Stepavly's blog

By Stepavly, 2 years ago, translation, In English

All problems were created by MikeMirzayanov and developed by me (Stepavly) and Supermagzzz.

1462A - Favorite Sequence

Editorial
Solution

1462B - Last Year's Substring

Editorial
Solution

1462C - Unique Number

Editorial
Solution

1462D - Add to Neighbour and Remove

Problem authors: MikeMirzayanov, Supermagzzz, Stepavly.

Editorial
Solution

1462E1 - Close Tuples (easy version)

Editorial
Solution

1462E2 - Close Tuples (hard version)

Editorial
Solution

1462F - The Treasure of The Segments

Editorial
Solution
 
 
 
 
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2 years ago, # |
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Thanks for quick editorial! Great contest too and interesting problems

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2 years ago, # |
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Thank you!

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2 years ago, # |
  Vote: I like it +46 Vote: I do not like it

Felt more like a div4 but fun problems nonetheless. Cheers.

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2 years ago, # |
Rev. 3   Vote: I like it +35 Vote: I do not like it

Another solution for D using dynamic programming.

Let's consider $$$dp[i][k]$$$ — bool variable, that means "is it possible divide $$$a_1, a_2, ..., a_i$$$ on $$$k$$$ segments of equal sum".

Initially, $$$dp[0][0] = true$$$, others — $$$false$$$.

How to count $$$dp[i][k]$$$? If we can divide $$$a_1, ..., a_i$$$ on $$$k$$$ segments of equal sum, it means that this sum is $$$(a_1+...+a_i)/k$$$ (let's called it $$$s$$$)

So we need to find such $$$j$$$, that $$$a_j+...+a_i$$$ = $$$s$$$. We know that $$$a_i \geq 1$$$, so if this $$$j$$$ exists — it is only one. We can find this $$$j$$$ using binary search, or map with prefix sums, or just maintain $$$n$$$ pointers (one for each $$$k$$$), e.t.c

So if there is no such $$$j$$$, $$$dp[i][k] = false$$$. In other case $$$dp[i][k] = dp[j-1][k-1]$$$.

To find answer, we need to find maximal $$$k$$$ such that $$$dp[n][k] = true$$$. It means we can divide it on $$$k$$$ segments, so we need $$$n-k$$$ operations.

Code: 101285918

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    2 years ago, # ^ |
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    I also thought the same approach, i just stored the index of first element of last partition. I think each will be visited only once.

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    2 years ago, # ^ |
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    brilliant, thanks!

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2 years ago, # |
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Bruh, problem C got a way easier solution. Just brute force result from $$$1$$$ to $$$123456789$$$ and then, store the result and just handle when $$$N>45$$$ and that is all. Oh, make sure also to use pragma optimizations and unrolling loops for this funny solution to pass. Here is my code. Or, you can play it safe and handle few more N's like I did in contest. Here is my second code.

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    2 years ago, # ^ |
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    Funny thing ikr..i played it safe for 40,41,...45..etc. Till 39 the answer fits in 1e6 so no TLE issues.

    C
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    2 years ago, # ^ |
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    or just go with all the permutations $$$O(9*9!)$$$ sub

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    2 years ago, # ^ |
      Vote: I like it +45 Vote: I do not like it

    I Don't know what's worse, my life or your code's indentation

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    2 years ago, # ^ |
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    there is also a faster way, we need to check all subsets of set {1,2,...,9} using something like bitmasks.
    this works with O(9 * 2^9)

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      2 years ago, # ^ |
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      Yes, I know that solution. But I was trolling with the above solutions so I can see some few people who desperately tries to hack me. Hahahha.

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    2 years ago, # ^ |
    Rev. 2   Vote: I like it +2 Vote: I do not like it

    There's another way around Click

    You can get solution in $$$O(1)$$$

    Edit: Mahfel have a look, this is far faster then $$$O(9*2^9)$$$

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      2 years ago, # ^ |
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      yes,you're definitely right.
      but copying 45 numbers in an array is kind of boring for me,what about you? :)

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    2 years ago, # ^ |
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    Or you could just brute force over the subsets from 1 to 2 ^ 10 — 1 and check if the sum is of the digits is the same or not. If it is, then just take the min like this : 101355465

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2 years ago, # |
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The formulas in the Editorial of Problem E1 do not reflect the formulas used in the Code.

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    2 years ago, # ^ |
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    Yes, I think so.

    They mistakenly wrote $$$\frac{cnt[x]\times cnt[x]\times cnt[x]}{6}$$$ instead of $$${cnt[x] \choose 3} = \frac{cnt[x]\times (cnt[x] - 1)\times (cnt[x] - 2)}{6}$$$ and $$$\frac{cnt[x]\times cnt[x]}{2}$$$ instead of $$${cnt[x] \choose 2} = \frac{cnt[x]\times (cnt[x] - 1)}{2}$$$

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2 years ago, # |
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    2 years ago, # ^ |
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    Who told you to look on the internet? during the contest

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      2 years ago, # ^ |
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      Who has forbidden you to look on the internet? During the contest?

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        2 years ago, # ^ |
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        Reasonable difficulty parameters of div 3.....

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          2 years ago, # ^ |
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          I am not talking about the difficulty parameters of div3. I am talking about the fact you mentioned: "You can't look through the internet during the contest". There is no rule against using google/prewritten code in codeforces. You may even consider "googling" a special skill for CP :D

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2 years ago, # |
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I have one small doubt , during the contest I used printf for printing output and I got 4 WAs and after contest I submitted same solution by using cout and it got accepted.Why so?

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    2 years ago, # ^ |
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    Don't mix cout with printf when you are using fastIO, printf is faster so, it might output the result before the cout does.

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      2 years ago, # ^ |
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      Ohh,thanks . I will never forget this in my life.

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2 years ago, # |
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Please help me with this solution of F, 101358483 I am basically trying to count the number of elements that will be good with one element

I am using a set to get the number of elements good with it before that element and upper_bound to get the number of elements after that element.

So, I get the number of elements good with any element and store the maximum of it And therefore the answer is n- (the number calculated above) Any help will be highly appreciated.:)

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2 years ago, # |
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In problem F — The Treasure of The Segments, how do we make sure that the i-th start segment and the i-th end segment (which we use to calculate the current value) — both these start and end points belong to the same segment? Isn't the hypothesis that we iterate over all segments. But in many cases, when sorting the start and end points separately, it should violate the hypothesis that the i-th segment is being considered.

e.g. (1, 2), (3, 7), (4, 5), (6, 9), (8, 10)

Left endpoints in sorted order : 1 {belongs to 1st segment}, 3 {2}, 4 {3}, 6 {4}, 8 {5}

Right endpoints in sorted order : 2 {1}, 5{3rd segment and NOT 2nd}, 7 {3}, 9 {4}, 10 {5}

Even if it is true that the cases for l > R and r < L are handled separately, I cannot understand how calculating these half-values for the same position in sorted order ensures reaching the optimal answer.

Edit: Looks like I didn't read the editorial code carefully. We are considering the i-th segment only (by iterating over the original vector of pairs v). Thanks to both the gentlemen who replied.

???

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    2 years ago, # ^ |
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    We can say if a segment $$$(a,b)$$$ coincides with segment $$$(c,d)$$$, then $$$c<=b$$$ (vice versa may not be true). So, for a particular segment $$$(a,b)$$$ we can find all those segments whose $$$start<=b.$$$

    In the above picture if I calculate such segments for red segment, I'll get $$$5$$$ such segments (including the red segment itself).Now, we have to remove such segments in which $$$end<a$$$ because such segments (segment $$$1$$$ in this example) will surely be included in the above ans but in actual they don't intersect with red segment. Thus, we get $$$5-1=4$$$ segments intersecting with red segment (including itself).

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      2 years ago, # ^ |
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      I fail to see how this answers my question. Please note that I had solved this question, just without sorting the two arrays independently. That's my issue — how can you ignore that you're not considering the same segment anymore? It's been bothering me a lot and I'm sure it's something silly that I'm missing. Thanks nevertheless.

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        2 years ago, # ^ |
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        It isn't necessary that $$$i^{th}$$$ index of both the arrays after sorting belong to same segment. The proof above still remains valid.

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    2 years ago, # ^ |
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    For each segment, we are calculating the number of segments that end before the current one starts and the number of segments that start after the current one ends. Now, think a minute and see that these two values will never have a common value.

    Lets say current segment starts at L and ends at R
    1) All segments that end before L will have start and end both less than L. 
    2) All segments that start after R will have start and end both greater than R.
    
    So, you can see these two can never have a common because first value has [l,r] less than L and second value has [l, r] greater than R. They can never intersect.
    
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2 years ago, # |
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I had a slightly different approach to D using more of an analytical/brute force method.

Similar to the reasoning presented in the posted solution, the sum of the overall array will always stay the same, meaning that the original value of each part of the array will be preserved either as an individual number in the final array or as a component of another number in the final array.

As such, it can be seen that the number at an index of 1 must always be included in the final array in some form, allowing for an iterative solution over the array to be created.

Iterating over all values i from 1 to n and keeping the cumulative sum sum of each number that was iterated upon to represent one "fixed" value in the final array, this sum can then be validated by iterating over the remainder of the array. When iterating over the remainder of the array, keep a sum cSum of numbers that have already been reached. If that sum is equal to the sum of the fixed window, reset cSum to 0 and continue and if it is greater than the sum, then break from the iteration since that means it doesn't work. Store the number of times cSum was equal to sum.

Finally, take the maximum number of times that cSum was reset through all iterations, add 1 to signify the initial reset at the end of the first window, and subtract from n for the final answer.

This solution would run with an O(n2) time complexity in its worst-case.

Code: 101330471

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2 years ago, # |
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Why is time limit for E1 2 secs but time limit for E2 4 secs?

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2 years ago, # |
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Problem C can be done by bruteforcing all $$$2^9$$$ possible numbers of different (non null) digits that are the smallest in lexicographical ordering for that set of digits, since the solution must satisfy this constraint.

Example

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2 years ago, # |
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Here's a fairly simple $$$O(n \log(an))$$$ solution for D: 101370002

It can also be optimized to just $$$O(n \log n)$$$.

Also quick note, I'm still seeing Russian in the English title of this post ("Разбор").

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    2 years ago, # ^ |
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    can you please explain it a lit bit? Thanks!

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      2 years ago, # ^ |
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      Sure! I actually didn't explain this in my stream (I came up with it after my stream).

      Let's say the sum of the array is $$$s$$$ and we want to know whether we can end up with a final array of length $$$len$$$ with all equal elements. Then we need to cut the array up into $$$len$$$ subarrays, each with sum $$$\frac{s}{len}$$$.

      If we compute the prefix sums of the $$$a_i$$$, this means we'll need to find one prefix sum matching each of $$$\displaystyle \frac{1}{len} \cdot s, \frac{2}{len} \cdot s, \dots, \frac{len}{len} \cdot s$$$. Since $$$a_i > 0$$$ we really just need $$$len$$$ different prefix sums that are divisible by $$$\displaystyle \frac{s}{len}$$$.

      If we have a particular prefix sum $$$p$$$, what values of $$$len$$$ does it work for? It turns out we take $$$\displaystyle x = \frac{s}{\gcd(s, p)}$$$ and then we want all multiples of $$$x$$$. (For example if $$$p = \frac{3}{5} s$$$ then $$$x = 5$$$.)

      We compute GCDs, generate all these counts, and then do a sieve-style summation to cover all multiples, and we're done.

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        2 years ago, # ^ |
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        To get to $$$n \log n$$$, notice that the bottleneck is computing the GCDs which takes $$$\log(an)$$$ time each iteration: 101370002. However we only care about the value of $$$g$$$ when $$$\displaystyle len = \frac{s}{g} \leq n$$$, or namely when $$$\displaystyle g \geq \frac{s}{n}$$$. So we can stop our GCD algorithm once we go below $$$\displaystyle \frac{s}{n}$$$, which means it only takes $$$\log n$$$ time.

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        2 years ago, # ^ |
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        neal can you tell what exactly does x signify. I understand that if i can divide sum into x parts than it is possible to divide it into all divisors of x parts as well. for example if we can divide sum into 4 parts we can also divide it into 2 parts as well, just by clubbing the two parts into one.

        So instead of taking all multiples of x should not we take divisors of x?

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2 years ago, # |
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I am trying to grasp on what case this submission (101340630) for problem D is failing. According to the editorial, a check to verify if k is the answer can be implemented greedily. In the above implementation, i try to pick the min-element in the original array and add it to min(left-element, right-element) before deleting that min-element. Is that theory wrong?

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    2 years ago, # ^ |
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    Yes, example 5 6 2 6 3 gives the wrong solution(or 3 6 2 6 5 depending on your code). The answer is 3, but greedy will give 4 for one of these inputs.

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2 years ago, # |
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https://codeforces.com/contest/1462/submission/101325108 Please tell me what i did wrong as i think i have applied the same thing as mentioned in the editorial.

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2 years ago, # |
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I got WA in D , can anyone prove why my idea is incorrect? Every time I check whether all the elements are equal or not, if they are equal just print the current number of operation else pick the smallest element and add it to the smallest neighbour and increase operation count by 1, my sub link:- https://codeforces.com/contest/1462/submission/101310473

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    2 years ago, # ^ |
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      2 years ago, # ^ |
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      ??

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        2 years ago, # ^ |
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        I answered to this exact question in the link I pasted, anyway this is the answer. Example 5 6 2 6 3 gives the wrong solution(or 3 6 2 6 5 depending on your code). The answer is 3, but greedy will give 4 for one of these inputs.

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          2 years ago, # ^ |
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          OMG! got it, when they have equal values in both sides it fails to choose optimally

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            2 years ago, # ^ |
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            Not true. Reason is that greed will just fail. :)

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    2 years ago, # ^ |
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    I did the same in the contest like an idiot without thinking. Simply put, it's wrong. Adding the smallest to the one of it's neighbouring elements seems to work, but there is no way that it should work.
    Eg. {9, 1, 5, 3, 2}

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2 years ago, # |
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Another solution for problem B:

Lets create a $$$DP[idx][idx2][state]$$$. $$$idx=$$$prefix of first string, $$$idx2=$$$prefix of second string, $$$state=0,1,2$$$. Transition is to check if $$$s[idx]=t[idx2]$$$ where $$$s$$$ is the first string and $$$t="2020"$$$. If $$$state=1$$$, change it to $$$2$$$. Because $$$state=0$$$ means that we didn't delete anything, state=1 means we are currently deleting, $$$state=2$$$ means we are not allowed to delete anymore. And another transition depending on the state. If state is equal to $$$0$$$, then it will turn $$$1$$$ as you are forced to delete that number. If state equals to $$$1$$$, you will keep deleting. Otherwise, you have nothing to do and you didn't find an answer. I hope you liked my overkill solution!

Warning, bad indented code
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2 years ago, # |
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E2

For those who are looking how to calculate for a NcR % mod for huge N and R , for E2.

#define mod 1000000007
const int MAXN = 200000;
int fact[MAXN];
int ifac[MAXN];

int ncr(int n, int r) {
    if( n < r or r < 0 )
        return 0;
    return fact[n]*(ifac[r] * ifac[n-r] %mod) %mod;
}

int power( int x, int y ) {
    int a = 1;
    for( ; y>0; y>>=1, x=x*x%mod )
        if( y&1 )
            a = a*x %mod;
    return a;
}

void preNCR() {
    fact[0] = 1;
    for( int i=1; i<MAXN; ++i )
        fact[i] = fact[i-1]*i %mod;
    ifac[MAXN-1] = power(fact[MAXN-1], mod - 2) %mod;
    for( int i=MAXN-1; i>=1; --i )
        ifac[i-1] = ifac[i]*i %mod;
}

just call the preNCR() in main().

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2 years ago, # |
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What is wrong in this? Problem 2 101403407

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    2 years ago, # ^ |
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    You should consider two more cases: - when string begins with "2020" - when string ends with "2020"

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2 years ago, # |
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What's wrong with my solution of E2? link

Upd. Wow! I find the problem! AC.

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2 years ago, # |
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Thanks a lot for the contest and the editorial learnt many things from this round!

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2 years ago, # |
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can anyone explain whats wrong with my solution for E1 ``` public static void solve1() {

int n = in.nextInt();
    int[] arr = new int[n + 1];

    for (int i = 0; i < n; i++) {
        int x = in.nextInt();
        arr[x] = arr[x] + 1;
    }
    int ans = 0;
    for (int i = 2; i < n; i++) {
        ans += arr[i - 1] * arr[i] * arr[i + 1];
    }
    for (int i = 1; i < n; i++) {
        ans += arr[i] * (arr[i] - 1) / 2 * arr[i + 1];
    }
    for (int i = 2; i <= n; i++) {
        ans += arr[i - 1] * arr[i] * (arr[i] - 1) / 2;
    }
    for (int i = 2; i < n; i++) {
        ans += arr[i - 1] * arr[i + 1] * (arr[i + 1] - 1) / 2;
    }
    for (int i = 2; i < n; i++) {
        ans += arr[i + 1] * arr[i - 1] * (arr[i - 1] - 1) / 2;
    }
    for (int i = 1; i <= n; i++) {
        ans += arr[i] * (arr[i] - 1) * (arr[i] - 2) / 6;
    }
    System.out.println(ans);
}

} ```Is it something related to the data type this solution is not passing or 5th pretest

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2 years ago, # |
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Thank you for great contest!

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2 years ago, # |
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Very Interesting problems!!

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2 years ago, # |
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in problem F how the output of this test case 1

4

1 2

2 3

3 5

4 5

it should be 2 right? correct me if i am wrong

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    2 years ago, # ^ |
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    It should be 1 because we can provide the required property with the 3rd segment by deleting only the 1st segment.

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I am confused between E1 an E2 if E1 is lower version of E2 then why solution of E2 without mod is not passing E1 it is giving wrong answer on test case 5 can anyone explain this ?

my submission of E1 converted from E2 101642503

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    2 years ago, # ^ |
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    You are using mod operator while evaluating Factorial , nCr , invfact

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      2 years ago, # ^ |
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      below is code without mod operation it won't even paas sample test cases

      #include<bits/stdc++.h>
      #define rep(i,n) for(int i = 0; i < (n); ++i)
      #define drep(i,n) for(int i=n-1 ; i > =0; i--)
      #define all(a) a.begin(),a.end()
      #define pb push_back
      using namespace std;
      typedef long long int ll;
      const int N = 300500;
      const int mod = 1000000007;
      
              
       ll C(ll n ,ll k)
       {
           
           ll ans =1;
           if(k >n-k)
           k=n-k;
       
           for(ll i=1; i<=k;i++)
           ans*=(n-i+1),ans/=i;
       
           return ans;
       } 
      
      void solve(){
      
          ll n,m,k,ans=0;
          cin>>n;
          m=3;
          k=2;
          vector<ll> v(n);
          for(ll i=0;i<n;i++)
              cin>>v[i];
          sort(all(v));
          for (ll i = 0; i < n; i++) {
              ll l = i + 1;
              ll r = upper_bound(v.begin(), v.end(), v[i] + k) - v.begin();
              ans = (ans + C(r - l, m - 1));
          }
              
          cout<<ans<<"\n";
       
      
      
      
      
      }
      int main(){
       
          //#ifndef ONLINE_JUDGE
          //freopen("input.txt","r",stdin);
          //freopen("output.txt","w",stdout);
          //#endif
          ios::sync_with_stdio(false);
          cin.tie(nullptr);
          cout.precision(10);
          cout << fixed;
      
          int _;
          cin>>_;
          while(_--)solve();
      }
      
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2 years ago, # |
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Problem E has $$$\mathcal{O}(n \log n)$$$ solution, which doesn't use, that elements are in $$$[1, n]$$$. Let's sort our array, and calculate number of possible subsets if minimal element in subset is $$$a_i$$$. Let $$$l$$$ be max index, such that $$$a_l \leqslant a_i + k$$$, let $$$x$$$ be numbers equal to $$$a_i$$$ in range $$$[i, l]$$$ in array, and $$$M$$$ is number of other numbers in this range. So if in chosen subarray $$$a_i$$$ is minimal value, then all subarray is in this range. So number of possibilities to choose this subarray is $$$\sum_{i=1}^x C^i_x \cdot C^{m - i}_M$$$, where $$$C^k_n$$$ is number of possibilities to choose $$$k$$$ elements from $$$n$$$ elements, also known as binomial coefficient which can be easily find as $$$C^k_n = \dfrac{n!}{(n - k)!k!}$$$. If we precalculate factorials, and numbers, that is inverse modulo $$$10^9 + 7$$$ to factorials, we can calculate $$$C^k_n$$$ for $$$\mathcal{O}(1)$$$(Warning: if $$$k < 0$$$ or $$$k > n$$$ we must return 0). Because $$$a$$$ is sorted, we can find $$$l$$$ using two pointers technique and calculate $$$x$$$ for $$$\mathcal{O}(n)$$$ total. Because sum of $$$x$$$ is $$$n$$$ it will be $$$\mathcal{O}(n)$$$ time and $$$\mathcal{O}(n \log n)$$$ time to sort array. We can precalculate factorials and inverse factorials for $$$O(n \log A)$$$ using binary pow or extended gcd. Also we can calculate inverse factorials for $$$\mathcal{O}(n)$$$ using linear sieve technique which described here, but it is not necessary. Space complexity is $$$\mathcal{O}(n)$$$

Submission, which can help to understand solution: https://codeforces.com/contest/1462/submission/103030183

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19 months ago, # |
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Can anyone tell what is wrong with problem E2 submission 120341826.

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3 months ago, # |
Rev. 2   Vote: I like it 0 Vote: I do not like it

What is wrong in this? Problem E2 178055245