, 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:-

Pascal, Binomial coefficients are the numeric factors of the products in a ...

Binomial coefficients are the numeric factors of the products in a power of a binomial such as (x + y)n. For example, (x + y)2 = x2 + 2 x y + y2 has the coefficients 1 2 1. Binomia

Logic families and lsi devices, We have used logic symbols in the past, but...

We have used logic symbols in the past, but not really though about the actual real devices. Semiconductor companies have taken the logic symbols are manufactured them into logic f

Write a code to implement the base and derived class, Study the given hiera...

Study the given hierarchical class diagram and additional information, and answer the questions that follow: Sale Company: string unitPrice: double

Define the increment and decrement operators in c language, Define the Incr...

Define the Increment and Decrement Operators in c language? C offers two special operators -and ++ called decrement and increment operators respectively and these are unary ope

Explain enumerated constants, Enumerated Constants Enumerated constants...

Enumerated Constants Enumerated constants enable the creation of new types and then explain variables of these types so that their values are restricted to a set of possible va

Board coloring, color representation 0,1,2,3,4,5,6,7...

color representation 0,1,2,3,4,5,6,7...

Scope resolution operator, what are the significances of scope resolution o...

what are the significances of scope resolution operator? Illustrate with example

Odd even program, Write a program called OddEven that will prompt the user ...

Write a program called OddEven that will prompt the user for an integer and print/display a message indicating whether it is even or odd. Continue prompting for numbers from the us

How does a union differ from a structure, Problem: (a) (i) What is a...

Problem: (a) (i) What is a structure? (ii) How does a structure differ from an array? (b) Declare a structure, called account, that will contain the following data me

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