, 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:-

Bulk listing posting for a site like ebay, Project Description: I posted...

Project Description: I posted listings on a site that is like eBay but for video games. I post the similar listing many times daily, but need something that will let me post

C program for exchange first & last character, Normal 0 false ...

Normal 0 false false false EN-US X-NONE X-NONE MicrosoftInternetExplorer4

Displays the lower case and upper case alphabetical letters, Write a progra...

Write a program that displays both the lower case and upper case alphabetical letters using the following Format Lowercase        Uppercase a                        A

Decode the code, Smugglers are becoming very smart day by day. Now they hav...

Smugglers are becoming very smart day by day. Now they have developed a new technique of sending their messages from one smuggler to another. In their new technology, they are send

Summations, How do you write the code for summations

How do you write the code for summations

201 it, overload assignment opertor to assign the data of one object to ant...

overload assignment opertor to assign the data of one object to anthor

Luminous jewel polishing neckiace, Byteland county is very famous for lumin...

Byteland county is very famous for luminous jewels. Luminous jewels are used in making beautiful necklaces. A necklace consists of various luminous jewels of particular colour. Nec

What are the different types of endless loops, What are the different types...

What are the different types of endless loops? An endless loop can be of two types: i.) A loop that is intentionally designed to go round and round until the condition withi

Define the object-oriented terms, Question : (a) Define the following O...

Question : (a) Define the following Object-Oriented terms: (i) Encapsulation (ii) Inheritance (iii) Abstraction (iv) Polymorphism. (b) What are objects in Lingo progra

How do you access the values within an array, How do you access the values ...

How do you access the values within an array? - Arrays comprise a number of elements, which depends on the size you assigned it during variable declaration. - Every element

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