, 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:-

Explain the class invariant, Explain the class invariant. - It's a cond...

Explain the class invariant. - It's a condition that ensures correct working of a class and defines all the valid states for an object. - When an object is created class inv

Library functions, is getchar() is a C++ library function?

is getchar() is a C++ library function?

Homework, 5 questions. plus i will provide the "vector.h" for the questions...

5 questions. plus i will provide the "vector.h" for the questions that needs it

Minimization and karnaugh maps, There are formal ways of reducing Boolean e...

There are formal ways of reducing Boolean expressions in order to minimize the logic circuit. The two elementary ways of minimization are using Boolean expressions/De Morgan Theore

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

Identifier and constant, What are  Id e n t i f ie rs a n d C o...

What are  Id e n t i f ie rs a n d C o n s t a n ts in C++? Id e n t i f ie r a n d C o n s t a n t : I d e n t i f ie r

Programming, I have a C++ programming assignment due on 8th January. As I a...

I have a C++ programming assignment due on 8th January. As I am out of country and cannot complete it, I would like to know how much fees would you charge to complete the assignmen

What is the best fit algorithm, The Best fit algorithm: The best fit metho...

The Best fit algorithm: The best fit method occurs the smallest free block whose size is greater than or equivalent to n. An algorithm to get such a block by traversing the whole

Program to print a series, Write a program called Series that will print/di...

Write a program called Series that will print/display a series of numbers starting with 1 and ending with the last number that is less than 30. The series should include only odd n

C program for removing specified charecter , #include stdio.h> #include ...

#include stdio.h> #include conio.h> #include string.h>   void del(char[],char *); main() {           char str[30],ch,*pp;           clrscr();           p

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