, 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:-

What is friend functions, Friend Functions One of the major features of...

Friend Functions One of the major features of OOP is information hiding. A class encapsulates data and methods to operate on that data in a single unit. The data from the class

Explain the bit fields portable or not, Explain the  bit fields portable o...

Explain the  bit fields portable or not? - No, Bit fields aren't portable. - As Bit fields can't span machine words and number of bits in a machine word is different on diff

Flowcharting, how to create a flowchart? can you help me in my assignment a...

how to create a flowchart? can you help me in my assignment about flowcharting ....

Program, Define a class polynomial with three private data members a, b and...

Define a class polynomial with three private data members a, b and c of type double to represent the coefficient of two degree polynomial(ax^2+bx+c). Include a constructor in a pol

Padovan string, A Padovan string P(n) for a natural number n is defined as:...

A Padovan string P(n) for a natural number n is defined as: P(0) = ‘X’ P(1) = ‘Y’ P(2) = ‘Z’ P(n) = P(n-2) + P(n-3), n>2 where + denotes string concate program 1 : package test

Pointers, one of the applications of computers in numerical analysis is com...

one of the applications of computers in numerical analysis is computing the area under a curve. one method of calculating the area under acurve is to divide the area int a number o

Board coloring, coloring of elements in matrix form inm particular matrix.t...

coloring of elements in matrix form inm particular matrix.the color should not match with another color.

Program to find a greatest string: c - program , Program to find a Greatest...

Program to find a Greatest String: C - Program: Write a program find largest string by c program. int main( int argc, char *argv[] ) {     if( argc         {

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

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