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.

Stack making use of the linked list, Q. Implement a stack making use of the...

Q. Implement a stack making use of the linked list. Show the PUSH and POP operations both. A n s . Stack implemantation using linked list # include # include

Queues, Queue is a linear data structure utilized in several applications o...

Queue is a linear data structure utilized in several applications of computer science. Such as people stand in a queue to get a specific service, several processes will wait in a q

Red-black tree after insertion, The above 3 cases are also considered conve...

The above 3 cases are also considered conversely while the parent of Z is to the right of its own parent. All the different kind of cases can be illustrated through an instance. Le

Explain th term input and output- pseudocode, Explain th term input and ou...

Explain th term input and output-  Pseudocode Input and output indicated by the use of terms input number, print total, output total, print "result is" x and so on.

Explain stacks, What are stacks? A stack is a data structure that organ...

What are stacks? A stack is a data structure that organizes data similar to how one organizes a pile of coins. The new coin is always placed on the top and the oldest is on the

State flowchart that take temperature input using pseudocode, Write an algo...

Write an algorithm using pseudocode which takes temperatures input over a 100 day period (once per day) and output the number of days when the temperature was below 20C and the num

Hw7, Handout 15 COMP 264: Introduction to Computer Systems (Section 001) Sp...

Handout 15 COMP 264: Introduction to Computer Systems (Section 001) Spring 2013 R. I. Greenberg Computer Science Department Loyola University Water TowerCampus, Lewis Towers 524 82

Determine about the post conditions assertion, Determine about the Post con...

Determine about the Post conditions assertion A  post condition is an assertion which should be true at completion of an operation. For instance, a post condition of the squ

Analyze an algorithm, In order to analyze an algorithm is to find out the a...

In order to analyze an algorithm is to find out the amount of resources (like time & storage) that are utilized to execute. Mostly algorithms are designed to work along with inputs

What are the dynamic arrays, What are the Dynamic arrays Dynamic arrays...

What are the Dynamic arrays Dynamic arrays are convenient for programmers since they can never be too small-whenever more space is needed in a dynamic array, it can simply be e

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