, 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:-

Want wellness software, Project Description: We are looking to have soft...

Project Description: We are looking to have software that we will use to track employee information regarding our wellness program. We would like the system to be able to follow

Can any constructor throw an exception?, Can any constructor throw an excep...

Can any constructor throw an exception? How to handle error while the constructor fails?

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

C, algo of stack using two queue

algo of stack using two queue

Functions and stack frame, Each function has its own stack frame between %f...

Each function has its own stack frame between %fp and %sp. Let Caller calls Callee. Then Caller's %sp becomes callee's %fp, and callee's %sp set to be a new value (a smaller one be

Jewel polishing, Byteland county is very famous for luminous jewels. Lumino...

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

Source code, I hv an assignment to do, I almost done. But i cant find whats...

I hv an assignment to do, I almost done. But i cant find whats wrong- my code is to make a simple calculator using function''s all 4 patterns. I did like this- #include int add

#task1, program for factorial

program for factorial

Program is to define a class as employee, Program is to define a class as e...

Program is to define a class as employee: Write a program to define a class as employee and collect information about them by using classes and object class employee   {

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