question but as I am customising the values in the question the missing numbers don't come? can u give some test cases in which you are getting answer for this formula only sp that I can approve that this formulae works for every possible cases not only what he has given there

[@mySpace940]

how in explanation high

[@ritikanand3425]

Bhaiya the GfG link to the question in a2z DSA Sheet the question is bit different to what explained in video for example in the test case n = 3 , k=1 {32 , 59 ,77} the first missing number is 33

[@chirag.3082]

woozy of a question

[@amitfritz11]

I just wonder this is only first video bit difficult to understand both brute force and optimal.

[@loveglobe]

jab tak suraj chaand rahega , striver tera naam rahega

[@dhamotz4737]

can someone explain me the missing number formulae in the brute force as its setting correct for the case which striver has taken but once I am changing the values in the array and trying to find the new missing number I am not getting what I should get, did I get the question in a wrong manner , am I missing any key point of the question ?

[@akworld2739]

your brute force solution is optimal solution for me 🤣🤣

[@VishalGupta-xw2rp]

13:10 opposite polarity

[@ambaradhikari7425]

Bro by when your whole dsa sheet will be covered, placement coming up?any eta approx?

[@adityakanwar8370]

+1

[@rohandas6298]

int missingK(vector < int > vec, int n, int k) { int low=0,high=n-1; while(low

[@CodeMode9313]

Habibi batai toh mast hai tum ....correction :) @ 21:18 time stamp ie TC be logn

[@preritphoenixgupta330]

Hi Striver, I'm a final year student and our placement season is coming soon can you give some tips. Also, there are some topics which I need to work upon like Stack n Queues when can we expect those series/ playlist from You. I like your way of teaching and approach, I know you are caught up with a lot of work but if you could bring those series soon or suggest some alternatives that would be great.

[@pulkitjain5159]

bhai stack m mujhe bhi dikkat aai thi par bhaiya ka largest histogram wala solution dekhna , dono parts , then leetcode ke question lagana nahi aaye toh uske solution dekhle , fhir aane lagega comfidence m bhi yahi kara hu bhai

[@preritphoenixgupta330]

@@pulkitjain5159 okay, thanks bhai

[@saketsoni2587]

stack me sirf monotonic stack wala ek concept hai jo baar baar dikh jata sawalo me, wo largest histogram wale me covered hai

[@preritphoenixgupta330]

@@saketsoni2587 Ok Thanks

[@rhul0017]

intuition behind incrementing k is not clear, are we assuming kth element is k inititally and why incrementing k leads to answer, i understood the code but intuition is not clear

[@anshulrawat3458]

bhaiya bs ques tha ki : jaise aap figure out krrh ho ki 1,2,3,4 ideally 4,7,9,10 arr m hone chaiye the. so inko substract kre to missing number milenge. iska logic nhi bnra dry run krte wkt. mtlab wo missing number maths se aara h but kaise aaya ye nhi feel ara..

[@Manishgupta200]

Optimal code takes much time to understand

[@umangkumar2005]

int missingK(vector < int > arr, int n, int k) { int low=0; int high=n-1; int mid=low+(high-low)/2; while(low

[@badrirao6472]

why cant we use arr[mid] -- (mid + 1 ) formula to calculate the missing number instead of the formula arr[high ] -- (high + 1) ??