, C/C++ Programming

Assignment Help:
Question 1 / 1
You have an N x N chessboard and you wish to place N kings on it. Each row and column should contain exactly one king, and no two kings should attack each other (two kings attack each other if they are present in squares which share a corner).

The kings in the first K rows of the board have already been placed. You are given the positions of these kings as an array pos[ ]. pos[i] is the column in which the king in the ith row has already been placed. All indices are 0-indexed. In how many ways can the remaining kings be placed?

Input:
The first line contains the number of test cases T. T test cases follow. Each test case contains N and K on the first line, followed by a line having K integers, denoting the array pos[ ] as described above.

Output:
Output the number of ways to place kings in the remaining rows satisfying the above conditions. Output all numbers modulo 1000000007.

Constraints:
1 <= T <= 20
1 <= N <= 16
0 <= K <= N
0 <= pos_i < N
The kings specified in the input will be in different columns and not attack each other.

Sample Input:
5
4 1
2
3 0

5 2
1 3
4 4
1 3 0 2
6 1
2

Sample Output:
1
0
2
1
18

Explanation:
For the first example, there is a king already placed at row 0 and column 2. The king in the second row must belong to column 0. The king in the third row must belong to column 3, and the last king must beong to column 1. Thus there is only 1 valid placement.

For the second example, there is no valid placement.

Related Discussions:-

Explain about the expressions in c language, Explain about the Expressions ...

Explain about the Expressions in c Language? An expression is the combination of constants, variables and operators arranged as per the syntax of the language. Some of the illu

How can i present printing for my class fred?, A: Use operator overloading ...

A: Use operator overloading to present a friend left-shift operator, operator #include class Fred { public: friend std::ostream& operator ... private: int i_; // onl

Add guts to vs 2008 c++ windows service, Add guts to VS 2008 C++ windows se...

Add guts to VS 2008 C++ windows service Project Description: I have a shell windows32 service written in 2008 VS C++. I want the functionality part started. Need someone too

Binary search tree is constructed by repeatedly, Assume that a Binary Searc...

Assume that a Binary Search Tree is constructed by repeatedly inserting exact values in to the tree. Argue that the number of nodes examined in searching for a value in the tree is

Array, how to do an array

how to do an array

Static optimality theorem, Question 1 Describe the following with respect ...

Question 1 Describe the following with respect to pointers in C language- Pointers and Arrays Usage of Pointers in functions Write programs in C to demonstrate the

Program to list the cities and their states, The program will ask the user ...

The program will ask the user to enter: '1' to List the cities(and their state abbrev)  from largest to smallest (by their population) with their population '2'  to List the

Define procedure to return the sum of the odd elements, (a) Define a proced...

(a) Define a procedure (deep-member x e) that takes a list x and an element e and returns #t if the element e is in the list or in any lists that the list x contains. e.g., (dee

Need android app development, Project Description: I am seeking a develo...

Project Description: I am seeking a developer who can start an app from scratch and get it delivered to me as soon as possible. It is a little android based app. A background on

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