Count the number of ways to construct a sequence of nested spheres
How to get 40 points
First of all, let’s note that the number of ways construct a sphere of the radii of R is equal to the product of the number of lower hemispheres of the radii of R multiplied by the number of upper hemispheres of the radii of R. Let’s call this number S[R].
Now, let’s denote the number of ways to construct a sequence of K nested spheres with the largest sphere having the radii of R by F[K][R]. Let’s take F[0][0] equal to one.
The rules for the recalculation of f[K][R] are straightfowrward: we need to pick a sequence of (K-1) spheres, where the largest sphere has the radii less than R. The number of such sequences (let’s denote it by W[K][R]) is equal to the sum of F[K-1][J] for all J < R. Now we need to add a sphere of the radii R to the end of each of these sequences. Considering that there are S[R] ways to create a sphere of the radii of R, we obtain that F[K][R] = W[K][R]*S[R].
The number of sequences of K nested spheres will clearly be equal to the sum of F[K][J] for all J between 1 and C.
This solution is capable of solving the first two subtasks, but is too slow to solve the last one.
How to get 100 points
The solution’s idea remains the same.
Let’s find a way to calculate the values of F[][] in O(1) time. For achieving this, let’s note that the value of W[K][R] equals to the W[K][R-1] + F[K-1][R-1]. So now, using the old values of W[][], we can calculate the new one in O(1).
Now, since the calculation of every state runs in O(1), we get the total complexity of O(C2), which fits for our problem.
This one is my favorite question in the OCT15 challenge. By some examinations, I knew for a given c, we need to find the sum of product of elements in every subset of size c+1. By googling, I came across a generating function for the solution. I had never coded a polynomial multiplication before. Using a naive n^2 multiplication I was able to solve it. But, instead of finding the result modulo 10^9+7 I found modulo 10^9+9. After getting WA, I tried to come up with another logic and came up with the dynamic programming solution as given above (solving dp by myself gives a lot of pleasure :)). After solving it with dp approach, I tried debugging the first generating function approach and found my mistake. Then I got AC for that.
Thanks to the initial mistake, I solved a DP problem.
Can anybody take a look at my solution please https://www.codechef.com/viewsolution/8430787
I used the same dynamic approach as the OP but I get a wrong answer on one of the test cases.
I suspect it maybe a miscalculation with the modulus.
Wherever you are doing subtraction add mod value to it i.e. 1000000007. Like in a[i+half] = even[i] - twiddle change it to
a[i+half] = even[i] - twiddle + 1000000007.
Sorry i am unable to confirm if it will give AC because i don’t know vectors but i too was getting WA in nearly same test cases and got AC by adding mod value where i was doing subtraction.
@ricola86 While adding currCount to prev(prev+=currCount) , prev can go out of range of int.
So,just take it as unsigned long long and just apply mod operation on it. i.e
@sid9406 Change “long int” to “long long int”
As a long int is a signed integral type that is at least 32 bits, while a long long or long long int is a signed integral type which is at least 64 bits
@sid9406
At various places your code might go out of the range of long int and hence cause overflow. You are required to use long long int instead.
Here is the link to your updated solution. https://www.codechef.com/viewsolution/8532367
Hello,
I am a newbie here and never played with DP or modulus thing before. So i learned about modulus from somewhere and implemented this solution. Its getting WA on some cases. I think there is some problem with my 10^9+7 implementation. Can anyone please figure it out? I would be so thankful
Can anyone tell what was the problem with my solution? Was able to pass few files of 2nd and 3rd subtask.Tried alot to get pass all the files,but i think some problem with modulo operation.Please tell me where was I missing something…here’s my solution.Would be very thankful.
I am getting WA in only one of the test cases. I am really stuck. I have tried almost everything. Somebody please help. Here’s the link to my code… https://www.codechef.com/viewsolution/8534532
