, 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:-

Decodethecode, 6999066263304447777077766622337778 -----> message sent by th...

6999066263304447777077766622337778 -----> message sent by the first smuggler. my name is robert---------> message decoded by the second smuggler. Where ‘0’ denotes the "space". Ex

C Program with android, Hello, I would like to know if you can help in C pr...

Hello, I would like to know if you can help in C programs that work on android.

Project, Project Overview A certain financial institution (bank) wishes to ...

Project Overview A certain financial institution (bank) wishes to promote its new business products/services by conducting road shows in rural areas. Their aim is to encourage peop

Explain brief about class and objects, Question 1 Write a program that acc...

Question 1 Write a program that accepts a 3x3 matrix from the user and finds the transpose of it Question 2 Explain Brief about class and objects. Also describe friend functi

Charity Ball Organizer, Charity Ball Organizer Many charities support good...

Charity Ball Organizer Many charities support good causes, but one of the difficulties each of them has is organizing their fundraising events. After nearly a semester of C progra

Tree, Write algorithm and program for the conversion of a Tree to a Binary ...

Write algorithm and program for the conversion of a Tree to a Binary Tree

Luminous and jewels, Byteland county is very famous for luminous jewels. Lu...

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

Explain syntax rules for writing constructor functions, Syntax rules for wr...

Syntax rules for writing constructor functions Its name must be similar as that of the class to which it belongs. It is declared with no return type (not even void). Ho

When do employ "const" reference arguments in function?, A: 1.      By u...

A: 1.      By using const protects you against programming errors which inadvertently alter data. 2.      By using const allows function to procedure const and non-const actu

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