### C. The Busiest City

Author: Suhendry Effendy

Let W(x) be the set of cities which are direct neighbours of city x. To determine the business of city x, for each city w ∈ W(x), we should count how many cities are there which will visit city w in its path to city x; let this multiset of counts be CW(x). Imagine city x as the root of the tree, then CW(x) corresponds to a multiset containing the size of each subtree w ∈ W(x).

Once we have CW(x), calculating the business of city x is easy. We only need to sum all products from multiplying two different members of CW(x), i.e. those pairs of cities will visit city x in their path. Be careful with duplicates though.

The challenge is how to calculate CW(x) for all city x ∈ V. One naive way is by computing CW(x) independently for each x ∈ V using any traversal algorithm. However, this approach will surely get TLE as the size of the tree is quite large, i.e. N <= 20,000. An O(N2) won’t do.

When we compute CW(x) for a particular city x using traversal algorithm (x as the root), we also partially compute CW(y) for all y ∈ V – {x} except for y’s parent. However, the size of y’s parent subtree can be computed easily, i.e. any cities which are not in y’s child should be in y’s parent. Therefore, we can compute CW(x) for all x ∈ V in one go.

This approach has O(N) time complexity.

### 12 Responses to “ACM-ICPC 2013 Jakarta – Problems and Analysis”

1. are you sure there isn’t mod operation ?

and this : j = j + 1, why it isn’t j = j-1 ?

• Ah, you’re right, it should be j =j – 1 (updated).

MOD operation is not needed, What we really need is whether a two substrings have a same hash value or not, not the hash value itself. There are only addition and multiplication operators, so overflowing the result doesn’t matter.

2. ^that comment above is for pasti pas

3. Halo Mr. Suhendry.
Saya ingin sekali bisa berkompetisi di ACM ICPC. Saya Mahasiswa tingkat 2 di salah satu perguruan tinggi di bandung. Tapi skill koding saya tidak terlalu bagus. algoritma sorting saja masih bingung. Gimana ya kiat nya untuk belajar algoritma yg baik dan benar agar bisa nanti suatu saat ke ACM ICPC?

4. How to determine which prime number should be used? I tried some prime numbers and the result is not as expected.

• (Problem F). Just use large prime number (larger is better, its chance to collide is smaller). I used 1000003 and it’s fine.

• I have implemented it and submitted on Live Archive, but got WA 😀
Is there something wrong with my implementation? Could you please check it? http://pastebin.com/ECJX9yEa

• I didn’t read your code, but it failed the first sample input: PASTIPAS.

• Yes and it works if I do MOD operation, but still WA on Live Archive. Does your solution with above algorithm still work on LA? Maybe you/others have added more test cases to break that hash function? Or my implementation wrong?

• I’m the one who send the data to LA and I’m pretty sure LA’s admin was quite busy to do any changes on the dataset.

BTW, I’ve just noticed an error in F’s pseudocode. There is one line which is wrong. Try to figure that out! 🙂

hint: pay attention to the rolling hash (when you do the multiplication with prime number); you might want to check other resources on rolling hash.

5. ^ problem F Pasti Pas!

6. Problem H can be solved by Dynamic Programming,here I find two states,one is index of the current question,another is wrong answers used/left so far, and then minimize the answer. But this solution does not work,though sample test case gives correct output. I saw another boolean state in some accepted codes in HUST, which tries both minimizing and maximizing. Can you please explain why another state is needed here?