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Competition Arena > AlienAndSetDiv1
SRM 605 · 2013-12-22 · by Witaliy · Dynamic Programming
Class Name: AlienAndSetDiv1
Return Type: int
Method Name: getNumber
Arg Types: (int, int)
Problem Statement

Problem Statement

Alien Fred wants to destroy the Earth. But before he does that, he wants to solve the following problem.

He has the set {1, 2, 3, ..., 2N}. He wants to split this set into two new sets A and B. The following conditions must all be satisfied:

  • Each element of the original set must belong to exactly one of the sets A and B.
  • The two new sets must have the same size. (I.e., each of them must contain exactly N numbers.)
  • For each i from 1 to N, inclusive: Let A[i] be the i-th smallest element of A, and let B[i] be the i-th smallest element of B. The difference |A[i] - B[i]| must be greater than or equal to K.

You are given the two ints N and K. Let X be the total number of ways in which Fred can choose the sets A and B. Return the value (X modulo 1,000,000,007).

Constraints

  • N will be between 1 and 50, inclusive.
  • K will be between 1 and 10, inclusive.
Examples
0)
2
2
Returns: 2

The initial set is {1, 2, 3, 4}. The following 6 pairs of subsets are possible in this case: A={1, 2} and B={3, 4} A={1, 3} and B={2, 4} A={1, 4} and B={2, 3} A={2, 3} and B={1, 4} A={2, 4} and B={1, 3} A={3, 4} and B={1, 2} The first option and the last option are both valid. The other 4 options are invalid. Note that order of the two sets matters: the option A={1,2} and B={3,4} differs from the option A={3,4} and B={1,2}.

1)
3
1
Returns: 20
2)
4
2
Returns: 14
3)
10
7
Returns: 40
4)
10
1
Returns: 184756

Submissions are judged against all 53 archived test cases, of which 5 are shown here. Case numbers match the judge’s.

Coding Area

Language: C++17 · define a public class AlienAndSetDiv1 with a public method int getNumber(int N, int K) · 53 test cases · 2 s / 256 MB per case

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