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.

State about the simple types - built-in types, State about the Simple types...

State about the Simple types - Built-In Types Values of the carrier set are atomic, that is, they can't be divided into parts. Common illustrations of simple types are inte

Write an algorithm to find outputs number of cars, A company is carrying ou...

A company is carrying out a survey by observing traffic at a road junction. Every time a car, bus or lorry passed by road junction it was noted down. 10 000 vehicles were counted d

High-level and bubble algorithm , 1. Give both a high-level algorithm and a...

1. Give both a high-level algorithm and an implementation (\bubble diagram") of a Turing machine for the language in Exercise 3.8 (b) on page 160. Use the ' notation to show the co

Algorithm, Write an algorithm for compound interest.

Write an algorithm for compound interest.

Merging 4 sorted files containing 50, Merging 4 sorted files having 50, 10,...

Merging 4 sorted files having 50, 10, 25 and 15 records will take time  O (100)

Difference between prism''s and kruskal''s algorithm, Difference among Pris...

Difference among Prism's and Kruskal's Algorithm In Kruskal's algorithm, the set A is a forest. The safe edge added to A is always a least-weight edge in the paragraph that lin

Efficient algorithms.., implementation of fast fourier transforms for non p...

implementation of fast fourier transforms for non power of 2

Applications, Arrays are simple, however reliable to employ in more conditi...

Arrays are simple, however reliable to employ in more condition than you can count. Arrays are utilized in those problems while the number of items to be solved out is fixed. They

What is algorithm, What is Algorithm A finite sequence of steps for a...

What is Algorithm A finite sequence of steps for accomplishing some computational task. An algorithm should Have steps which are simple and definite enough to be done

Give the example of bubble sort algorithm, Give the example of bubble sort ...

Give the example of bubble sort algorithm For example List: - 7 4 5 3 1. 7 and 4 are compared 2. Since 4 3. The content of 7 is now stored in the variable which was h

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