, 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:-

Functions overloading, Functions Overloading This a capability in which...

Functions Overloading This a capability in which a C++ program can have several functions performing similar tasks on different data types. When an overloaded function is calle

LOOPS, HOW CAN WE EASLY LEARN C++

HOW CAN WE EASLY LEARN C++

Write a program to illustrate array with strings, Write a Program to illust...

Write a Program to illustrate Array with Strings? main() { static char name[]="devdas"; int i; i=0; while(name[i]!='\0') { printf("%c",name[i]); i=i+1; } } In the

Inheritance, example of program to ad two numbers

example of program to ad two numbers

Explain multidimensional arrays, Multidimensional Arrays - Every dimens...

Multidimensional Arrays - Every dimension is specified in separate brackets e.g. int arr[4][3]; This is a two-dimensional array with 4 as row dimension and 3 as

Define generic bitwise operations, Define Generic Bitwise Operations? ...

Define Generic Bitwise Operations? Bitwise operators only work on an incomplete number of types int and char. It turns out there's above one kind of int. In particular there's

Define the recursion function in c, Define the Recursion Function in C? ...

Define the Recursion Function in C? In C, it is potential for the function to call themselves a function is describing 'recursive' if a statement within the body of a function

Define polymorphism?, Define Polymorphism? A: Polymorphism let a client ...

Define Polymorphism? A: Polymorphism let a client to treat distinct objects in the similar way even if they were developed from distinct classes and exhibit different behaviors.

#padovan string in c, #write a program that counts the number of occurances...

#write a program that counts the number of occurances of the string in the n-th padovan string p(n)

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