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Analysis of Codeforces Round #476 (Div. 2) [Thanks, Telegram!]
By KAN, 7 years ago, translation, In English
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7 years ago, # |
← Rev. 3   Vote: I like it +60 Vote: I do not like it

The most brilliant solution to problem D must be the one with max-flow min-cut theorem in my opinion :)

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    7 years ago, # ^ |
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    oh, I think about using maxflow here. But I think it is hard to make network here. Moreover complexity of such solution would not pass in TL, am I right?

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    7 years ago, # ^ |
      Vote: I like it +22 Vote: I do not like it

    well, in my opinion, just simple observation was required.

    Since, we are given that frogs can jump on the distance of "L" , we can maintain the window of the size "L", and for this window, we can find the sum, wherever the sum is minimum , that is our answer. Because it will become bottleneck for all frogs. :) .

    http://codeforces.net/contest/965/submission/37608075

    This is link to my on contest solution. It took me less than 10 minutes to solve this D. it was way too much easier than normal D.

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      7 years ago, # ^ |
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      lol your solution is max-flow min-cut theorem.

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        7 years ago, # ^ |
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        hmmm, sorry about that. I don't know much algorithms. I don't know what I have implemented is maxflow or something else.

        I just implemented with my intuition. I will look into Maxflow algo.

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          7 years ago, # ^ |
            Vote: I like it +9 Vote: I do not like it

          It's not the max-flow algorithm, it's just the idea of max-flow min-cut theorem. In your solution, you are using the fact that "max-flow is min-cut", where min-cut is the min(sum) of a length L. ;-)

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

      Nice solution!

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      6 years ago, # ^ |
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      your remark only justifies that your output must be greater or equal to the real answer, since real answer cannot be greater than the bottleneck; but you give no proof that your output "IS" the real answer. Though, with some careful thought, you can actually prove this, or more specifically, you can easily construct a solution /scheme where the frogs with the same num of bottleneck can jump across the bank

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      4 years ago, # ^ |
      ← Rev. 3   Vote: I like it +3 Vote: I do not like it

      A pretty late reply keeping in mind the contest happened 2 years ago, but I used a very similar logic, instead I maintained a dp, where dp[i] gives the max frogs ith place can hold which allows them to reach the riverbank, and then calculated minimum sliding window sum of length L over that dp.

      I got an accepted verdict but clearly our logic is different (Feel free to correct me if I am wrong). Any thoughts on why this is working out?

      AC submission:

      https://codeforces.net/contest/965/submission/91799129

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7 years ago, # |
  Vote: I like it +38 Vote: I do not like it

D can be solved with O(n) compexity. Imagine a graph where it is n * 2 vetices. From source you have edges to 1, 3 .. 2 * k — 1 vetices with capacity INF. From i'th vertice if i is odd you have edge to i + 1 vertice with capacity a[i]. From i'th vertice if i is even you have edges to i + 1, i + 3, i + 2 * k — 1 with capacity INF. if i is even and i / 2 >= n — k you have edge to sink (smth like that i can make little mistakes) And you can instead of building such a big graph and running max flow algorithm just try to find minimum cut. And after some greedy thoughts it is clear that you must choose segment [i, i + k — 1] with minimum sum of a[j] where j belongs to [i, i + k — 1]. It can be done with just a pair of loops in your code. See my implementation for details.

http://codeforces.net/contest/965/submission/37610259

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    7 years ago, # ^ |
      Vote: I like it +39 Vote: I do not like it

    Another (maybe easier) proof is that, if you imagine you know the solution with the maximum number of frogs and simulate the process for sequentially with all the frogs, making sure that the left-est frog moves at all times, you can see that every time in this process the frogs will be in a contiguous segment of length at most l. So the solution should be at most the minimum sum over all l-length segments. Once we found this upper bound, proving that it is the answer is straightforward.

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    7 years ago, # ^ |
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    hello there,can you please tell me why must i choose continue segment? what if i Don't choose one of the continue edge? i think that this maybe a minimal cut ,too

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      7 years ago, # ^ |
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      when you take i'th vertice to first set ( by cut ) if i is even you need to take next k vertices with odd i to first set (otherwise you'll add INF edges to your cut) therefore it is clear that it must be k consecutive odd vertices which goes in first set when his connected even vertices goes in second set. And as it must be k consecutive a[i] you can just not add other a[i] to your cut.

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    7 years ago, # ^ |
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    I solved problem using fenwick tree, greedy approach. But I dont understand your solution. Why it is important if i is even or odd? How can that be important?

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7 years ago, # |
← Rev. 2   Vote: I like it +7 Vote: I do not like it

Can someone explain why my solution passed tests. I want to believe that complexity is but i can't proove it.
Shortly it is dynamic programming on tries. dpv, x = minsum. Where v is number of vertice in tries. x — number of words that we didn't written in final set of prefix (it means that we will write it higher in tries — with smaller prefix).
There I do stupid smth like knapsack on a tree. dpv, x = min(dpv, x, dpto, y + dpprevz for all y, z witch satisfies condition y + z == x. It is usual knapsack on a tree.
So it should work in O(n2). But i added condition dp[v].size() = min(depth, cnt[v]) where cnt[v] — number of terminal vertices in subtree. And it gives states in dp because it is a trie. But there is also transitions and i've stuck here how to estimate number of transitions?

This is implementation http://codeforces.net/contest/965/submission/37615468.

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7 years ago, # |
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Can i solve problem div. 2 C using bisection method?

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7 years ago, # |
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Is this logic correct?

For C, Bonus 1:

Same logic as given.

Just one change: to find xMax formula used earlier was: n / ( k * (i — 1) + 1 ), where i is the current D (in a for loop of D). (I did + 1 at-last to include Arkady as leftover use was not allowed). It should be less or equal to M.

Here, we just have to first check:

if(n % (k * (i — 1)) != 0) then Arkady will get leftover in last level and (n / (k * (i — 1)) in other levels. (Need to handle a case when value of n / (k * (i — 1)) exceeds M as it will be added to leftover and so on...)

else same as earlier.

If this is correct then can anybody tell me how to make it work for large values of D? (1 <= D <= n)

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    7 years ago, # ^ |
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    I don't think that works.

    36 2 9 3

    when d = 1 or 2 : impossible

    when d = 3 : possible distributions = 6,7,8 , formula gives 6. best is 7.

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7 years ago, # |
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For E, I had right idea but failed in implementing minimizing depth.

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

There is a much simpler, two pointer solution to D. Probably similar to the one bicsi gave.

The idea is to maintain a 0...w array 'reach' where reach[i] tells us the number of frogs that have reached the i'th unit at the i'th step. Note that reach[i] can't be greater than a[i], because we can't accommodate more frogs than the number of stones. We start by having infinite number of frogs having reached the 0th unit. For any i <= l, reach[i] = a[i]. This is because the frogs from 0th unit can directly jump till here.

The key insight here is that for any i > l, we should start letting the leftmost frogs who can reach i, jump till i. I.e first all frogs from the (i — l)th unit jump till i, then (i — (l-1))th and so on. We do this till either i'th unit's capacity is reached, or we've run out of frogs. You can use a pointer 'j' to track where the leftmost frogs are. Just make sure that j >= i — l. Answer is reach[n].

http://codeforces.net/contest/965/submission/37625008

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    7 years ago, # ^ |
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    Thanks. I found this easier to understand than the editorial.

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7 years ago, # |
  Vote: I like it +6 Vote: I do not like it

I don't get why in C one doesn't need to compute min x for the iterated d like in the editorial. Computation of max x always works, but for me it seems that sometimes max x could make us take candies more than d times for the first person. Why is it never the case?

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    7 years ago, # ^ |
    ← Rev. 4   Vote: I like it +10 Vote: I do not like it

    what's more confusing is that if for some d, if max(x) > M then taking x = M will always be valid for this d !!! I really cannot account for this.

    37640931(should fail!)

    37648582(probably correct)

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7 years ago, # |
  Vote: I like it +6 Vote: I do not like it

Hi! What is "smaller-to-larger optimization"? Does someone has a link to read about it?

Thanks

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7 years ago, # |
  Vote: I like it +1 Vote: I do not like it

Does a binary search solution works for C ?

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7 years ago, # |
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how can i solve C's bonus 2 part?

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7 years ago, # |
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Anyone else solved D with BIT?

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7 years ago, # |
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can someone please explain E!

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    6 years ago, # ^ |
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    Firstly,we build a trie tree for all names.Now,the total length of these original names is the total depth of all names.

    As we go from the bottom to the top of the trie tree,if a node doesn't contain a name, it is obviously to place the name which is deepest(longest name) to current node,this case is optimal.

    And after we go to the top of the trie, the ans will be the total depth of the trie

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6 years ago, # |
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Haha, this problem is also solvable via DP. Let dp[i] — the max number of frogs that can get up to distance i. We calculate dp[i] based on values of dp[i — l]...dp[i — 1], only we delete dp[i] frogs from the dp array starting from index i — l, not to count duplicate frogs. This TLs on test #16, so I simply keep track of the current sum dp[i — l]...dp[i — 1] in a variable, which runs in ~200 ms.
Code: https://codeforces.net/contest/965/submission/46261137

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5 years ago, # |
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Editorial to https://codeforces.net/contest/965/problem/C is one of the most arrogant ones I ever did read on codeforces.

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4 years ago, # |
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Wow, so many solutions to problem D. Here is yet another one :P

I do a DP on a greedy. I break the entire $$$w$$$ length into $$$w/l$$$ segments of length $$$l$$$ each. And for each segment, I try to fill up this segment in the rightmost way, greedily. This can be done by DP.

88428808

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