, 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 static class members, Static Class Members As we already know a...

Static Class Members As we already know all the objects of the class have dissimilar data members but invoke the similar member functions. Though, there is an exception to this

Write a program that reads a line of characters, Write a program that reads...

Write a program that reads a line of characters from the user and displays that entire line after converting any uppercase characters to lowercase also change any lowercase charact

Write a function that computes the total interest charged, You are going to...

You are going to write a function that computes the total interest charged on a credit card before it is paid off. List all the inputs the function will need.

Make qtav videoplayer simple integrateable for application, Make QtAV Video...

Make QtAV Videoplayer simple integrateable for Qt Applications Project Description: I'm preparing an application for Windows and Mac using QtCreator. I want a videoplayer

Write code to implement constructor, Study the following  class diagram, ad...

Study the following  class diagram, additional information  and answer  the  questions that follow: MovieTicket movieName: string TicketPrice: doub

write a scheme procedure to evaluate expression, (a) Write a Scheme proced...

(a) Write a Scheme procedure to evaluate the expression: 7/6+2*5+(3*2+6*7)*4. (b) Write a Scheme procedure to evaluate the expression: 2*(-1+(-3+4*2-7)*3/(3*2)).

Palindrome, A palindrome is a string that reads the same from both the ends...

A palindrome is a string that reads the same from both the ends. Given a string S convert it to a palindrome by doing character replacement. Your task is to convert S to palindrome

Boardcoloring, how to fill the blank spaces in the board of 4*4 matrix with...

how to fill the blank spaces in the board of 4*4 matrix with the minimum of 4 colors and the condition is the adjacent element should not have the same colour

Decoding, how to decode a number from mobile keypad

how to decode a number from mobile keypad

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