Dynamic programming., Data Structure & Algorithms

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?

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 T lines, containing the answer for each case. Output each result modulo 1000000007.

1 <= T <= 20
1 <= N <= 40
-1 <= s_i < N

Sample Input:
-1 -1 2
-1 -1 -1
0 1 2 3
1 1
-1 -1 -1 2

Sample Output:

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.
Posted Date: 6/30/2012 6:58:09 PM | Location : United States

Related Discussions:- Dynamic programming., Assignment Help, Ask Question on Dynamic programming., Get Answer, Expert's Help, Dynamic programming. Discussions

Write discussion on Dynamic programming.
Your posts are moderated
Related Questions
Explain Optimal Binary Search Trees One of the principal application of Binary Search Tree is to execute the operation of searching. If probabilities of searching for elements

Write an algorithm to add an element at the end of circular linked list.   Algorithm to Add the Element at the End of Circular Linked List. IINSENDCLL( INFO, LINK, START, A

Here,  m represents the unordered array of elements n  represents number of elements in the array and el  represents the value to be searched in the list Sep 1: [Initialize]

The most common way to insert nodes to a general tree is to first discover the desired parent of the node you desire to insert, and then insert the node to the parent's child list.

How to create multiple queue on single array?

There are three kinds of tree traversals, namely, Postorder , Preorder and Inorder. Preorder traversal: Each of nodes is visited before its children are visited; first the roo

Describe Binary Search Tree (BST)? Make a BST for the given sequence of numbers. 45, 36, 76, 23, 89, 115, 98, 39, 41, 56, 69, 48 Traverse the obtained tree in Preorder, Inord

Normally a potential y satisfies y r = 0 and 0 ³ y w - c vw -y v . Given an integer K³0, define a K-potential to be an array y that satisfies yr = 0 and K ³ y w - c vw -y v

Step 1: Choose a vertex in the graph and make it the source vertex & mark it visited. Step 2: Determine a vertex which is adjacent to the source vertex and begun a new search if

How sparse matrix stored in the memory of a computer?