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Tutorial of Codeforces Round 553 (Div. 2)

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Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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thanks for tutorial and your effort

Thank you for fast editorial!

Please stop this shit

Nice Problem

Fast System Testing

Quick Editorial

Overall Great contest :)

+

Specialist. :)Ya :)

Wasn't perfect — placement of B and D was wrong

Here's how i did problem D. 52982122

Just sort the array according to the below comparator.

Proof: Let there be two pairs a and b. The dissatisfaction is i*(a1 + a2 — b1 — b2 ) + n*(b1 + b2) — a1 — a2 . We have to just consider the i term as rest are constant terms. Sort it according to a1 — b1 > a2 — b2

Thx! Easy to understand !!

the formula given is Ai(i -1) + Bi(N-i). So if you take two pairs A and B. then Ai and Bi for A and B are A1,A2 and B1,B2 respectively. Then total dissatisfaction due to both would be A1(i-1) + A2(N-i) + B1(i-1) + B2(N-i). So this should reduce to (A1 — A2 + B1 — B2)i + constants. Now Please tell how did you get A1+A2-B1-B2 for 'i' term.

I used divide and conquer in E. Let $$$f(l,r)$$$ equals answer for segment $$$[l;r]$$$ and $$$half = (l+r)/2$$$ then $$$f(l,r) = f(l,half) + f(half+1,r) - min(arr[half], arr[half+1]) * (n - max(arr[half], arr[half+1]) + 1)$$$.

Oh! Egor Letov is alive!

Hi, I went through your submission but couldn't understand the intuition behing Divide and Conquer.

Could you please explain your intuition behind it ....

Thanks in advance !

I used the same approach as him so I will try to explain it.

Let say we want to find the answer for an array A. Now imagine that for some of the ranges (l, r) the two halves of A always belong to different components.

For example the array A is: 2 4 6 2 7 3 and the range is (2, 3) or (6, 10). For these type of ranges we can just calculate the answer of each half seperately and sum them up.

However this is not always the case since the exist some ranges for which the right point of the first half is connected to the left point of the second half. Say the range (2, 6) or (1, 10) in the example.

How to handle these cases? Well we will sum them up similar to what we do with the first case. Now the answer will contain some invalid components — for each range similar to (2, 6) or (1, 10) we have counted the middle component twice. Now what we have to do is to substract from the answer the number of ranges for which the two border points remain the same. This is the meaning of the last term in his recurrence equation.

Thanks !!

This is boolshit))

Have you coded your solution? I'm sure that it is wrong. Firstly, I think that $$$m_{i, i} \neq m_{i, j}$$$. Secondly, you can't compute the answer by multiplying the probabilities (your last sentence), because they are not independent.

You are right! I am stupid))

For problem D, you don't really need to sort by index. "array d in non-decreasing order". I solved without sorting D.

Yes, It is already sorted :)

It is very thankful for brilliant tutorial.

can somebody explain me problem c and I have seen some solution like (calc(R) — calc(L — 1) + mod) % mod here he is adding mod, why? if we are not adding mod then 6 test case fail.please help me. Thank u

It depends on your language. Languages like C and C++ don't return values between $$$0$$$ and $$$MOD-1$$$ while taking mod of a negative number. Instead they return the 'negative mod'. $$$-5mod4$$$ should be $$$3$$$, but $$$-1$$$ is returned. While $$$-1$$$, is correct, it's not what we want. So, we add an extra $$$MOD$$$ and take mod again to ensure the result lies between $$$0$$$ and $$$MOD-1$$$. Adding an extra mod should always be done if you're subtracting 2 numbers and taking their mods.

Thanks bro

For problem C, this is my solution https://codeforces.com/contest/1151/submission/53005511 The solution uses the logic given in the editorial. I have tried placing MOD in all possible location and still not getting the correct answer. Anyone help? :)

Anyone please :)

In your fun(), it's enough if you just calculate the pow(2, i) without the mod. By subtracting, what you're essentially doing is just dividing the variable x by 2. So taking mod on the variable x would affect the loop because modular division is not similar to modular addition or subtraction where you can take mod wherever and it wouldn't affect the answer.

So, using pow(2, i) on line 39 and removing line 50 would be the way to go.

Yeah thanks bro :)

Dalgerok

IN E editorial, Shouldn't it be:

we must find the number of pairs (l,r) such that ai is not on the range [l,r] and ai−1 is on the range [l,r].

instead of:

we must find the number of pairs (l,r) such that ai is on the range [l,r] and ai−1 is not on the range [l,r].

No, because $$$b_i$$$ must be $$$1$$$ and $$$b_{i-1}$$$ must be $$$0$$$.

Got it thanks :)

The explanation of problem B is not helpful! Can anyone explain it?

first take element from first column from each row and take their XORs. If xor!=0, simply print the index of elements and exit. If xor==0, then iterate all elements of the table. If in a given row, current element is different from element in first column, then , if we replace the first element with this element, our xor will become non-zero.

thanks for this simple and easy explaination. can you plz explain problem C also??

to find sum of numbers from L to R, you need to do (sum of first m numbers in this sequence)- (sum of first L-1 numbers in the sequence). This is a simple observation, you can check this by taking first 10 natural numbers.

Now, to find sum of first L-1 numbers , you need to count the number of odd no. and number of even nos. till (L-1). To count both, start a loop from i=1 , double it on every iteration while increasing count of odd and even numbers alternatively. But, keep in mind the last count which you will add, which may not be power of 2.

finally, suppose, you got 'a' odd numbers and 'b' even numbers. then sum= a*a + b*(b+1) (simple AP series sum formula) you can do similar calculation for first M numbers.

http://codeforces.com/contest/1151/submission/53007448

check my code to see how I have done it.

The last problem is so awesome! By the way, is there some problem that has similar "style" to the last one? I mean, its not dp on the book, it's like... creativeness on how to define dp state?

For F, how do we use matrix exponentiation when the dp has more than 1 dimension?

https://threads-iiith.quora.com/Solving-Dynamic-Programming-with-Matrix-Exponentiation#

When $$$f[i][j]$$$ can be represented as a linear combination of $$$f[i - 1][k]$$$ for some $$$k$$$'s, it is possible to define a transition matrix from $$$f[i - 1]$$$ to $$$f[i]$$$. Let this matrix be $$$M$$$. Then by multiplying $$$M^n$$$ with the vector $$$f[i]$$$ you can jump to $$$f[i + n]$$$.

Here's my submission for B. https://codeforces.com/contest/1151/submission/52967808

Could someone explain the judge's verdict of XOR being less than 0 for testcase 24?

For the problem D. Why my solution https://codeforces.com/contest/1151/submission/53019943 is getting runtime error.

when I change the compare function now it gives WA. what is the problem now and before. https://codeforces.com/contest/1151/submission/53019888

Anyone Please :)

I don't really know about JAVA, but in C++, for a false comparison, you have to return 0. Why don't you try changing the -1 to 0.

https://codeforces.com/contest/1151/submission/52980095 This is the same code written in c++ but it is also giving runtime error on test case 8.

I tried out your code, with a single change. I changed your compare statement, from f>=0 to f>0 and it worked.

Runtime Error — https://codeforces.com/contest/1151/submission/53027297

Accepted — https://codeforces.com/contest/1151/submission/53027346

As to why this happens, I am clueless. Maybe someone can give some insight to this.

Thanks. But someone please tell why it was not working previously.

In Problem

Bwe can also useRANDOM SHUFFLE!!!.We can Random Shuffle all the elements in each row and then check the xor for each column that whether it is greater than zero or not.

P.S.-I have applied random shuffle 200 times.Luckily it passes all the tests :P

Here's link to my solution : 53025553

That was just a lucky try. I might get WA on submitting the same solution

I have done following in problem C. Function calculates the sum in set till number n.

ev — next even sequence start od — next odd sequence start

then for each iteration, I calculate start and end of that sequence and calculate their sum by AP. It is giving wrong answer on test case 1 1e18. Is there an overflow ? I cannot find the bug in function calc.

code link

CODEI have found a solution with O(1) complexity for Problem C. See 53051961

Can anyone tell is it really a O(1) complexity? (I am just new to algorithm and I don't know is it right)

Thank you :)

No, it is $$$O(\log{N})$$$.

Can someone explain the approach behind E problem ? Whats the logic for calculating f(l,r) ?

For problem D .By changing the compare statement, from f>0 to f>=0 my code gets runtime error.

Runtime Error — https://codeforces.com/contest/1151/submission/53027297

Accepted — https://codeforces.com/contest/1151/submission/53027346

As to why this happens, I am clueless.

Someone please tell why it started giving runtime error.

Someone Please reply :(

i still cant understand problem c can anyone explain me?

For Problem E — The editorial states "using technique contribution to the sum". What is this technique ??

https://codeforces.com/blog/entry/62690

Great Editorial!

My solution for Problem C works fine for smaller size of input but it failed for larger value. But, I'm pretty sure that I took the modulo correctly. Tried a lot to debug but failed. Could you please give a look in my code?

You should multiply by inverse modulo values instead of dividing on them.

Are you talking about the lines

`even /= 3;`

,`odd /= 3;`

?Yes

can any one help me with problem C. I am getting wrong answer for big values. https://codeforces.com/contest/1151/submission/57858024

Can someone tell me how to solve B using dp?