### 4qqqq's blog

By 4qqqq, 7 weeks ago,
Solution

B. Divan and a New Project

Solution

C. Divan and bitwise operations

Solution

D1. Divan and Kostomuksha (easy version)

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D2. Divan and Kostomuksha (hard version)

Solution

E. Divan and a Cottage

Solution

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 » 7 weeks ago, # |   0 Auto comment: topic has been updated by 4qqqq (previous revision, new revision, compare).
 » 7 weeks ago, # |   +3 Auto comment: topic has been updated by 4qqqq (previous revision, new revision, compare).
 » 7 weeks ago, # |   +11 Is the dynamic programming approach used in D1 a known concept?
•  » » 7 weeks ago, # ^ |   +19 I'm not sure what you mean by "known" here, but the idea isn't too insanely extraordinary, at least for D1.
 » 7 weeks ago, # |   +30 Why is the runtime for D2 log(log(n))? Does does the average number between 1 and n have about log(log(n)) unique prime factors or something? Why is that?
•  » » 7 weeks ago, # ^ |   +16 I think it's related to https://en.m.wikipedia.org/wiki/Divergence_of_the_sum_of_the_reciprocals_of_the_primesAnd prime seive where inner loop is only over primes has this many iterations:n/2 + n/3 + n/5 + n/7...(Factor out n)
•  » » 7 weeks ago, # ^ |   +8 The answer to you question is yes, the numbers from 1 to n have in total O(nloglogn) unique prime factors (this is result from classic sieve of erasthothenes for listing prime numbers). So each number has on average loglogn unique prime factors.
•  » » 7 weeks ago, # ^ |   +8 It is the result of Mertens' theorem.
•  » » 5 weeks ago, # ^ |   0 I see this problem before, but instead of counting the maximum sum, we need to count expect value of the sum. Can you help me with this :(((
 » 7 weeks ago, # |   +114 Imagine statements were this short
 » 7 weeks ago, # |   +16 Here's an $O(n\log n)$ solution for E (with $O(\log n)$ query time). For a given sequence of $k$ temperatures, let $f(T)$ be the answer for the query $T$. Then we have $f(i+1)=f(i)$ for $2k$ different values of $i$, and $f(i+1)=f(i)+1$ for all other values of $i$. (I won't prove this, but you can try it out for yourself.) We solely have a data structure that stores the $2k$ values of $i$ for which $f(i+1)=f(i)$. On receiving $T_i$, we add $a$ and $b$ to the data structure, where $f(a)=T_i-1, f(a+1)=T_i, f(b)=T_i, f(b+1)=T_i+1$.Answering a query reduces to determining how many stored values are below $T$. I used a PBDS and binary searched to handle insertions which means the complexity is actually $O(n\log^2n)$ but in principle this can be made into $O(n\log n)$.Implementation: https://codeforces.cc/contest/1614/submission/137071970
 » 7 weeks ago, # |   0 For the second question, my approach seems to be $O(Tn)$
 » 7 weeks ago, # | ← Rev. 2 →   +58 $cnt_i$ is the amount of $a_i=i$. Really? I think $cnt_i$ is the amount of $j$ such that $a_j\bmod i=0$.
 » 7 weeks ago, # |   -6 That feeling when you wasted 4 attempts on problem C because of wrong modulo :’)
 » 7 weeks ago, # |   0 Problem C solution before contest : https://math.stackexchange.com/questions/712487/finding-xor-of-all-subsets
 » 7 weeks ago, # |   -25 What's the f**k!
•  » » 7 weeks ago, # ^ |   -15 Bro,Can you find your dear mommy?
 » 7 weeks ago, # |   0 In question B, it is given how the businessman will travel for first 10 years(5256000 minutes) only. And it is asked to choose the cordinates such that it minimises the time for walking within first 10 years only, no info. about what to consider if he can't visit every building in that time, what to print in that case the minimum time < 10 years by visiting only some good buildings or just try to minimise the time only if buildings can be travelled within 10 years or something else can't decide.
•  » » 7 weeks ago, # ^ |   +8 I think we shouldn't focus on 10 years time, that's of no use.
•  » » » 7 weeks ago, # ^ |   0 If that info. is of no use it should not be there in the problem statement. I could not solve the problem just because someone has not used correct wording to explain. Anyways now i get it that i should not give any importance to story part. Thanks for replying!
 » 7 weeks ago, # |   0 My solution in Problem B was clearly of time complexity O(nlogn) and I still got TLE!
•  » » 7 weeks ago, # ^ | ← Rev. 2 →   0 You are storing index of each a[i] using a hashMap. Suppose that there are many a[i] which are identical in that case at some point the List map.get(i) will reach a limit and will have to increase its size and cost of that is o(N) which will make it a quadratic equation. That is one thing I see.
•  » » 6 weeks ago, # ^ |   0 Use an ArrayList of Integers and Collections.sort(), it's always O(nlogn). Arrays.sort() is O(n^2), although docs say it is O(nlogn).
 » 7 weeks ago, # |   +47 Terrible editorial for D1 and D2 with no code ? Its very confusing,probably some translation error
•  » » 7 weeks ago, # ^ | ← Rev. 4 →   +30 Correct me if I'm wrong, but there seems to be multiple errors in editorial of D1.Let $dp[i]$ be the maximum answer for all arrays, the last element of which is divisible by $i$.should beLet $dp[i]$ be the maximum answer if we can pick from the whole array, and every element of the resulting array is divisible by $i$.Initially, $dp[i]=cnt[i]⋅i$, where $cnt[i]$ is the amount of $a[i]=i$.should beInitially, $dp[i]=cnt[i]⋅i$, where $cnt[i]$ is the number of elements in $a$ that is divisible by $i$.Edit: Unfamiliar with comment formatting
•  » » » 7 weeks ago, # ^ |   0 and the complex is O( C logC ) , or it will be change ? I could not implement editorial logic so can you sher your code ? THNX ^_^
•  » » » » 7 weeks ago, # ^ | ← Rev. 5 →   +3 Yes, it is still $O(C log C)$, since $\frac{n}{1} + \frac{n}{2} + ... + \frac{n}{n} = O(n log n)$. You can see it in my implementation. https://codeforces.cc/contest/1614/submission/137105361Edit: Still unfamiliar with Codeforces comment format
•  » » » » » 7 weeks ago, # ^ |   0 THNX ^_^
•  » » » 7 weeks ago, # ^ |   0 Thank you
•  » » » 7 weeks ago, # ^ | ← Rev. 2 →   +10 In D2， we have to compute cnt too, but computes it takes O(ClogC). So is the real complexity of D2 O(ClogC)?
•  » » » 6 weeks ago, # ^ |   0 I don't understand. If $a = [10, 15]$ , $dp_5 = 5 \cdot 2 = 10$, but clearly the answer for such $a$ is $20$
 » 7 weeks ago, # |   0 Can’t understand E’s solution. Can anyone explain more detail?
 » 7 weeks ago, # |   +19 Here are the video Solutions for problems A-D1 In case you are interested.
•  » » 7 weeks ago, # ^ |   0 Superbly, helpful great!
 » 7 weeks ago, # |   0 Submission for CCould anyone please explain what's wrong in my code? I applied the exact same approach as in the editorial. Thanks in advance.
•  » » 7 weeks ago, # ^ |   +3
•  » » » 7 weeks ago, # ^ |   0 Thanks for the help.
•  » » » 7 weeks ago, # ^ | ← Rev. 2 →   0 Could you explain what difference does it make since the vector v has just 0's added to its end? And the bitwise OR remains the same if we bitwise OR the elements with 0's. I'm a bit confused. Thanks in advance.
•  » » 7 weeks ago, # ^ |   0 The size of vector v is m not n.
•  » » » 7 weeks ago, # ^ |   0 Thanks for correcting.
•  » » » 7 weeks ago, # ^ |   0 I'm still confused could u explain more?
•  » » » » 7 weeks ago, # ^ |   +1 the for-loop is m-size, so there may be more than n element in the vector, up to 2^n.
•  » » » » » 7 weeks ago, # ^ |   0 Thanks
 » 7 weeks ago, # | ← Rev. 3 →   +8 In E2, you can also write the following. Let's iterate the first number. It is clear that all subsequent gcds are divisors of this starting number. So you can do dp not on all numbers, but on divisors. And it works for $O(n*countDivider^2)$. If not iterated by the same number, then it is TL48). But you can sort all the numbers in descending order and make a cutoff in time (it is clear that the number in the answer will not be the smallest). And it's already OK)
 » 7 weeks ago, # | ← Rev. 2 →   +20 “where $cnt_i$ is the amount of $a_i=i$. ”I think $cnt_i$ is the amount of $j$ such that $a_j \text{ mod } i=0$.But I cannot understand how to get $cnt$ in $O(C \log\log C)$ time.
 » 7 weeks ago, # |   +3 There's an easier way to solve problem E. Let's say $f_i(x)$ is the temperature in the morning of the $i+1$-th day when the temperature is $x$ in the morning of the $i$-th day. Then for the query $x$ on day $i$ we just output $g_i(x)=f_i(f_{i-1}(f_{i-2}(...f_1(x)...)))$. Assuming that we've been able to solve for $g_{i-1}(x)$, we just need to solve for $g_i(x)$ in terms of $g_{i-1}(x)$.Firstly we can observe $\forall x_1 \le x_2,1\le i\le n,f_i(x_1)\le f_i(x_2)$, and then we can derive that $\forall x_1 \le x_2,1\le i\le n,g_i(x_1)\le g_i(x_2)$.So we can use binary search to find two positions $a,b(a \le b)$ satisfy $g_{i-1}(a-1)=T_{i-1},g_{i-1}(a)=g_{i-1}(b)=T_i,g_{i-1}(b+1)=T_{i+1}$, then $\forall x < a,g_{i}(x)=g_{i-1}(x)+1;\forall x>b,g_{i}(x)=g_{i-1}(x)-1;\forall a \le x\le b,g_i(x)=g_{i-1}(x)$. So we just need to insert $a$ and $b$ into some data structure which can support querying how many values are less than x. Here is my Implementation:137124792
 » 7 weeks ago, # |   +5 Still unsure about how to tackle D. Any hints?
•  » » 7 weeks ago, # ^ |   0 Can someone please explain D?
•  » » 7 weeks ago, # ^ |   +1 A useful video was posted here.
 » 7 weeks ago, # | ← Rev. 2 →   +5 Can anyone help me to understand jiangly solution for the problem E: https://codeforces.cc/contest/1614/submission/137002860What is the variable v and what the erase function does?
•  » » 7 weeks ago, # ^ | ← Rev. 2 →   0 I think the thing he's trying to do is maintain "how many numbers less than $x$ are removed/merged", while $v$ is the minimum number alive.For instance, if T = {1, 1, 0}, $v$ would first increase to 1, then stays at 1, finally go down to 0. And for the erase part, the segment tree will hold 1 at position 0 after the first operation (which means $v+0$ has 1 temperature merged into it).See my submission for more details. 137180586
 » 7 weeks ago, # |   +3 I was having a lot of trouble understanding editorial for D2, finally figured it out. Sharing my code here in case anyone is also confused like I was. 137185957The tricky part is actually calculating cnt[i] in O(CloglogC), you have to be very careful with double counting. As a simple example, say your array is [2, 4, 6, 12]. Here 12 is divisible by both 2*2 and 2*3, so while computing cnt[2] you might double count it.
•  » » 5 weeks ago, # ^ | ← Rev. 2 →   0 It's really nice explanation. As you mentioned, we have to loop for primes in advance to avoid double counting.
 » 7 weeks ago, # | ← Rev. 2 →   0 for B question i did the exact same thing assigning the main office coordinate to 0 next -1 next 1 then -2 and so on but i still it says my answer is wrong for test case 1 can anyone identify what's wrong in my code it would help me a lotlink to my submission code
•  » » 7 weeks ago, # ^ |   0 You have to sort the array first then where he visits most should be -1 then 1 then -2, so on. But you didn't sort anything.
•  » » » 7 weeks ago, # ^ |   0 if you see my submission you can see that i have sorted the array using the stl sort function
•  » » » » 7 weeks ago, # ^ |   0 You are printing the coordinates in the wrong order. You have to print it in the order they are given in the input, not in the order they are after you sorted them.
•  » » » » » 7 weeks ago, # ^ | ← Rev. 3 →   0 oh okay ill try that thanks
 » 7 weeks ago, # |   0 I didn't understand the approach for problem D1, can someone please give a more clearer picture
 » 7 weeks ago, # | ← Rev. 2 →   -8 1
 » 7 weeks ago, # |   0 i'm lost. in problem C we have ranges and the bitwise OR of each element in range.suddenly we're counting each bit of all elements? we don't even know the array, right? why don't we need to recover the array?? i'm confused.can someone please ease my confusion :( i need help
•  » » 7 weeks ago, # ^ |   0 Yes you are right! also as Editorial says you have to just take Bitwise OR of an array(Still if you don't have but you have their Bitwise OR) Even You can do that after making Array with those conditions and then you'll see that you are doing same thing.
•  » » » 7 weeks ago, # ^ |   0 still can't wrap the idea around my head.. i think i'll come back to this problem laterthanks for replying!
•  » » 7 weeks ago, # ^ | ← Rev. 2 →   0 Let's suppose that you have recovered the array for which you will have to firstly group all the intersecting ranges first because if two ranges intersect then you have to assign the intersecting variables such that they satisfy the OR value of both of the ranges. [This is going to take at least nlogn since to find the intersecting ranges you are going to sort the array of ranges by the first value]. Example input: a, b, c1 2 X2 3 YYou will have to assign a value to b such that the OR of both of the ranges is satisfied.Since you have recovered the array now, to calculate the coziness of the array you will have to generate all the subsequences of the array which is not possible under the given constraints.Let's stop for a moment and think what are the operations being performed:1. OR operation inside the ranges. We have already explored the OR operation through which we recovered the array somehow, but finding coziness from the subsequences is not possible under the given constraints.2. XOR operation inside the subsequences of the array and then their summation for the coziness value. Try to explore what is actually happening during the calculation of the XOR values and then of the coziness value. [Hint: Consider each bit individually while calculating the XOR.]
•  » » » 7 weeks ago, # ^ |   0 yes. this is what i thought, except i didn't know how to calculate the sum of all XOR subsequences before reading the editorial.why does OR-ing all the elements yields x tho?? (in the editorial)thanks for the reply!
•  » » » » 4 weeks ago, # ^ |   0 Or-ing all gives all possible set bits i.e x
 » 7 weeks ago, # |   0 Has anyone submitted problem B in Java? I'm getting tle on testcase 4.
•  » » 4 weeks ago, # ^ |   0 Same here. Have you got any solution?
•  » » 4 weeks ago, # ^ |   0 After extending This class, answer got accepted.
 » 7 weeks ago, # |   0 I understood the solution proposed for C but why O(NlogN) solution doesn't pass for problem C?Submission: 137045013
 » 7 weeks ago, # |   0 Submission for D2Could anyone please explain what's wrong in my code? I wonder why it were be Runtime Error. thank u guys.
 » 6 weeks ago, # |   0 Can someone help me why i am getting tle https://ide.codingblocks.com/s/646213
 » 4 weeks ago, # |   0 What is the dp solution for problem C?
 » 2 weeks ago, # | ← Rev. 2 →   0 ..