, 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:-

Quicksorting in linked lists, How do i write a code in C++ to bubblesort in...

How do i write a code in C++ to bubblesort in linked list

Define name mangling in c++??, A: The procedure of encoding the parameter t...

A: The procedure of encoding the parameter types along with the function/method name into a unique name is called as name mangling. The inverse procedure is called demangling. F

Input and output routines, Data is required to be fed into the program (inp...

Data is required to be fed into the program (input) and sent out of the program (output). Considering the draughtsman using a CAD station, the input is his commands to cause lines/

Implement a binomial tree class, a) Implement a binomial tree class with a ...

a) Implement a binomial tree class with a method that calculates the value of an option passed in to the class. The binomial tree should not rely on specific features of the differ

#titlethe Average Temperature in Paradise.., Writing and compiling a progra...

Writing and compiling a program from a given Use Case definition. Follow the Average Temperature in Paradise

What is a template in c++, Templates permit to create generic functions tha...

Templates permit to create generic functions that admit any data type as parameters and return value without having to overload the function with all the possible data types. Until

Arrays, how to declare multi dimensional array

how to declare multi dimensional array

Experiment with the small test matrix, For this assignment, I've provided a...

For this assignment, I've provided a data file called 'elevation.mat', which contains the elevation data you'll be working with.   Type load elevation.mat to get the varia

Function returning object, F u nction Returning Object: This program ...

F u nction Returning Object: This program is like to the previous program except the function returns object.  The main rule to be remembered is the function returning obj

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