, 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:-

I need cryengine sandbox speedometer and tachometer, I need Cryengine Sandb...

I need Cryengine Sandbox Speedometer and Tachometer We want to get working Tachometer and Speedometer for a car in latest Cryengine Sandbox. You will find how to make it usin

Explain pros and cons of cpp as a programming language, Write a 3-4 page pa...

Write a 3-4 page paper (350 words per page) in APA format detailing the development and use of C++ in academia and in industry. Explain the pros and cons of C++ as a programming la

Working of ordered linked list, Working Ordered linked list: • Eachint...

Working Ordered linked list: • Eachinteger in the queue is stored inside of a QueueItem. The QueueItem contains the integer, and a pointer to the next item in the queue. Fo

Program is to reverse the names stored in an array pointer, Program is to r...

Program is to reverse the names stored in an array pointer: Program is to reverse the 6 names stored in an array pointer as name[] void main()   {  clrscr();  char

Fraction coding, Create a program that asks the user for two integers which...

Create a program that asks the user for two integers which represent the numerator and denominator parts of fraction. Print out a simplification of the fraction. Example: Enter th

Battleship game, Create a program to print a battleship grid to the console...

Create a program to print a battleship grid to the console and mark squares as destroyed

Write a program that predicts users age, Write a program that predicts user...

Write a program that predicts users age: Write a program that predicts users' age (0-128 years old) with at most 7 questions. The game starts with asking the user whether he/s

C program to change feet and inches into meter, Aim: To implement a progra...

Aim: To implement a program to convert distance given in feet and inches into meters and centimeters and vice versa. Code:                         class mcm; class

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