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.

Postfix expression algorithm, Write an algorithm to calculate a postfix exp...

Write an algorithm to calculate a postfix expression.  Execute your algorithm using the given postfix expression as your input : a b + c d +*f ↑ . T o evaluate a postfix expr

Define graph, A graph is a mathematical structure giving of a set of vertex...

A graph is a mathematical structure giving of a set of vertexes (v1, v2, v3) and a group of edges (e1, e2, e3). An edge is a set of vertexes. The two vertexes are named the edge en

Define the external path length, Define the External Path Length The Ex...

Define the External Path Length The External Path Length E of an extended binary tree is explained as the sum of the lengths of the paths - taken over all external nodes- from

All pairs shortest paths, N = number of rows of the graph D[i[j] = C[i][...

N = number of rows of the graph D[i[j] = C[i][j] For k from 1 to n Do for i = 1 to n Do for j = 1 to n D[i[j]= minimum( d ij (k-1) ,d ik (k-1) +d kj (k-1)

Draw the process flow diagram, Draw the process flow diagram: Anand   ...

Draw the process flow diagram: Anand   Dairy (AD) sources 150,000 litres of milk daily from large number of local villagers .The milk is collected from 4:00 AM to 6:00 am and

Definitions of graph, A graph G might be defined as a finite set V of verti...

A graph G might be defined as a finite set V of vertices & a set E of edges (pair of connected vertices). The notation utilized is as follows: Graph G = (V, E) Consider the g

Algorithm for the selection sort, Q. Give the algorithm for the selection s...

Q. Give the algorithm for the selection sort. Describe the behaviours of selection sort when the input given is already sorted.

Indexed sequential files, Indexed Sequential Files An index is inserted...

Indexed Sequential Files An index is inserted to the sequential file to provide random access. An overflow area required to be maintained to permit insertion in sequence. I

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

Linear node is given by means of pointer, A linear collection of data eleme...

A linear collection of data elements where the linear node is given by means of pointer is known as Linked list

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