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.

Algorithm to sort a given list by quick sort method, Q. Write down an algor...

Q. Write down an algorithm to sort a given list by making use of Quick sort method. Describe the behaviour of Quick sort when input given to us is already sorted.

Column major representation, Column Major Representation In memory th...

Column Major Representation In memory the second method of representing two-dimensional array is the column major representation. Under this illustration, the first column of

Efficiency of binary search, Each of the comparison in the binary search de...

Each of the comparison in the binary search decrease the number of possible candidates where the key value can be searched by a factor of 2 as the array is divided into two halves

The game tree, An interesting application or implementation of trees is the...

An interesting application or implementation of trees is the playing of games such as tie-tac-toe, chess, nim, kalam, chess, go etc. We can depict the sequence of possible moves

Graphs, c program to represent a graph as an adjacency multilist form

c program to represent a graph as an adjacency multilist form

Tradeoff between space and time complexity, We might sometimes seek a trade...

We might sometimes seek a tradeoff among space & time complexity. For instance, we may have to select a data structure which requires a lot of storage to reduce the computation tim

Linked list implementation of a queue, The fundamental element of linked li...

The fundamental element of linked list is a "record" structure of at least two fields. The object which holds the data & refers to the next element into the list is called a node .

Various passes of bubble sort, Q. Show the various passes of bubble sort on...

Q. Show the various passes of bubble sort on the unsorted given list 11, 15, 2, 13, 6           Ans: The given data is as follows:- Pass 1:-     11   15   2     13

Prime''z algorithem, Ask question #explain it beriflyMinimum 100 words acce...

Ask question #explain it beriflyMinimum 100 words accepted#

Illumination of wire frame, Illumination of wire frame The colour or sh...

Illumination of wire frame The colour or shade that a surface appears to the human eye depends primarily on three  factors : Colour and strength of incoming illumination

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