, 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:-

Program to Find the Factorial of a Given Number, Program1: Write a progr...

Program1: Write a program to find the factorial of a given number. The input is user given. Final output is printed out on to the screen. Program2: Write a program to gene

Polindrome, A palindrome is a string that reads the same from both the ends...

A palindrome is a string that reads the same from both the ends. Given a string S convert it to a palindrome by doing character replacement. Your task is to convert S to palindrome

Need help, how to make basics strong and best logic skills what are the bes...

how to make basics strong and best logic skills what are the best way to be a expert programmer ? what counts a lot knowledge or practice?

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

Programming Assignment 4, For this program, you are going to modify your pr...

For this program, you are going to modify your previous program (program 3) so that it will now have a menu to see if the user wants to read the input from a file or interactively.

C programming language, write an algorithm that reads a postive integer n a...

write an algorithm that reads a postive integer n and then finds and prints the sum of all integers between 1 and n (inclusive) that are disvisible by 7. please write this using c

Described the order that objects in an array is destructed?, Described the ...

Described the order that objects in an array is destructed?

Program, Byteland county is very famous for luminous jewels. Luminous jewel...

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

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