### maroonrk's blog

By maroonrk, history, 3 years ago,

We will hold AtCoder Regular Contest 123.

The point values will be 300-400-600-700-700-1000.

We are looking forward to your participation!

• +122

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 » 3 years ago, # |   0 Hope for a good contest!
 » 3 years ago, # |   +2 Ah, It's too hard! :(
 » 3 years ago, # |   -7 For the first time I solve three problems in ARC.I'm so happy :)
•  » » 3 years ago, # ^ | ← Rev. 2 →   0 How did yo solve it? Can you explain your idea?
•  » » » 3 years ago, # ^ |   0 I think my solution is not so good.You can read the official editorial now.
•  » » 3 years ago, # ^ |   0 How did you solve $C$? Please tell.
 » 3 years ago, # |   +10
 » 3 years ago, # |   +1 How to solve C?
•  » » 3 years ago, # ^ |   +9 Indeed how to solve $C$. Greedy algorithms like taking largest possible number fail. I felt it was kind of similar to yesterday's A
•  » » 3 years ago, # ^ |   +10 Digit dp-esque dp worked for me
•  » » » 3 years ago, # ^ |   0 colud you elaborate ?
•  » » » » 3 years ago, # ^ |   +14 First, use the fact that the answer should be maximum 10 (or even lower couldn't bother to prove a tighter bound), and then we should think about how each of $a_i$ contributes to each digit of n. A length k number will contribute k digits of n from the first digit to the kth digit once, so instead of figuring out what the individual $a_i$ could be, we could shift our focus to how many numbers focus on a specific digit of n. Let $b_i$ denote the number of $a_i$ that contributes to the ith lowest digit. Then, it should be clear that $b_i$ is non_increasing similar to a cumulative frequency. Now, we just want to know if it is possible to create n from a sequence of $b_i$ that is where digit dp comes in. The first parameter of the dp is the current position starting from the lowest digit, and the second is $b_i$ at that position and finally, the last parameter is how much we carried over from the last digit.
•  » » » » » 3 years ago, # ^ |   0 Amazing use of digit dp!
•  » » » » » 3 years ago, # ^ |   0 I didn't understand why you use array f in your solution you did not update array f.
•  » » » » » » 3 years ago, # ^ |   +1 I mean I did use the array to store the dp results in the line int &res = f[pos][choice][up]? Next time when you comment please read the code carefully and then comment.
•  » » 3 years ago, # ^ |   0 dp digit
•  » » » 3 years ago, # ^ |   +12 I have a greedy solution, but I can't prove it :https://atcoder.jp/contests/arc123/submissions/24372393
•  » » » 3 years ago, # ^ |   0 How did you learn digit DP? I have tried learning it a couple of times already but have never been able to understand it. What kind of prerequisite/background does one need for really understanding it? I currently can only solve classic DP problems.
•  » » » » 3 years ago, # ^ |   -8 I had to learn after I couldn't solve this question, yet I couldn't solve C
•  » » » » 3 years ago, # ^ |   +1 I learned it from this blog post Link:. The explanation is great and also has a handful of problems which you can solve to practice digit dp.
•  » » 3 years ago, # ^ | ← Rev. 3 →   0 for a given k can we do it? if we can answer this then its easy just do k++ until we get one. It will never go too far. Now lets try to answer the first part that for a given k can we do it? Try to think of a dp state. run a loop from right to left digits one by one in n. ( i=1 to len(n)) i=1 corresponding to the rightmost digit.we will pass three variables after every iteration i. lowest and highest carry, and mx_k that is the maximum no. of i-1 digit numbers possible up to this point. and lowest and highest carry should correspond to mx_k.tough to explain the mx_k part. Give a good read and think you will get what I meant to say.my solution
•  » » » 3 years ago, # ^ |   0 lovely explanation, thanks!!
•  » » 3 years ago, # ^ | ← Rev. 2 →   +16 Another solution with dfs: The restriction that no digit can be 0 is troublesome, so I considered to clear out this. We minus n with numbers like 111111, 1111 first, and then the digits can be 0,1,2, which is a greedy problem similar to 1530A. Thus it can be proved that the answer is not greater than 5, and we are able to solve it by dfs. For each number, we only need to fix its length, and minus n with 11..1 with the same length. In the end check whether n (after minus) can be constructed by numbers which digits are 0 or 1 or 2. With a little amount of optimization, the solution was accepted.
•  » » » 3 years ago, # ^ |   +8
•  » » » 3 years ago, # ^ |   0 Another implement https://atcoder.jp/contests/arc123/submissions/24377005
 » 3 years ago, # |   +3 how to solve D? there's no editorial for it
•  » » 3 years ago, # ^ | ← Rev. 3 →   +5 If $a_i > a_{i+1}$, it's optimal to choose $b_i = b_{i+1}$, else it's optimal to choose $c_i = c_{i+1}$. Then, the $b_i$ and the $c_i$ can be uniquely determined for a fixed $b_1$ and they have the form $\mid b_1 - k \mid$ ($k$ is different for each $b_i$ and $c_i$). The optimal $b_1$ is the median of the $2n$ values of $k$.
•  » » 3 years ago, # ^ | ← Rev. 2 →   +10 ternary search on the value of $B_1$, knowing that $B_i=B_{i-1}+max(A_i-A_{i-1},0)$ and C as the complement of B
•  » » » 3 years ago, # ^ |   0 Can you share your submission? My ternary search fails for some reason. Submission
•  » » » » 3 years ago, # ^ |   0
•  » » » » 3 years ago, # ^ |   0 I think you make an overflow in Calc, sum can be up to 1e15*2e5 which is to big
•  » » » » » 3 years ago, # ^ | ← Rev. 2 →   +5 Thanks. The actual bug was that minimum sum can be over 1e18. So I have to take initial value as LLONG_MAX. Also as you pointed out in the ternary search, 1e15 will overflow. So taking low as -1e13 and high as 1e13 now worked for me. Even 1e12 is bad.
•  » » 3 years ago, # ^ |   +19 It's the first editorial in E. Seem like the author put it in the wrong place.
•  » » 3 years ago, # ^ | ← Rev. 3 →   0 One of the (almost) middle elements can be 0After fix we do simple greedy to left and rightarc123/submissions/24365978
 » 3 years ago, # |   +58 Err......Starting from C, the problems are too hard for me:(I have to say, contests in AtCoder are becoming more and more challanging. Is that because the problem setters are stronger and stronger or I'm weaker and weaker?
•  » » 3 years ago, # ^ |   0 I think AtCoder is turning harder and harder.
•  » » 3 years ago, # ^ |   +30 All the latest ARCs are mostly hard, you also need to get used to the ARC problems, on my first ARCs I always had a bad performance and the problems seem quite difficult, however after some contests, you will find the problems more accessible (excluding all F's, and some E's, and the other problems are still hard, but at least you can elaborate more on how to solve them). They are really fun and you can learn and enjoy a lot. I am really grateful to all atcoder writers, coordinators, and staff, the contests are great.
 » 3 years ago, # |   +8 Why number of contestant is so small than number of contestant at any begginer contest !!
 » 3 years ago, # |   +31 The approach of problem D is similar with 1406D - Three Sequences, 1442A - Extreme Subtraction.
 » 3 years ago, # |   0 How large could the answer be for problem D? I thought the answer could go up to $10^{18}$ which was a terrible mistake as I got 7 WA because of it and changing the limit to LLONG_MAX just solved the issue.
 » 3 years ago, # | ← Rev. 5 →   +1 For A the approach I followed is,Let mean of consecutive differences in the array be dd;So I iterated on differences from (dd — epsilon) to (dd + epsilon) (epsilon can be anything I considered 2) and checked all possible arrays for a particular difference and took the array with minimum operations. It got accepted but I cannot prove it. Can anyone help me with the proof?Here's my submission Task AThanks in advance :)
 » 3 years ago, # |   +54 SpoilerARC likes floor_sum
•  » » 3 years ago, # ^ |   +43 Spoilerwhile I hate :(
 » 3 years ago, # |   0 How to solve B?
•  » » 3 years ago, # ^ | ← Rev. 2 →   0 First sort all the three input arrays(A,B,C) and then count for valid triplets such that the upper bound of first element from the first array A uniquely exists in second array B and upper bound of that element from second array B uniquely exists in third array C. Codesort( a.begin(), a.end() ); sort( b.begin(), b.end() ); sort( c.begin(), c.end() ); int count = 0; for(int i = 0; i < n; i++){ auto itr1 = upper_bound( b.begin(), b.end(), a[i] ); auto itr2 = upper_bound( c.begin(), c.end(), *itr1 ); if ( itr1 == b.end() || itr2 == c.end() ){ break; } else{ count += 1; b.erase(itr1); c.erase(itr2); } } cout << count << "\n"; 
•  » » » 3 years ago, # ^ | ← Rev. 2 →   0 thanks nice explanation :)
•  » » » » 3 years ago, # ^ | ← Rev. 4 →   0 It's surely TLE.How can you expect erase function to work in $log(n)$ complexity. I used ordered set to erase the elements whose complexity is $log(n)$ unlike vectors. code... #include #include #include using namespace __gnu_pbds; using namespace std; #define ordered_multiset tree, rb_tree_tag,tree_order_statistics_node_update> #define ordered_set tree, rb_tree_tag,tree_order_statistics_node_update> #define int long long int void Malena(){ int n,x;cin>>n; ordered_multiset os,os1,os2; for(int i=0;i>x,os.insert(x); } for(int i=0;i>x,os1.insert(x); } for(int i=0;i>x,os2.insert(x); } auto Upper_Bound1=[&](int element)->int{ int pos=os1.order_of_key(element+1); if(pos==os1.size()) return -1; else{ return *(os1.find_by_order(pos)); } }; auto Upper_Bound2=[&](int element)->int{ int pos=os2.order_of_key(element+1); if(pos==os2.size()) return -1; else{ return *(os2.find_by_order(pos)); } }; int cnt=0; for(auto ele:os){ int a=Upper_Bound1(ele); int b=Upper_Bound2(a); if(a!=-1 and b!=-1){ cnt++; os1.erase(os1.find_by_order(os1.order_of_key(a))); os2.erase(os2.find_by_order(os2.order_of_key(b))); } } cout<>t; while(t--){ Malena(); } return 0; } 
•  » » » » » 3 years ago, # ^ | ← Rev. 2 →   0 I mean all self-balancing binary search trees, such as the std::(multi)set (red-black tree) or avl trees, allow deletion in $O(log(n))$ complexity due to its self balancing nature. For this specific problem, I used std::multiset which worked under 150ms.
 » 3 years ago, # |   0 Thanks a lot for a detailed editorial like this.
 » 3 years ago, # |   0 Will you provide the code for F?
 » 3 years ago, # | ← Rev. 2 →   0 In Problem C Can Anyone Explain A number can be written as the sum of K good numbers if and only if it can be written as the sum of the following: An integer between K and 3K; The sum of at most K good numbers, multiplied by 10. The above statement in Editorial. It would be a Great Help