, 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:-

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

GPA Calculator, I am having trouble declaring a variable and returning a va...

I am having trouble declaring a variable and returning a value from my function.

Program for hangman game problem, Program for Hangman Problem   #inclu...

Program for Hangman Problem   #include   #include   #include   #include   #include   static void playGame();   static void printMistakes(int n);   st

Describe problem with runtime type identification?, Describe problem with R...

Describe problem with Runtime type identification? A: The run time kind identification comes at cost of performance penalty. Compiler maintains class.

Decodethecode, decode smugglers are very smart in day by day

decode smugglers are very smart in day by day

Palindrome, A palindrome is a string that reads the same from both the ends...

A palindrome is a string that reads the same from both the ends. Given a string S convert it to a palindrome by doing character replacement. Your task is to convert S to palindrome

Program for construct a struct - user defined data type, Define a user-defi...

Define a user-defined data type (struct) called Car to represent a car in the context of a car dealership database. Car must have at least the following characteristics: Make Model

C program to compute the factorial, Write a C program to compute the factor...

Write a C program to compute the factorial of  5 i.e 1x2x3x4x5 etc #include stdio.h   void main()   {   char promt;      int factor;   factor = 1*2*3*4*5;   printf("The fac

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

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

Explain the functions strlen ( ), Question 1 Consider you have to find out...

Question 1 Consider you have to find out average marks of 100 students in a class. Write simple program(s) using different iteration statements to accomplish it Question 2 Expla

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