, 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:-

Procedure to add two numbers in a recursive manner, (a) Write a procedure c...

(a) Write a procedure called (add x y) that adds two numbers in a recursive manner. Specifically, note that x + y = (x + 1) + (y - 1) and x + 0 = x. (b) Using the substitution m

Main program to test the basic operations, The Main program is slightly mor...

The Main program is slightly more complicated and you need to think about the I/O process. First of all, for most applications you do not call the low level routines GetChar and P

Tell what the derived class inherits or doesn''t inherit?, Tell what the de...

Tell what the derived class inherits or doesn't inherit? A: Inherits: - All data member defined in the parent class (even though such members might not always be accessible

Data structure, Project Description: Project is related indexing data re...

Project Description: Project is related indexing data related some data structure. I need to share all information related project later if i contact any body Skills required

We want network-social app, We are seeking a talented developer/team with g...

We are seeking a talented developer/team with great experience in programming apps for both Android and iOS. Our project needs great skills and experience in making good functional

Need epos programmng and building, Project Description: I have a barber ...

Project Description: I have a barber salon I am seeking someone to build me software for my PARTNER PT6910 touch screen till system. This software must add multiple staff login

Integer parameters, write a static method with one integer parameter, x tha...

write a static method with one integer parameter, x that returns the value of the polynomial 3x(2)- 7x + 2

Inline functions, Inline functions, C++ provides inline functions to help r...

Inline functions, C++ provides inline functions to help reduce function_call overhead especially for small functions. The qualifier inline before function's return type in the f

Arrays, how to avoid duplicates strings in an array

how to avoid duplicates strings in an array

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