, 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:-

Padovan String, A Padovan string P(n) for a natural number n is defined as:...

A Padovan string P(n) for a natural number n is defined as: P(0) = ‘X’ P(1) = ‘Y’ P(2) = ‘Z’ P(n) = P(n-2) + P(n-3), n>2 where + denotes string concatenation. For a string of t

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

I want packet capture analysis, I want Packet capture analysis Project D...

I want Packet capture analysis Project Description: Need assistance in debugging some packet capture Skills required is C Programming

Write procedure that compute recursive method, A function f is defined by t...

A function f is defined by the rule that f(n) = n if 0≤n≤3 and f(n) = f(n - 1) + 2f(n - 2) + 3f(n - 3) if n> 3. (a) Write a procedure that computes f by means of a recursive pro

Write a program to sort an array of strings, Write a program to sort an arr...

Write a program to sort an array of strings. Use new and delete operators. Write a program to find the factorial of a number using recursion. If we do not accept the number

Star, how can i print any english work using star .?

how can i print any english work using star .?

Padovan string, A Padovan string P(n) for a natural number n is defined as:...

A Padovan string P(n) for a natural number n is defined as: P(0) = ‘X’ P(1) = ‘Y’ P(2) = ‘Z’ P(n) = P(n-2) + P(n-3), n>2 where + denotes string concatenation. For a string of t

Explain bit-wise operators, Bit-wise Operators Some applications requir...

Bit-wise Operators Some applications require operations to be done on dissimilar bits of a byte separately. Bit-wise operators offer a facility to do just that. There are vario

Program for greatest common divisor – c++ program, Greatest Common Divisor ...

Greatest Common Divisor (GCD) - The greatest common divisor (GCD) of two integers is the largest integer that will evenly divide both integers. The GCD algorithm involves intege

Beti, how is a beti a beti

how is a beti a beti

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