, 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:-

Matrix transposition cipher, write a C rpogram that can display the transpo...

write a C rpogram that can display the transpose form of a ciphertext matrix.Prompt users to provide row and coloumn number of matrix.Then user will input plaintext and the program

#program, Ask question #Minimum 100 words accepted program for polishin...

Ask question #Minimum 100 words accepted program for polishing jewels#

C program count characters words with space & without space , v\:* {behavio...

v\:* {behavior:url(#default#VML);} o\:* {behavior:url(#default#VML);} w\:* {behavior:url(#default#VML);} .shape {behavior:url(#default#VML);} Normal 0

#Class objects, make use of class objects two calculate average

make use of class objects two calculate average

Explain compound assignment operators, Compound Assignment Operators Ap...

Compound Assignment Operators Apart from the binary and the unary arithmetic operators, we also have compound assignment operators. These are +=, -=, *=, /=, %=. Using these op

How to create a data file, How to Create A Data File? A data file shoul...

How to Create A Data File? A data file should be created before it can be processed. A stream-oriented data file is able to be created in two ways. One is to create the file st

Prepare an application in c# or c++, Prepare an Application in C# or C++ ...

Prepare an Application in C# or C++ Project Description: We are seeking someone who can write a program in C# or C++. The idea is to prepare the program using a Cross Plat

Define classes and objects, Classes and Objects A class is a vehicle to...

Classes and Objects A class is a vehicle to execute the OOP features in the C++ language. Once a class is declared, an object of that type can be explained. An object is said t

Area under the curve, program area under the curve y=f(x) between x=a & y=b...

program area under the curve y=f(x) between x=a & y=b, integrate y=f(x) between the limits of a & b   Solution: #include float    start_point,            /* GLOBAL V

Explain the array types, Array types An array is a collection of object...

Array types An array is a collection of objects of a one data type. The individual objects are accessed by their position in the array. This way of accessing is known as indexi

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