the_hyp0cr1t3's blog

By the_hyp0cr1t3, 5 days ago, In English

1451A - Subtract or Divide

Tutorial
Code (C++)
Code (Java)

Idea by ridbit10

1451B - Non-Substring Subsequence

Tutorial
Code (C++)
Code (Java)

Idea by the_hyp0cr1t3

1451C - String Equality

Tutorial
Code (C++)
Code (Java)

Idea by Ashishgup

1451D - Circle Game

Tutorial
Code (C++)
Code (Java)

Idea by Utkarsh.25dec

1451E1 - Bitwise Queries (Easy Version)

Tutorial
Code (C++)
Code (Java)

Idea by Ashishgup and ridbit10

1451E2 - Bitwise Queries (Hard Version)

Tutorial
Code (C++)
Code (Java)

Idea by FastestFinger, Ashishgup and ridbit10

1451F - Nullify The Matrix

Tutorial
Code (C++)
Code (Java)

Idea by Jeel_Vaishnav

 
 
 
 
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5 days ago, # |
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If you prefer solutions in video format, here's some for A-E2 (along with the regular screencast of bricking all of the problems)

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    5 days ago, # ^ |
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    In C, is the TLE due to using python?

    Edit: using sys.* in place of input does the job. So yeah, I guess.

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      4 days ago, # ^ |
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      You can use the following lambda functions to save time.

      Lambda functions
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    4 days ago, # ^ |
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    Here is hindi video editorial for A to E2, with solutions and thought process. here

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    9 minutes ago, # ^ |
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    I almost implemented replica of E2 solution but getting WA on TC 4. 3 cases I considered. ALL unique (I got N-1 as a XOR of first and ith element), first and ith elements are same, any 2 random element are same. https://codeforces.com/contest/1451/submission/99655336

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Hope I will become CM today after 10 months of continuous contests :) .. that proves hardwork can do anything.. nice round btw ;)

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    5 days ago, # ^ |
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    Congrats PR_0202 you just got what you hoped :D

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      5 days ago, # ^ |
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      Thank you soo much buddy :)

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        3 days ago, # ^ |
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        wow you solved all the Q ...congrats buddy...a well deserved CM![user:PR_0202]

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    4 days ago, # ^ |
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    if in c problem z can also be converted to a then how can we do that ??

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      4 days ago, # ^ |
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      It is explicitly written in the problem statement, that character should not be equal to z while conversion.

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      4 days ago, # ^ |
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      If we can increment 'z' to 'a' then, For every alphabet we calculate the required value of increment of frequency f[i]=(freqB-freqA).

      Then if every f[i] is divisible by k and sum of all f[i] is 0. It is possible to convert the string, because the extra string (f[i]) can be converted into any charecter we want.

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        4 days ago, # ^ |
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        so in one iteration we calculate all f[i] and then check sum of all character f[i] should be 0?? so it means f[i] can also be negative??

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          4 days ago, # ^ |
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          Yes, it will be negative when you need more charecters... also check it all f[i] are divisible by k.

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5 days ago, # |
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Hi, In today's D, I found the maximum number of moves possible, and checked its parity in order to decide the answer. But this gave me WA on pretest-5. I am unable to figure out the error. Can some one please elaborate if I have made a logical error, or some implementation error.

Link to my submission. https://codeforces.com/contest/1451/submission/99180269

Thanks a lot!!

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    5 days ago, # ^ |
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    You probably had made a mistake in you code , because you logic is wrong but answer is right. Optimal path is not necessary the path with maximum moves but in this case it is, suppose two players are playing a game where each player turn by turn have to pick any number of stone from a pile of n stones and last person to pick the stone lose the game. Now u can clearly see that optimal strategy is not the one with maximum moves.

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    5 days ago, # ^ |
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    my submission link I have also done the same. My solution gets accepted.

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    4 days ago, # ^ |
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    i*i could possibly lead to integer overflowing for d = 1e5 and k = 1, you should change i to long long instead of int

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Thanks for the really fast editorial !

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E1 E2 is really well written kudos for the awesome round :)

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I miss Ashishgup's solutions in friends standings, ofcourse he can't participate in his contest XD. But yeah I learn a lot from his solutions.

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For E2, after (n-1) XOR queries and finding two numbers $$$a, b$$$ whose XOR is all ones (so case 2, all numbers are distinct). Can we pick a third number $$$c$$$, AND it with $$$a$$$ and $$$b$$$, the sum of those 2 outputs gives $$$c$$$ and we are done (find rest of the array with XOR that we did already)?

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5 days ago, # |
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In C I was solving for the case when the segment did not necessarily only contain the same letters. Do you guys think it is much more difficult or solvable at all?

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Good editorial;)

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I wasn't able to implement in time my idea of E1, but did someone think like this too? My key idea was that given

$$$a \oplus b, b \oplus c, c \oplus a, a \& b, b \& c, \text{ and } c \& a$$$

$you$ could calculate $$$a, b$$$ and $$$c$$$. I will use this idea to calculate $$$a_1, a_2, a_3$$$. Then I will apply the XOR between $$$a_1$$$ and every other $$$a_i$$$ for $$$4 \leqslant i \leqslant n$$$, and from that I can calculate $$$a_i$$$ ($$$a \oplus b = c \Leftrightarrow b = a \oplus c$$$). This will use $$$n + 3$$$ operations, but I can fix it by using that $$$c \oplus a = (a \oplus b) \oplus (b \oplus c)$$$.

Great contest and thanks for the fast editorial btw.

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    4 days ago, # ^ |
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    Can u just confirm one thing that in E1(easy version ) whether giving that n is power of 2 and nos are in range [0,n-1] is of any importance or not ?my sense is that — the solution would be same if these two constraints are not there ?Am i right or not ?

    I think they are given for E2 mainly.

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      4 days ago, # ^ |
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      It doesn't depend on the numbers being in the range $$$[0: n-1]$$$ nor $$$n$$$ being a power of two. It only depends on $$$n \geqslant 3$$$.

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It's been a while since I enjoyed a problem set so much. Hats off.

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[Deleted]

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hey, I used the same approach for E1 but got WA on pretest 4. Can anyone please have a look at my solution and tell me where I went wrong. Thanks

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This is how the editorials should be. Properly explaining the solution with proper reasoning.

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Amazing Problemset !

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If I am not wrong in problem D we can solve for all initial points instead of (0,0) only, i think there are only some parallel lines parallel to y = x which are losing positions and rest all are winning positions and these parallel lines can be found in O(d) time .

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    5 days ago, # ^ |
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    I think you are correct, we first need to set all points outside the circle to be winning position, and just evaluate point near perimeter, which gives information about the whole line.

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      5 days ago, # ^ |
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      Looking at the graph, can't we say that a position is a losing position if there is a winning position directly above or directly right of it, and a position is winning if both the positions adjacent to it are losing?

      By that logic, we can just count the number of steps played if the players go from (0,0) to the rightmost point (24,0) in this case), and then straight upwards till they can stay inside ((24,4) in this case)?

      For example; d=5,k=2: (0,0)->(2,0)->(4,0)->(4,2) so we can tell if (0,0) is a winning position or not, based on the number of steps.

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      5 days ago, # ^ |
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      Yess , exactly this one . I didn't knew to attach images but this image is self explanatory . Thanks a lot for making my point clearer. We just need to set those points as losing positions which have no move available and then all other points can be retrieved by just drawing a line with slope = 1 at that point

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      4 days ago, # ^ |
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      Thanks, it is very helpful to come up with the idea !!

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      4 days ago, # ^ |
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      which colour is winning state in this??

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      4 days ago, # ^ |
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      This can be proven like so: If a point (x,y) is losing, then (x-1,y) and (x,y-1) are winning. Now the point (x-1,y-1) can only go to these two points, so it is losing as well. This proves that if a point is losing all points on that diagonal are losing as well.

      If a point(x,y) is winning, then it means at least one of the points (x+1,y) and (x,y+1) is losing. Let us assume it is (x+1,y) (the lower diagonal). As we have proved, that entire diagonal is losing, so all points on the diagonal of (x,y) have at least one losing state they can go to, so they are all winning.

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      2 days ago, # ^ |
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      Why only (kx,ky) consider???

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Why going to the point $$$(kz, kz)$$$ in D is an optimal strategy?

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    5 days ago, # ^ |
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    It is not optimal strategy! it is what player 2 can force. If $$$(kz, k(z+1))$$$ is inside circle then also $$$(k(z+1), kz)$$$ is inside circle. If these two are winning positions then $$$(kz, kz)$$$ will be losing position.

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I really appreciate that solutions in Java are also provided and taken into consideration for time limits, especially for interactive problems. Thanks for the amazing round!

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Imagine spending 1 and half hour for solving, coding and trying to debug a misunderstood problem.

Thats my story for E1 E2 this contest :(( Thought "XOR i j" was xor of all elements from i to j lol. Anyways the questions were really great, Thanks for the round!

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Here's my solution E2, which only differs from the official solution in the second case.

Find the values $$$a_1 \oplus a_2, a_1 \oplus a_3, \dots, a_1 \oplus a_n$$$ by using $$$n-1$$$ queries.

Case 1: At least one value of $$$a_1 \oplus a_2, a_1 \oplus a_3, \dots, a_1 \oplus a_n$$$ is repeated (or $$$0$$$). Treat the same as the official solution.

Case 2: The values $$$a_1 \oplus a_2, a_1 \oplus a_3, \dots, a_1 \oplus a_n$$$ contain all numbers from $$$[1, n-1]$$$. Let $$$j$$$ and $$$k$$$ satisfy $$$a_1 \oplus a_j = 1$$$ and $$$a_1 \oplus a_k = 2$$$. These must exist by pigeonhole. Now you know that $$$a_1$$$ and $$$a_j$$$ differ only on the smallest bit, so querying $$$a_1 \land a_j$$$ will get you all of the bits of $$$a_1$$$ except the last one. Similarly, the smallest bit of $$$a_1$$$ and $$$a_k$$$ must be the same, so querying $$$a_1 \land a_k$$$ will give you the last bit of $$$a_1$$$. Now you can put these two results together to reconstruct all $$$\log_2 n$$$ bits of $$$a_1$$$ and you are done in $$$n+1$$$ queries.

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    5 days ago, # ^ |
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    I think you need to do a lot of case work since numbers can be same. Also why will $$$a_1 \oplus a_2, a1 \oplus a3,...., a_1 \oplus a_n$$$ contain all numbers from $$$[1, n-1]$$$? You can easily take some numbers same, also it is not necessary that $$$j, k$$$ such that $$$a_1 \oplus a_j = 1$$$ and $$$a_1 \oplus a_k = 2$$$ exists.

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      5 days ago, # ^ |
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      No, you don't need any casework. If some of the numbers are the same, treat it as case 1 in the official editorial solution (I didn't bother writing it because its the exact same as the editorial). Otherwise, the $$$n-1$$$ values $$$a_1 \oplus a_2, a_1 \oplus a_3, \dots, a_1 \oplus a_n$$$ are guaranteed to have all values within $$$[1, n-1]$$$ because they are all distinct.

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        4 days ago, # ^ |
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        If in C problem if we have to minimize the number of steps performed then how we can do this??

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    5 days ago, # ^ |
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    Sir, can you please tell me on which case my solution failed. I used a similar approach. Please have a look. Thanks

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Is editorial for C correct? test case: 1 3 2 aaa bcb

aaa -> bba -> bcb (so answer should be possible) but code from editorial say No.

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I have another way to explain E2, and I want to list it here in case it may help someone else.

An important attribute of XOR operations is that it points out the differences between two binary sequences.

By XORing every $$$a_i$$$ where $$$i\in[2, n]$$$ with $$$a_1$$$, we can get an array of the differences of all other elements from $$$a_1$$$. Now, if we know what $$$a_1$$$ actually is, we will know what every element else is.

To obtain that array mentioned above, we have already used up $$$n - 1$$$ opportunities. We only have 2 left. So the problem now is how to obtain the actual value of $$$a_1$$$ in two queries.

Here we discuss two separate situations.

  1. There are no pairs of elements in the array that have equal elements. Note that the problem tells us that all elements in the array are within the range $$$[0, n - 1]$$$. That means in this case the array is simple a permutation of $$$[0, n - 1]$$$.

Therefore, there must exist a number $$$a_i$$$ such that $$$a_1\oplus a_i=n-1$$$. That is, $$$a_i$$$ is complementary to $$$a_1$$$.

What are we talking about this for? Note that if we select any other number $$$a_j$$$ where $$$j\ne i \wedge j\ne 1$$$, we can get its actual value by two AND operations with $$$a_1$$$ and $$$a_i$$$ respectively and ORing the two parts. Also, we know that $$$a_1 \oplus a_j \oplus a_j=a_1$$$. We already have $$$a_i \oplus a_j$$$, so one XOR and we will get $$$a_1$$$. In this case we shall get the value in exactly two steps.

  1. There exist a pair of elements in the array that has equal elements. Hey, by requesting an OR (or an AND, makes no difference) and we will get the value of the two elements. Then by XORing as described above we will get what we need. In this case we only need one step.

Okay. Now it is clear, and the only thing that's left is to show us the code:

  using u32 = uint32_t;

  u32 n RU; // we can't use u16 because 1u << 16 will be an overflow.

  // First we query the xors.
  vector<u32> xo(n + 2, 0); // of course xo[1] = 0.
  for (u32 i = 2; i <= n; ++i) {
    cout << "XOR 1 " << i << endl; // endl to flush.
    xo[i] RU;
  }

  // Then we find if there are any two elements that are equal.
  u32 eq[2] {}; {
    vector<u32> used(n + 2, 0); // 0 means unused.
    for (u32 i = 1; i <= n; ++i) {
      if (used[xo[i]]) {
        eq[0] = used[xo[i]];
        eq[1] = i;
        break;
      }
      used[xo[i]] = i;
    }
  }

  // Now we decipher a_0.
  u32 a0; {
    if (eq[0]) {
      cout << "OR " << eq[0] << ' ' << eq[1] << endl;
      a0 = ru() ^ xo[eq[0]];
    } else {
      u32 q = find(&xo[2], &xo[n], n - 1) - &xo[0]; // Position of the complementary of a_0.
      u32 p = (q == 2 ? 3 : 2);
      cout << "AND 1 " << p << endl;
      u32 t1 RU;
      cout << "AND " << q << ' ' << p << endl;
      u32 t2 RU;
      a0 = (t1 | t2) ^ xo[p];
    }
  }

  // Aha, we've found the answer.
  cout << "! " << a0;
  for (u32 i = 2; i <= n; ++i) {
    cout << ' ' << (a0 ^ xo[i]);
  }
  cout << endl;
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Could somebody tell me what is wrong with my code for problem C? I am not using the frequency array approach. I think I have accounted for all the possible conditions and just cannot find what I am missing. It is giving output wrong output "Yes" for a test case in pretest 2 but since that particular test case is not visible, I don't have any clue as to what's wrong.

~~~~~ ~~~~~

Link to the code.

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Problem D is simply just:

Find a point $$$P(k×x,k×y)$$$ with the maximum Manhattan distance from $$$O(0,0)$$$ and an euclidean distance from it at most $$$d$$$, if its Manhattan distance is odd then the first player will win.

($$$x$$$ and $$$y$$$ are any positive integers).

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Can anyone tell me what is wrong with this approach in Question C .as i am sorting both string and checking every k substring ..it will. S1(i) will be either equal to s2(i) or if s1(i) <s2(i) then we will check for k blocks .if there is such consecutive k blocks then we will move further otherwise NO.. Link to my submission: https://codeforces.com/contest/1451/submission/99185412

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    5 days ago, # ^ |
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    Try removing all equal elements from both strings at the start.

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      4 days ago, # ^ |
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      thanks ..after removing equal elements at start my rest solution works fine

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Can anyone please tell me why I'm getting Idleness limit exceeded on Test 1 in E1 ? 99199797

EDIT: Got it.

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Why in problem D player 2 should always go to some point such that x = y? Why is it always optimal for player 2?

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Could someone explain why the proposed solution for D does not consider points of the form (az, bz) where a and b are unequal, while considering potential terminal points for deciding the winner?

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    5 days ago, # ^ |
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    This is because if both play optimally, these fields will never be used.

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      5 days ago, # ^ |
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      Could you elaborate on this? I believe my question is directed towards the reason why these points are suboptimal (at least that's what I was hoping to convey).

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        From what I understood, no matter who plays, they can always divert it to that maximal point

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D can be solved with binary search and some precomputation. Basically we have the condition $$$p^2+q^2 \leqslant d^2$$$. We can introduce two integers $$$n$$$ and $$$m$$$ and write $$$p = kn$$$ and $$$q = km$$$ which gives $$$k^2(n^2+m^2)\leqslant d^2$$$. Now since the players can only increase either $$$x$$$ or $$$y$$$ then we take $$$n$$$ and $$$m$$$ for points $$$(0,1), (1,1), (1, 2), (2, 2), (2, 3), (3,3), (3,4) ...$$$. Now if we compute $$$(n^2+m^2)$$$ and sort it we get the following sequence $$$1,2,5,8,13,18,25...$$$ which is given by the general formula $$$a_l=\text{ceiling}(l^2/2)$$$. Now we can rewrite the initial condition as $$$(n^2+m^2) \leqslant d^2 / k^2$$$. Once we have all this we can precompute $$$a_l$$$ from $$$l=1$$$ to $$$l = 100000\sqrt{2}$$$, store the sequence in a sorted array and binary search this array for such an $$$l$$$ such that $$$a_l \leqslant d^2 / k^2$$$. If the found $$$l$$$ is divisible by 2 then "Utkarsh" will win otherwise "Ashish".

I tried to implement this like 11 times during the contest but had a lot of error. Only after the contest I got a passing solution. If someone is interested then here it is: 99201613

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    5 days ago, # ^ |
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    Initially, the problem gave $$$d^2$$$ instead of $$$d$$$. $$$1,2,5,8,13,18,25...$$$ was the reason it was changed to $$$d$$$. Funny enough there are 3 OEIS series if one tries to search for values of d at which winner changes. here. One is supposed to search using the first 24 terms to find correct OEIS series.

    Also one advise don't use library ceil/floor functions. Just use integer based functions. math.floor can be replaced with // and math.ceil(a/b) can be written as (a+b-1)//b

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      5 days ago, # ^ |
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      Hmm... good point but the formula for the sequence is not necessary (although I agree that some luck is required :). I gave it since I used it in my solution but you can also precompute the sequence using the points $$$(0,1),(1,1),(1,2),...$$$. I guess it should also work.

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        5 days ago, # ^ |
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        If one notices $$$(0,1),(1,1),(1,2),..$$$ then there are 100 ways to get an AC :) . OEIS is required for those who want to get an AC without any crucial observation by just using formula written there as a BlackBox.

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    4 days ago, # ^ |
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    A simple binary search solution will work for $$$D$$$, without any precomputation. The solutions goes as follows:

    • Find the maximum $$$x \in \mathbb{N}$$$ such that $$$2 x^{2} k^{2} \leq d^{2}$$$. It is very simple to see that $$$x \in \Big [ 0, \frac{1}{\sqrt{2}} \frac{d}{k} \Big ] \cap \mathbb{N}$$$. For simplicity, we can drop the $$$\frac{1}{\sqrt{2}}$$$ part of our upper bound which will make everything integral.
      Now, this point $$$(xk, \space xk)$$$ is the farthest point of this form which is still inside the circle. And it takes exactly $$$2x$$$ moves to reach such a point.

    • If any of the points $$$((x + 1)k, \space xk)$$$ or $$$(xk, \space (x + 1)k)$$$ lie inside the circle (odd moves), then Ashish wins, else (even moves) Utkarsh wins.

    Time Complexity: $$$O \Big (\log_{2}{\big \lfloor \frac{d}{k} \big \rfloor} \Big )$$$
    Space Complexity: $$$O(1)$$$

    Here's the code: 99193957.

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      4 days ago, # ^ |
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      And it is very easy to convert this binary search solution to a constant time solution. It is easy to see that $$$x = \Big \lfloor \frac{1}{\sqrt{2}} \frac{d}{k} \Big \rfloor$$$.

      Time Complexity: $$$O(1)$$$
      Space Complexity: $$$O(1)$$$

      Here's the code: 99270210.

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A bit more explanation about Problem F please?

I understand that the logic of Nim Game works here, but why do we start out with the diagonals? What is the purpose of the diagonals?

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    5 days ago, # ^ |
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    It’s slightly more complicated than you may have expected. I suggest taking a look at problem 1149E (Election Promises) and read the explanation using game theory, and then try to prove that the nimber for each position (i, j) is (alephnull ^ (n — i + m — j)) * a[i][j] where alephnull is the smallest ordinal number.

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https://youtu.be/2CRJHN5-9Ks made a video on the solution of the problem D , take a look if you want to.

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I have a problem with interactive problem.

Can I use ios::sync_with_stdio(0); when I slove it?

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For E2, I tried all $$$\binom{\binom{4}{2} \times 3}{5}$$$ possible sets of queries, but none of them yielded a bijection ($$$f:[0,3]^4 \rightarrow [0, 3]^5$$$). What's up with this paradox?

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,.

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    5 days ago, # ^ |
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    Hence your rating. You have misunderstood the problem and still think the problemsetters and those who have solved the problem are wrong

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    5 days ago, # ^ |
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    When you divide 81 by its proper divisor you will get 3, it will take two more steps to reach 1. Hence, the answer is 3 (and not 2). The same applies to 21 also. Remember that the goal was to reach 1.

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[Solved] problem D why going to kz,kz is optimal

can't player2 move the same direction with player1? I've been thinking and trying to prove this is worse Can someone tell me? thx

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    5 days ago, # ^ |
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    My thinking, I think this is the proof.

    We can know that at the right beginning of Game, both players know who will win when player2 go to (kz, kz).

    So the winner will try to walk to (kz, kz), but the loser will try everything not to walk there.

    In the end, we can prove this by easy implementation they must go to (kz, kz). So the path to (kz, kz) is the optimal to the winner

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    5 days ago, # ^ |
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    Say both of them move in the same direction. Now both of them already know where they will end up if they continue moving (both of them know (d/k) and hence the total moves). So the one which will be in a winning position will enjoy the walk while the one losing will try to counter by moving perpendicularly. So moving in the same direction is a contradiction and can never occur in an optimal game. This idea leads to a very easy implementation.

    D
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      4 days ago, # ^ |
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      Suppose Player 1 and Player 2 in their first moves move right. Now suppose that Player 1 will lose if they continue to go right so Player 1 moves up and Player 2 moves right. Now they are not in (kz, kz) position. Why this strategy is not optimal for Player 2?

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For Problem F, how do we prove that the game is finite? It seems almost counterintuitive given the nature of adding to paths.

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    4 days ago, # ^ |
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    At the start of the game, the players already know the winner and loser.

    The winner can make the game finite from the following strategy:

    Pick any cell (i, j) to be the starting cell if the matrix with top left corner (0, 0) and bottom right corner (i, j) (excluding the cell (i, j)) contains only 0's.

    Specifically, if the top left cell is not 0, a player can make it 0 by choosing it as the starting cell. In that case, that cell cannot be chosen again as the starting cell, as stated in the game rules.

    Following the same pattern, a player can then recursively do the same with the rest of the matrix (starting with cells such as (0, 1) or (1, 0)).

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    4 days ago, # ^ |
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    Let $$$s[k]$$$ be the sum of the $$$a[i][j]$$$ such that $$$i+j=k$$$.
    You can prove by induction that, for every length $$$l$$$ of $$$s[]$$$, you end in a finite number of moves. It's obviously true for $$$l=1$$$.
    For $$$l>1$$$, you can divide the sequence of moves in a finite number of finite segments, such that you decrease $$$s[1]$$$ only at the end of the segments. Those segments have finite length because, if you don't decrease $$$s[1]$$$, it's like having $$$l' = l-1$$$.

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    4 days ago, # ^ |
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    No matter what moves the players make, the game is going to end eventually. The reason is that whenever a cell is increased then there is a cell coming before it that is decreased. Here is a formal proof: Order the cells in a single row of length n*m such that the diagonal ordering is preserved. like this for instance

    | 0 | 1 | 5 | 6 |

    | 2 | 4 | 7 | 10 |

    | 3 | 8 | 9 | 11 |

    Let a[] be the array corresponding to this ordering (len(a) = n*m = N). Now, every single move will change a subsequence of this array so that the leftmost element that is changed is decreased by at least 1. We can do induction on both the length of a[] and the values of a[0] to prove that eventually we will have a[] = [0,0,...,0] (in other words do induction on the tuple (a[0], len(a[])) using the usual ordering of tuples). There are two cases

    1. Eventually there is an operation involving a[0]. In this case a[0] is reduced and so we end up with a smaller tuple (a[0], len(a[])) and use induction hypothesis

    2. No operation involves a[0]. But in this case we are effectively working on an array of length N-1. So by induction, eventually we will have a[1] = a[2] = ... a[N-1] = 0. But the only valid operation after this would involve reducing a[0]. So we again end up in case 1.

    A proof that almost works, but is not correct, is to consider the array a[] as a number in base B for some large B (so a[] corresponds to the number a[N-1] + a[N-2]*B + a[N-3]*B^2 + ... a[0] * B^(N-1)) and argue that after each step the number is decreased because a leading index is decreased. However this doesn't work since we cant fix large enough B because the values of a[] can get arbitrarily large (but this does give the correct intuition). Instead we are working with the set of polynomials of degree N=n*m with non-negative integer coefficients with the natural ordering. Even though there are infinitely many polynomials less than the current one and bigger than 0, reducing the polynomial with each step still ensures we reach 0 eventually, which is interesting

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NVM

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    4 days ago, # ^ |
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    First learn C++, the command initializes with values 0 only. Also search atleast 10 times on web before commenting.

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In D if player 2 knows that going diagonally is a losing situation, won't he just mirror player 1's move (so if 1 goes right 2 goes right and vice versa)?

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    4 days ago, # ^ |
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    If player 1 makes his first move right, then player 2 has 2 choices $$$~-$$$ move up, or move right. If he moves up, then player 1 can move right. If he moves right, then player 1 can move up. Either way, player 1 can force them to stay on the line $$$x-y=k$$$ after every turn of his. We also know that the point $$$(k(z+1), kz)$$$, which is on the line $$$x-y=k$$$ and lies inside the circle, is a losing point for player 2. So player 1 is guaranteed to win.

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Is D is solvable in O(1) complexity? 99220580

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in order to ensure that we can make xor(r1+c1)=0 by decreasing, we select such a cell (r1,c1) whose largest set bit is equal to the largest set bit of xor(r1+c1). can someone please explain me this.

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    4 days ago, # ^ |
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    and how do we proof that game is finite.

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    4 days ago, # ^ |
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    The solution is to go through bits, and change the rest of bits after i, we subtract 2^i, and add at max 2^i-1, subtract 1 atleast. ith bit has gotta be set for property of xor.

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Can someone please tell me that which case am I missing in my solution, PROBLEM D

MY SOLUTION

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4 days ago, # |
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Hi, In 'A' problem, I first checked if a proper divisor exists for 'n' if yes i divided 'n' with it's max proper divisor else I subtracted '1' from 'n' and repeated this process till 'n' reaches '1' while incrementing the moves counter. But this gave me WA on pretest-2 (more precisely 'n'=25). I am unable to figure out the error. Can some one please elaborate if I have made a logical error, or some implementation error.

Link to my submission. https://codeforces.com/contest/1451/submission/99135132

Thanks a lot!!

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    4 days ago, # ^ |
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    It may be also possible that subracting 1 from n first, and then dividing (n — 1) by its proper divisors gives the optimal answer. for n = 25, your algorithm does 25 -> 5 -> 4 -> 2 -> 1. But optimal solution should be 25 -> 24 -> 2 -> 1

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    4 days ago, # ^ |
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    Note that even if you divide n by its max proper divisor, there may be other proper divisors after you subtract 1 from n some times. However, it is optimal to turn n into 2 first, then subtract 1 from n. If n is already an even number, there is no need to do anything. While if n is an odd number, you can subtract 1 from n first.

    According the approach above, it is very easy to get the answer when n<=3, and when n>3, answer is just 2 if n is even, or 3 if n is odd.

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      4 days ago, # ^ |
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      Thank You so much. You made it Crystal Clear.

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Cna someone help me with whats wrong in this code for problem C.

void solve(){
    int n, k; cin >>n >> k;
    string a, b; cin >> a >> b;
    sort(a.begin(), a.end());
    sort(b.begin(), b.end());
    bool ok = true;
    for(int i = 0; i < n; i += k){
        string c1 = "", c2 = "";
        for(int j = i; j < i + k; ++j){
            c1 += a[j];
        }
        for(int j = i; j < i + k; ++j){
            c2 += b[j];
        }
        if(c1 == c2){
            continue;
        }
        bool same1 = true;
        for(char ch : c1){
            if(ch != c1[0]){
                same1= false;
            }
        }
        bool same2 = true;
        for(char ch : c2){
            if(ch != c2[0]){
                same2 = false;
            }
        }
        if(!same1 || !same2 || c1[0] > c2[0]){
            ok = false;
        }
    }
    if(ok) cout << "Yes" << endl;
    else cout << "No" << endl;
}

int32_t main(){
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
    int t;
    cin >> t;
    while(t--){
        solve();
    }
}

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4 days ago, # |
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This contest is so good for its succinct statements, interestring and challenging problems without too long code, and quick but perfect editorial. Thanks for perfect preparation for this! I expect to have such contests again!

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Guys, What is the solid proof in problem D that the second player would always have it better to return to the $$$y=x$$$ line?

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    4 days ago, # ^ |
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    I think it's not 'always'. It's only when (kz, k(z+1)) is outside the circle, that he can and will keep returning the token to the y=x line.

    If (kz, k(z+1)) is inside the circle, he would like to keep returning to the y=x+k (or x=y+k) line but he can't. On the other hand Player 1 can, regardless of Player 2's move.

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      4 days ago, # ^ |
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      You apparently misunderstood my question, Do you know why the answer is true? why isn't it that both players just go right? that's when both steps are available.

      Why the $$$2nd$$$ player always wants to get back to the state where its $$$(kz,kz)$$$ ?

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    4 days ago, # ^ |
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    The 'return to the y=x line' is basically just a game strategy that can be used by both players.

    If (kz,kz+k)/(kz+k,kz) is outside the circle, then the 2nd player can use this strategy to win. (if 1p move right, then 2p move up, vice versa)

    If the points are inside the circle, then since 1st player's steps must always step to (0,k)/(k,0), the 1st player can use this strategy similarly (if 2p move right, then 1p move up, vice versa), which will reach (kz,kz+k)/(kz+k,kz) which is the final step of the game.

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99129900 Problem A

This Solution give RTE for input of prime no. greater than 10^6

But it pass in system testing

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Is that equation written on the first line of the solution of E1 well-known? If yes, where can I find it proof?

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Why this submission 99184173 in B didn't get TLE ?

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It seems not difficult after I saw the solution of F. but I just want to know how to come up with this solution...Is this a common method to solve game theory problems?

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for(int i = 2; i <= 3; i++) for(int j = i + 1; j <= n; j++) if((xorvals[i] ^ xorvals[j]) == n — 1) { b = i; c = j; }

can someone explain me how is above code able to find two numbers with xor as n-1 without compairing all pair of numbers??

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    4 days ago, # ^ |
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    Since the array is indexed from 1 to n, that means that: there is only one element before a_2 (which is a_1).

    The reason i must have max 2 different values is because there might appear a situation where: (assume that we only use i=2) xorvals[1]^xorvals[2]==n-1, which is not scanned by the loop.

    As mentioned in the editorial, numbers in [0,n-1] appear exactly once. -----(1) So by having two i values guarantees that there is a pair of xorvals which satisfy: xorvals[i]^xorvals[j]==n-1, i=/=1, j=/=1 since if xorvals[1]^xorvals[x1]==xorvals[1]^xorvals[x2]==n-1, it directly implies that x1==x2, which contradicts fact (1).

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why (kz, kz) position going to be optimal for both the players ???

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In problem D : I found out the maximum number of possible moves that are possible for the given 'd' value (call it mx ) .Then i output :

  • player 1 , if mx%2 == 1 ;

  • player 2 if mx%2 == 0

I think this is correct because the player who is winning according to the mx value will always be able to make the game last mx rounds(by increasing the min(x ,y) ) . I am not sure of this strategy , did someone else used this method ?

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I DON'T KNOW WHAT IS WRONG WITH MY CODE IT IS FAILING WHEN n=25; my output comes 4 but it says the correct answer is 3. can anyone please explain what am I missing?

HERE IS MY CODE

import java.util.*; public class Main{ public static void main(String []args){ Scanner sc=new Scanner(System.in); int t=sc.nextInt(); while(t-->0){ int moves=0; int n=sc.nextInt(); int p=n-1; while(n!=1&&n%p!=0){ if(p==2){ n--; moves++; p=n-1; } else{ p--; if(n%p==0){ moves++; n=n/p; p=n-1; } } } if(p==1){ moves++; } System.out.println(moves); }

} }

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Can someone please explain that why in problem c they add the frequency have[i] to have[i + 1] ? Thanks in advance!

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    4 days ago, # ^ |
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    We keep exactly $$$need[i]$$$ occurrences of the $$$i$$$-th character. The remainder must be converted into something else, otherwise the frequencies will not be equal. So we add $$$have[i] - need[i]$$$ to $$$have[i+1]$$$ by performing operations of the second type some number of times.

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I think the C++ code for problem D is wrong, isn't it? If you declare x,y,d to type int, it will cause "integer overflow" at some where like d*d or (x + k) * (x + k).

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Can you explain the key idea in the circle game question?

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1451A — Subtract or Divide.

Hello. I am a mathematician, I solved the problem very suboptimally. But still, I think I decided correctly. Why tests fail? Where is the mistake? :)

Mathematical algorithm. If the number is prime, I subtract one. Otherwise, I look for the maximum divisor, and divide by it.

import java.util.Arrays;
import java.util.Scanner;

public class minus_del {

    static boolean isPrime(int n) {
        for (int i = 2; i < n; i++) {
            if (n % i == 0)
                return false;
        }
        return true;
    }

    public static int largestDivisor(int n) {
        for (int i = n / 2; i >= 2; i--) {
            if (n % i == 0) {
                return i;
            }
        }
        return 1;
    }

    public static void main(String[] args) {

        Scanner scanner = new Scanner(System.in);
        int count = scanner.nextInt();
        boolean d = false;
        for ( int i=0; i<count; i++ ) {

            int value =   scanner.nextInt();
            int shag = 0;
            while ( value > 1 ) {
                d = isPrime(value);
                if (d) { value = value-1; }
                    else { value = value / largestDivisor( value ); }
                shag++;
            }

            System.out.println(shag);
        }

    }
}

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I have a problem in C, I cannot understand what's wrong in my approach very similar to the editorial. I just decrease the frequency of matched characters and continue;

Here's my submission: https://codeforces.com/contest/1451/submission/99278861

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I am not clear with the claim in Problem E2 editorial that there will be serveral pairs (j,k) with xor N-1 ?? why is that true?

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    3 days ago, # ^ |
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    The claim is in the case where every value is different.

    If every value is different, then, for each i

    j ≠ k => ai ⊕ aj ≠ ai ⊕ ak

    as such each i gives n different xor values (including 0, when it is xored with itself). Since n is a power of 2 we know that all the xor values with ai must be less than n, so precisely one of the values must be n-1. We therefore have a total of n (i,j) pairs with an xor value of n-1.

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problem D : can anyone explain in brief ????

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P c WA 3 way ? :( https://ideone.com/65UkTo

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29 hours ago, # |
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Okay, so Codeforces' anticheat system claim that my solution for problem 1451A in here is similar to user john21's solution to problem A (which you can have a look at here). And as such, they disqualify me from this contest. This is not true and I can guarantee that this is just coincidence, because, well, the solution of problem A is pretty much the same for everyone. However, my solution to problem B and john21's problem B is completely different. I think it is really unfair here because I did the entire contest on my own and still got disqualify. Can someone (admin, mod, MikeMirzayanov, etc) look into this please? Thank you very much.

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!!MISCoincide Codeforces Round #685 (Div. 2) https://codeforces.com/contest/1451

In the name of almighty Allah who has the knowledge of seen and unseen . The message has sent to me about the solution of 99130524 for the problem 1451A . It said that a significantly coincides with solutions Nushrat_Jahan/99125543 , Maskur_ICT_MBSTU/99130524 is really so pathetic to me. Really Codeforces is the best platform for competitive programmers . I really do appreciate the system of judging and the approaches followed by codeforces . But the issue is that whatever we have all is the virtual machine . It’s an abstract thing . The way the system judge my code and found that my code is coincide with the code of Nushrat_Jahan/99125543 is for the issue that we have followed the same approaches . And it is undoubtedly true that I had not taken any help from google or communicating with Nushrat_Jahan/99125543 . I’m not familiar with Nushrat_Jahan/99125543 in virtual world or real world . So how can I copy Nushrat_Jahan/99125543 ‘s code . The way I and Nushrat_Jahan/99125543 had thought is not any intentional case . The logic comes from divine source . So if my thinking is same with others “is it wrong to write that code” . How can I know that the other person’s thinking is the same as mine ? Can you? No we haven’t that power .
Finally I strongly opposed about the issue of coincide that the code was thought , solved and written by my own effort and also added that “ is it justice to skipped my problemB for the problemA “ Please recheck my code and make sure that the code was not coincide . It was my work . Thank you Codeforces.