Dynamic programming., Data Structure & Algorithms

Assignment Help:
Count Scorecards(30 points)

In a tournament, N players play against each other exactly once. Each game results in either of the player winning. There are no ties. You have given a scorecard containing the scores of each player at the end of the tournament. The score of a player is the total number of games the player won in the tournament. However, the scores of some players might have been erased from the scorecard. How many possible scorecards are consistent with the input scorecard?

Input:
The first line contains the number of cases T. T cases follow. Each case contains the number N on the first line followed by N numbers on the second line. The ith number denotes s_i, the score of the ith player. If the score of the ith player has been erased, it is represented by -1.

Output:
Output T lines, containing the answer for each case. Output each result modulo 1000000007.

Constraints:
1 <= T <= 20
1 <= N <= 40
-1 <= s_i < N

Sample Input:
5
3
-1 -1 2
3
-1 -1 -1
4
0 1 2 3
2
1 1
4
-1 -1 -1 2

Sample Output:
2
7
1
0
12


Explanation:
For the first case, there are 2 scorecards possible: {0,1,2} or {1,0,2}.
For the second case, the valid scorecards are {1,1,1}, {0,1,2}, {0,2,1}, {1,0,2}, {1,2,0}, {2,0,1}, {2,1,0}.
For the third case, the only valid scorecard is {0,1,2,3}.
For the fourth case, there is no valid scorecard. It is not possible for both players to have score 1.

Related Discussions:- Dynamic programming.

Unification algorithm, i want to write code for unification algorithm with ...

i want to write code for unification algorithm with for pattern matching between two expression with out representing an expression as alist

What are the structures used in file-system implementation, What are the st...

What are the structures used in file-system implementation? Several on-disk and in-memory structures are used to execute a file system a. On-disk structure include P

Array, extra key inserted at end of array is called

extra key inserted at end of array is called

Difference in grounded header and circular header Link List, Q. State the d...

Q. State the difference between a grounded header link list and a circular header link list?     Ans: A header linked list is a linked list which all the time c

Define dynamic programming, Define Dynamic Programming  Dynamic  progra...

Define Dynamic Programming  Dynamic  programming  is  a  method  for  solving  problems  with  overlapping  problems.  Typically, these sub problems arise from a recurrence rel

Techniques of representing polynomials using arrays, Q. Explain any three m...

Q. Explain any three methods or techniques of representing polynomials using arrays. Write which method is most efficient or effective for representing the following polynomials.

Singly linked list , The two pointers per number of a doubly linked list pr...

The two pointers per number of a doubly linked list prepare programming quite easy. Singly linked lists as like the lean sisters of doubly linked lists. We need SItem to consider t

Define chaining process of hashing, Chaining In this method, instead of...

Chaining In this method, instead of hashing function value as location we use it as an index into an array of pointers. Every pointer access a chain that holds the element havi

Create a binary tree , Create a class "box" that will contain a random inte...

Create a class "box" that will contain a random integer value v such that O

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd