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.

Explain how two dimensional arrays are represented in memory, Explain how t...

Explain how two dimensional arrays are represented in memory. Representation of two-dimensional arrays in memory:- Let grades be a 2-D array as grades [3][4]. The array will

#title., Ask quapplication of data structure estion #Minimum 100 words acce...

Ask quapplication of data structure estion #Minimum 100 words accepted#

Compare and contrast various sorting techniques, Q. Compare and contrast va...

Q. Compare and contrast various sorting techniques or methods with respect to the memory space and the computing time.

Database design and sql queries, In assignment, you have already started th...

In assignment, you have already started the process of designing a database for the Beauty Salon mini-case (enclosed again below), mainly in the phase of conceptual database design

Method to add an element in circular queue, Q. Let us consider a queue is h...

Q. Let us consider a queue is housed in an array in circular fashion or trend. It is required to add new items to the queue. Write down a method ENQ to achieve this also check whet

Determine about the logic gates, Determine about the logic gates Many e...

Determine about the logic gates Many electronic circuits operate using binary logic gates. Logic gates essentially process signals that represent true or false or equivalent i.

What are the advantages of using assertions, Using Assertions When writ...

Using Assertions When writing code, programmer must state pre- and subtle post conditions for public operations, state class invariants and insert unreachable code assertions a

Describe commonly used asymptotic notations, Q.1 Compare two functions n 2 ...

Q.1 Compare two functions n 2 and 2 n for various values of n. Determine when second becomes larger than first. Q.2 Why do we use asymptotic notation in the study of algorit

Effective way of storing two symmetric matrices, Explain an efficient and e...

Explain an efficient and effective way of storing two symmetric matrices of the same order in the memory. A n-square matrix array will be symmetric if a[j][k]=a[k][j] for all j

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