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.

Depth first traversal, A depth-first traversal of a tree visits a nodefirst...

A depth-first traversal of a tree visits a nodefirst and then recursively visits the subtrees of that node. Similarly, depth-first traversal of a graph visits a vertex and then rec

Explain the concept of hidden lines and surface removal, Explain the concep...

Explain the concept of hidden lines The problem of hidden lines or surfaces was implicit even in 2-D graphics, but we did not mention it there, because what was intended to be

Explain division method, Explain Division Method Division Method: - In...

Explain Division Method Division Method: - In this method, key K to be mapped into single of the m states in the hash table is divided by m and the remainder of this division

Stack and array, how to implement multiple stack using single dimension arr...

how to implement multiple stack using single dimension array in c

Time complexity, The  total  of  time  needed  by  an algorithm to run to i...

The  total  of  time  needed  by  an algorithm to run to its completion is termed as time complexity. The asymptotic running time of an algorithm is given in terms of functions. Th

Explain internal and external nodes, Explain Internal and External Nodes ...

Explain Internal and External Nodes  To  draw  the  tree's  extension  by  changing  the  empty  subtrees  by  special nodes. The  extra  nodes shown by little squares are know

Algorithm for binary search, Q. Write down the algorithm for binary search....

Q. Write down the algorithm for binary search. Which are the conditions under which sequential search of a list is preferred over the binary search?

Fifo, give any example of page replacement using fifo and use your own refe...

give any example of page replacement using fifo and use your own reference string

Find the optimal control, 1. Use the Weierstrass condition, find the (Stron...

1. Use the Weierstrass condition, find the (Strongly) minimizing curve and the value of J min for the cases where x(1) = 0, x(2) = 3. 2. The system = x 1 + 2u; where

Data communication, #question.explain different types of errors in data tra...

#question.explain different types of errors in data transmission.

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