, 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 comments in c++, Comments Comments are integral part of every p...

Comments Comments are integral part of every program . Comments help in coding, debugging and maintaining a program . The compiler ignores them. They should be used liberally i

Area under curve, Write a program to find the area under the curve y = f(x)...

Write a program to find the area under the curve y = f(x) between x = a and x = b, integrate y = f(x) between the limits of a and b. The area under a curve between two points can b

Develop a telephone billing system, Project Description: My project is a...

Project Description: My project is about telephone billing system. This project was my project in my college life. The project is quite easy, i needed C++ programming language..

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

Arrays, what is an array?

what is an array?

Board colouring, in this problem you are given a board in which some of the...

in this problem you are given a board in which some of the elements are placed..each element represent ancolor.fill the other elements in the board such that none of the adjacent e

Expression and their types in cpp, E x p r e s sion and their types: ...

E x p r e s sion and their types: An expression will be in form of mathematical expression with C++ syntax embedded with it. Expressions are of following types which m

Program is to find the maximum from two numbers, Program is to find the max...

Program is to find the maximum from two numbers: Program is to find the maximum from two numbers entered by the user having pointer variable as parameter void main()   {

Can inline functions contain a recursion?, A: No. Syntax wise it is permitt...

A: No. Syntax wise it is permitted. But then the function is no longer Inline. Since the compiler will never know how deep the recursion is at compilation time.

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