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   Problem Statement  

 Problem Statement for TaroCards

Problem Statement

    

Cat Taro has N cards. Exactly two integers are written on each card. You are given two int[]s first and second, each with N elements. For each i, the element first[i] represents the first integer on the i-th card, and the element second[i] represents the second integer on the i-th card.

It is known that for each x from 1 to N, inclusive, there is exactly one card with the first integer equal to x. In other words, all elements of first represent a permutation of integers from 1 to N, inclusive. On the other hand, second may contain duplicates, but all elements of second are only between 1 and 10, inclusive.

You are also given an int K. Taro wants to choose some subset of the cards (possibly none or all of them) in such a way that the total number of different integers written on the cards is less than or equal to K. Return the total number of ways to do that.

 

Definition

    
Class:TaroCards
Method:getNumber
Parameters:int[], int[], int
Returns:long
Method signature:long getNumber(int[] first, int[] second, int K)
(be sure your method is public)
    
 

Constraints

-first will contain between 1 and 50 elements, inclusive.
-first and second will contain the same number of elements.
-first will represent a permutation of integers between 1 and N, inclusive, where N is the number of elements in first.
-Each element of second will be between 1 and 10, inclusive.
-K will be between 1 and 2N, inclusive, where N is the number of elements in first.
 

Examples

0)
    
{1, 2}
{2, 3}
2
Returns: 3
In this case, there are four subsets of cards:
  • None of the cards. The number of different integers is 0.
  • Only the first card. The number of different integers is 2.
  • Only the second card. The number of different integers is 2.
  • Both the first and the second card. The number of different integers is 3.
However, the last subset has too many different integers. Thus, the answer is 3.
1)
    
{3, 1, 2}
{1, 1, 1}
3
Returns: 8
2)
    
{4, 2, 1, 3}
{1, 2, 3, 4}
5
Returns: 16
3)
    
{1, 2, 3, 4, 5, 6, 7}
{2, 1, 10, 9, 3, 2, 2}
3
Returns: 17
4)
    
{1}
{2}
1
Returns: 1
5)
    
{6, 20, 1, 11, 19, 14, 2, 8, 15, 21, 9, 10, 4, 16, 12, 17, 13, 22, 7, 18, 3, 5}
{4, 5, 10, 7, 6, 2, 1, 10, 10, 7, 9, 4, 5, 9, 5, 10, 10, 3, 6, 6, 4, 4}
14
Returns: 2239000

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This problem was used for:
       Single Round Match 613 Round 1 - Division II, Level Three