, 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:-

#title.jewel polish., Ask questionByteland county is very famous for lumino...

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

Result system, write a promgram using object oriented peramid

write a promgram using object oriented peramid

Static data meber and const data meber, can we use const data member in sta...

can we use const data member in static. member function with example.

Abstract array - c program, Abstract array - c program: AbstractArray:...

Abstract array - c program: AbstractArray::AbstractArray( int anUpper, int aLower, sizeType aDelta ) {     PRECONDITION( anUpper >= aLower );     lastElementIndex = a

Algorithm and flowcharts, algorithm to find out all the factors of given po...

algorithm to find out all the factors of given positive integers

Diploma in IT, Function fact explain how the process of recursion works in ...

Function fact explain how the process of recursion works in C++.In your answer assume that the function is called to calculate the factorial of 6?

File Input and Output, Given a bool variable isReadable write some statem...

Given a bool variable isReadable write some statements that assign true to isReadable if the file "topsecret" exists and can be read by the program and assigns false to isR

C code, get coding for padovan string

get coding for padovan string

C program for function of copy one string in other string, C Program for FU...

C Program for FUNCTION OF COPY ONE STRING IN OTHER STRING #include stdio.h> #include conio.h> int copy(char a[],char b[]); void main() {           char a[100],b[

#title prime number or not, to find prime numbers upto any number say "n" e...

to find prime numbers upto any number say "n" entered by user

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