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mesanu's blog

By mesanu, history, 3 years ago, In English

Thank you for participating!

1873A - Short Sort

Idea: flamestorm

Tutorial
Solution

1873B - Good Kid

Idea: mesanu

Tutorial
Solution

1873C - Target Practice

Idea: flamestorm

Tutorial
Solution

1873D - 1D Eraser

Idea: flamestorm

Tutorial
Solution

1873E - Building an Aquarium

Idea: flamestorm

Tutorial
Solution

1873F - Money Trees

Idea: mesanu

Tutorial
Solution

1873G - ABBC or BACB

Idea: flamestorm

Tutorial
Solution

1873H - Mad City

Idea: mesanu

Tutorial
Solution
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3 years ago, hide # |
 
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Problem H was awesome!

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You can avoid hard coding in problem C.

Value of cell $$$(i,j)$$$ is $$$\min(i,j,11-i,11-j)$$$.

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    dislike me >_<

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    Another approach is to take min Chebyshev distance from (i, j) to the 4 middle squares.

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    Thank you for the formula. Could you please provide a more general formula that works for concentric matrices where the values decrease from the outermost layer to the inner layers? ("Do you think this formula consistently works for matrices where the values increase from the outermost layer to the inner layer min(i,j,n+1−i,n+1−j)) and thanks.

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Problem G's walk-through was so clear I could understand the concept in a split second!

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For C, I asked chatGPT to provide me with a program to generate the matrix and then I used it. Happy to get skipped as the rating doesn't matter to me.

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    using chatGPT is legal tho

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    That is smart, wish I'd have thought of that

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      2 years ago, hide # ^ |
       
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      hello can you explain why direction of approach doesn't matter in B question like any proof if possible?

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        2 years ago, hide # ^ |
         
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        What do you mean?

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          2 years ago, hide # ^ |
           
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          B mei jaise greedy approach laga rhe hai na left to right jaate hue, so I'm asking right to left jaane pe same answer aayega and Better answer nahi aayega iski kya guarentee hai. I would love a proof of why Direction of approach does not matter.

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            2 years ago, hide # ^ |
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            Are you talking about this contest’s B? My solution was just brute force where I tried everything. I reset the variable after each iteration.

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              2 years ago, hide # ^ |
               
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              oh i'm really sorry i meant D (1d eraser)

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                2 years ago, hide # ^ |
                 
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                Well if you’re convinced that it works backward you can think of reversing the string and doing it backwards as the same thing as doing it forwards

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                  2 years ago, hide # ^ |
                   
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                  no i am not convinced that it works forward

                  according to me the ans should be min(forward approach, back approach)

                  greedy gives me the idea to approach from one single direction but how can you say that both directions will give same answer

                  here your reversing logic doesn't apply as say i claim forward approach takes 3 operation and backward approach takes 2 operations then on reversing also answer will be same i agree(2) but this time it will be from forward approach

                  how can you claim that only by checking from one direction you will get a answer same as backward approach

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                  2 years ago, hide # ^ |
                   
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                  Oh, I see.

                  Well, let's try to 'prove' that the forward approach always gives an optimal answer.

                  What my code is doing is it's going from 0 to n and checking if each character needs to be converted or not. If it does, start a window, otherwise move on to the next index. Notice that when we move on to the next index, we'll never come back to the previous one.

                  So why is this important? That means that when we see an element that needs to be converted, we have to start a window. You might say that there are multiple ways to start a window (for example if we want to convert i+1, we could start a window of size k>=2 at index i) so that an index is converted, but the most optimal way will always be when it's started at the index that needs to be converted, since that way more indices ahead can be affected.

                  If you're convinced that the forward approach is correct, you can see why the backward approach will also be correct from my above reply, thus showing that both approaches will give the same answer.

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Can someone explain why in problem B, it's optimal to increase the smallest digit ?

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    yes because if we notice that the ratio change of x+1/x (x is smallest digit) is large as compare to bigger digits so thats why it always gives ans..

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    if you add 1 to smaller number then you gain original product + (original — small). But if you add 1 to any other than smaller you gain -> Original product + (original — some other which is not smallest) . So first case will always be bigger

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    Say you have (3,3,2,3):

    Let's pretend you need to find the largest possible product with all these elements except one.

    This is obviously (3*3*3), as 2 is smaller than 3, and (3*3*2)<(3*3*3). Now we know that the excluded value is 2.

    Now that we've got (3*3*3) as the largest product excluding the smallest value, we can add 1 to the excluded value, and now we've increased the product by (3*3*3).

    We went from (3*3*3)*2 to (3*3*3)*3.

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    Based on AM-GM Inequality, a set of numbers with specific sum will have largest product if all the numbers are equal. Increasing the smallest digit will make these digits be closers to their average. It is not a solid proof but rather an intuitive way to quickly realize it.

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      2 years ago, hide # ^ |
       
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      hello can you explain why direction of approach doesn't matter in B question like any proof if possible?

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    assume x=a*b*c*d

    then (a+1)*b*c*d-x = b*c*d

    basically, increasing a single number by one increases the answer by the product of all other numbers, so it's best if b,c,d are the largest possible, which means a is the smallest possible

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$$$E$$$ can be solved in $$$O(n \log(n))$$$ and $$$F$$$ can be solved in $$$O(n)$$$.

For $$$E$$$, first sort the array $$$a$$$. The optimal value of $$$h$$$ is $$$\max_i(v_i)$$$ where $$$v_i=\min(a_{i+1}-1, \left \lfloor (x+PrefixSum([a_1:a_i]))/i \rfloor \right)$$$ if $$$v_i \geq a_i$$$ and $$$v_i=0$$$ otherwise (set $$$a_{n+1}$$$ as $$$\infty$$$ or handle the case $$$i=n$$$ separately).

$$$F$$$ can be done by sliding windows method.

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    3 years ago, hide # ^ |
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    don't you use sort in E?, which is already O(n log(n))

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    3 years ago, hide # ^ |
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    You can use binary search for finding solution. l = 0, r = 1e9

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      3 years ago, hide # ^ |
       
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      but r = 1e9 get wrong answer. must use r = 2^31 -1 or r = 2e9 + 7. i used 1e14, 1e15 and 1e18 then i got wrong answer. it was so boring :>

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        3 years ago, hide # ^ |
         
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        Why ?

        Its work fine for me , No need for this values .

        My submission 224465049

        And I think Binary Search is more simple than the formula and easier to work with for beginners.

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          3 years ago, hide # ^ |
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          I don't know. maybe the problem was from another thing. however this is my code who got wrong answer : 224488235

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            3 years ago, hide # ^ |
             
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            Mid is Overflow

            1e18 / 2 = 5e17 which cann't stored in an int

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              3 years ago, hide # ^ |
               
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              oh really? you are kidding! I knew that. i used define for contest who i don't forget using long long

              #define int long long

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Can someone explain why this code doesn't work for Problem E. I understood immediately that Binary Search would be used but my code fails on TestCase-7. TIA

https://mirror.codeforces.com/contest/1873/submission/224447874

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For problem F: Given, (l≤i<r). I don't understand why l and r can be same.

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Video Editorial For Problem A to H

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In f, we can use two pointers instead of binary search, so it can be reduced to O(2*n)

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Could someone help me, why this code is getting wrong answer in problem H https://mirror.codeforces.com/contest/1873/submission/224501501

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For Problem F,

Can someone explain if I take l = 2 and r = 2 as well, then how is 2<=2<2 ?

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    pick l=2 and r=2 , you will find that no such i satistied l<=i< r . That means you don't need to check any h[i]. So you can collect fruit from a[l] to a[r] (that's a[2] actually) . The same thing works when you want to collect fruit from only one tree.

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I found an exactly same problem as problem H (Mad City)

https://github.com/all1m-algorithm-study/uospc2021/blob/main/problems/Police_Thief/statements.md

This is from an intra-college contest held by University of Seoul in 2021.

There is no English statement, but if you use a translator you'll notice there are few differences.

Even the examples given in the descriptions are the same.

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Thanks for a good contest, although i joined late the experience was enjoable

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Problem E can be solved in $$$\mathcal{O}(n\log n + \log n\log (a_i+x))$$$.

First, we notice that the permutation of $$$a[i]$$$ does not matter at all.

So we can sort(a,a+n) first, and then when we want to calculate how much water we use when the height is $$$h$$$, we can use idx=lower_bound(a,a+n,h)-a, and then the water we use nowuse=idx*mid-s[idx-1].

$$$s[i]$$$ is the prefix of sorted $$$a[i]$$$, i from 0 to n-1. We can use this because for $$$idx\le i\le n-1$$$, we have $$$a[i] \gt h$$$, so the use of $$$i$$$ is $$$0$$$.

By using this way, we can avoid calculating max(0,...) with n times.

Since sort takes $$$\mathcal{O}(n\log n)$$$ and in every check in binary search we use lower_bound which is $$$\mathcal{O}(\log n)$$$, we have $$$\mathcal{O}(n\log n + \log n\log (a_i+x))$$$ in all.

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In problem c:

auto position = [](int i, int j)->int 
{
    int output;
    if((i+j)<=9){
        output = min(i, j);
    }else{
        output = (9-max(i, j));
    }
    output++;
    return output;
};
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    I use this equation : point = min(min(i,9-i),min(j,9-j)) + 1 it's the minimum distance to the edge + 1.

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for problem G, as mentioned in the tutorial, we can see the problem as each B choose one direction(left or right) to eat the A's, so we can use dp.

dp[i][0] means if the i-th B choose to go left, the maximum A's that the 1-th, 2-th, ..., i-th B can eat. dp[i][1] is similar, it means the i-th B choose to go right.

therefore, we can get the transition equation: dp[i][0] = dp[i-1][0] + i-th B's position — (i-1)-th B's position — 1 (because if the (i-1)-th B go right and the i-th B wants to left, it will have conflict, so (i-1)-th B can only choose to go left) dp[i][1] = max(dp[i-1][0], dp[i-1][1]) + (i+1)-th B's position — i-th B's position (if i-th B wants to go right, we don't need to care about the (i-1)-th B's choice)

and here is the implementation https://mirror.codeforces.com/contest/1873/submission/224561489

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please can someone suggests similar problems to F in which you do binary search on the answer plus some other computations?

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    In problem F i have first searched for a segment of divisible no.s and then i have applied sliding window technique . The time complexicity was 2.n which is actually O(n). Try this approach.

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Video Editorial (A-H) LINK TO YOUTUBE EDITORIAL

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Not getting how to solve F problem, can anyone explain the intuition?

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I request Div4's authors to make future rounds a little more challenging. This was on the easier side.

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For the last problem, I didn't notice the number of edges is n, I skipped the first line immediately assuming it just says there are n nodes. Then I thought maybe around 20 mins on this and was amazed how people can solve it while I was trying to prove it is a hard problem. It was like finding a bunch of induced cycles, which isn't an easy problem in general graphs. I can't blame that it wasn't explicit enough, since if I was reading the input format or the first line, it was clear there are n edges.

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    I've also read the problem like this.

    In such version, we can solve it at least as follows (or maybe easier):

    • for each vertex, determine whether it lies on any cycle
    • for each vertex, find distance from Valeriu
    • for each vertex, find distance from Marcel
    • Valeriu wins if there is a vertex on a cycle that is closer to Valeriu than to Marcel
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      3 years ago, hide # ^ |
       
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      I think you are right. I thought too deep about it: I thought the winning strategy is to walk along an induced cycle, otherwise, marcel can at some point go along a chord of a cycle and catch Valeriu. Finding a winning strategy is difficult I believe, the question didn't ask for the winning strategy, though. I think the reason I've thought too much about it is that, I overlooked that every vertex that lies on a cycle, also lies on an induced cycle, so I didn't need to check if a vertex is on induced cycle, if it is on a cycle, certainly there is an induced cycle the vertex is on it. So, yes it was easier to decide if he wins but not easy to find a winning strategy.

      Also one last and less important point: the approach you mentioned in general graphs could be quadratic to #vertices, so if the number of the vertices is big (like in this case), it could fail if it has too many edges (well this case didn't have that).

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        3 years ago, hide # ^ |
         
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        The first item (for each vertex, determine whether it lies on any cycle) can be performed with a single depth-first search, similar to finding articulation points or biconnected components.

        Finding distances is two breadth-first searches, one from Marcel and the other from Valeriu.

        So the solution is O(E) in total.

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          3 years ago, hide # ^ |
           
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          That’s correct, and O(|E|) in dense graphs could lead to O(|V|^2) and if |V| is big, like 1e5, then it will be TL. But, of course for this particular question it doesn’t happen.

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            3 years ago, hide # ^ |
             
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            When the graph is given explicitly, which is true in the majority of the problems, $$$O(|E|)$$$ is quite distinct from $$$O(|V|^2)$$$.

            If we can read it, which takes $$$O(|E|)$$$ already, we can certainly work with it in $$$O(|E|)$$$ as well.

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How to understand "Because we have a tree with an additional edge, our graph has exactly one cycle."? I think we are only gived a simple graph and there may be more cycle.

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    It follows from the statement "The roads are given that it is possible to get from any building to any other building going along the roads.". This means the graph is a connected graph. A connected graph with n nodes and n-1 edges can be proven to be a tree. There is edge left over after making the tree and adding it must create a single cycle (as every node is already connected).

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In hindsight my bridge-finding algorithm seems like an overkill :) 224589798

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    Could you explain the idea?

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      If you don't understand anything just read the offical solution :))) It's much faster, simpler and more elegant.

      With the given conditions, every bridge in the graph does not belong to the cycle, and thus every non-bridge belongs to the cycle. After we traverse on the graph we will find the full set of vertices that belong to the cycle. Start traversing from Valeriu's positon until you reach one that is in the cycle (possibly Valeriu's original position itself) and calculate the distance between the vertices. As the tutorial above indicates, this is Valeriu's entry to the cycle. We then calculate the distance between that entry vertice and Marcel's. The answer is No if the former distance is not smaller that the latter, or both Valeriu and Marcel share the same starting position.

      For an implementation of the bridge-finding algorithm, see https://cp-algorithms.com/graph/bridge-searching.html#implementation.

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Can somebody explain Problem F using BS Please.

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Can some please explain why I got wrong answer when the value assigned to 'hi' was 1e14 or 1e18?

https://mirror.codeforces.com/contest/1873/submission/224393419

This resulted in wrong answer in test case 4 but was accepted when I updated the value of 'hi' to 1e10.

Thanks.

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    Because when 1e14 or 1e18 is multiplied by 2*10^5 (maximum size of array) an overflow will occur (long long maximum value is approximately 9*1e18)

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Why in problem H, in test 2, in test case 3, the answer is NO? Test case: 1 18 7 15 14 6 14 8 6 18 4 13 3 12 11 9 14 2 14 17 14 11 11 5 1 7 16 11 15 11 14 18 1 13 10 8 13 14 12 6 UPD: Sorry I missed one test case, the answer for test case above was YES

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You can also watch the video editorials I made on the problems E , F, G and H

Enjoy watching and let me know what you think about them!

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H problem Clearing the array vis[N] is the most important !

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Problem H Idea is simple but implementation bit complex.

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Problem F can also be solved using Binary Search ... My code

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Can someone explain the second last sample test case for problem H?

8 5 3

8 3 5 1 2 6 6 8 1 2 4 8 5 7 6 7

I think Valeriu can always escape Marcel by choosing node 3 or 4, whichever one Marcel doesn't choose.

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G is the hardest problem I think, but solving it was gratifying

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for H,what if there are 2 entrances of the circle?

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I absolutely loved the editorial for problem G! Wow! It was so fun to read, and so easy to understand! It would be amazing if all editorials were like this: being longer is not necessarily bad if a longer editorial is better at explaining the solution than a shorter one.

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What exactly I am doing wrong here in Problem E. I solved this on a pen and paper, and seems to me that the calculations are correct. I am first sorting the heights and then start filling up from the leftmost side of the tank. My submission My solution

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    At the end, you're adding x/n.. instead, you need to add x/(i+1) where i is the index of the largest coral that gets submerged. Also, you need to use a larger data type.. I modified your code.

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why the answer of test case "ABAAB" in problem G is 2

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Hey, Can anyone help me with this runtime error? I have tried debugging and wasted a lot of time. Any help is appreciated.

https://mirror.codeforces.com/contest/1873/submission/226134316

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    In function dfs() last else block you are popping from the set without checking if it is possible to pop from the set Here is your AC code

    You can always you assert to figure out the mistake in your code.

    EDIT -> The word set in the first para is actually the stack you are using. I called it set as I was thinking about memory and pointers. In the last statement, "use assert"

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227178473 my dp with memoisation solution,store every preceding and proceeding B's and then use dp to choose the best possible combinations(note that:once u eat all the A's from right,u cant eat any left A's for all the B's proceeding that B).

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Problem F can also be solved in O(n) using sliding window approach. It is the modified version of the problem of Longest subarray having sum of elements atmost K. My submission — https://mirror.codeforces.com/contest/1873/submission/233766852

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2 years ago, hide # |
 
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The tutorial of problem G is beautiful, it was very informative for me to learn how to approach a problem :)

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2 years ago, hide # |
 
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Problem C can be solved using a triple for loop: since every "square" has a delta with the outer one of 1, that is constant, we can iterate trough the whole sub-square adding 1 to the final answer each time we find a 'X'. In this way, we will find an 'X' as many time as it worths.

int ans = 0;
for (int x=0; x<5; ++x)
    for (int i = x; i < 10-x; ++i)
        for (int j = x; j < 10-x; ++j)
            if (grid[i][j] == 'X') ++ans;

My sumbission as reference: 247543890

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23 months ago, hide # |
 
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Problem G becomes way easy you just have to find smallest consecutive A substring . The ans = Number of A(s) — Length of smallest consecutive A(s) substring . Submission = https://mirror.codeforces.com/contest/1873/submission/264596469

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20 months ago, hide # |
 
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dp soultion for G :

284204976

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14 months ago, hide # |
 
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did anybody else notice the names of the problems were inspired by kendrick's album? pretty cool!

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11 months ago, hide # |
 
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Can anyone point out where i'm going wrong in problem E. Here's my approach:

Water is only poured where aᵢ < h, so let’s define:

S = { aᵢ | aᵢ < h } — coral columns that need water

Let c = |S| (number of such positions)

Let s = sum(S) (total coral height to be topped off)

So, to compute the maximum tank height:

Let S = [aᵢ for aᵢ in a if aᵢ < min(a) + x] (we only consider values that could possibly be raised)

Let s = sum(S), c = len(S) compute h = x + s / c (GIF)

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9 months ago, hide # |
 
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Your code here...

#include <bits/stdc++.h>
using namespace std;
 
int main() {
    
    int t;
    cin >> t; 
    while (t--) {
        
        int sum = 0;
        vector<vector<char>> mat(10, vector<char>(10));
 
        for (int i = 0; i < 10; i++) {
            for (int j = 0; j < 10; j++) {
                char c;
                cin >> c;
                mat[i][j] = c;
                if (c == 'X') {
                    int layer = min({i, j, 9 - i, 9 - j});
                    sum += layer + 1;
                }
            }
        }
 
        cout << sum << endl;
    }
    return 0;
}