, 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:-

Compute the canny edges, If we take the input image and smooth it with a Ga...

If we take the input image and smooth it with a Gaussian of a significant size before computing the Canny edges does the number of edges change, and do the locations of these edges

Hwid spoofer for windows 7, Project Description: I want a simple program...

Project Description: I want a simple program that will spoof my hardware id. I should be able to prepare the id to spoof to in the program and press "random" button to spoof to

Car rental project, I need a project on car rental system using c programmi...

I need a project on car rental system using c programming only of college level

What are the different types of endless loops, What are the different types...

What are the different types of endless loops? An endless loop can be of two types: i.) A loop that is intentionally designed to go round and round until the condition withi

Pro, i need to do my home work

i need to do my home work

Write a c program to input a floating point number, Step 1 Define the start...

Step 1 Define the start of the program    It should be noted that within C all commands should end in a semi-colon. For most of your programs the definition of a program header as

Decoding, Smugglers are becoming very smart day by day. Now they have devel...

Smugglers are becoming very smart day by day. Now they have developed a new technique of sending their messages from one smuggler to another. In their new technology, they are send

Structure and classes in c++, want to understand the working of structure a...

want to understand the working of structure and classes

Decodethecode, 6999066263304447777077766622337778 -----> message sent by th...

6999066263304447777077766622337778 -----> message sent by the first smuggler. my name is robert---------> message decoded by the second smuggler. Where ‘0’ denotes the "space".

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