, 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:-

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

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

Writing a c++ program, how can I write a c++ program that generate all evn ...

how can I write a c++ program that generate all evn numbers less than 1000?

Programming an odds betting website, Programming an odds betting website ...

Programming an odds betting website Project Description: We want someone to program a odds betting website, Require someone with experience and skills! Skills required are

Text Editor, Add a function for saving the text stored in an array to a fil...

Add a function for saving the text stored in an array to a file. Your program must check whether or not the output file already exists, and if it does, your program must ask the us

Padovan string, padovan string program 1 : package test.padovanstring; ...

padovan string program 1 : package test.padovanstring; public class PadovanString {     public int stringOccurrences(int n, String str){        if(n >= 40)     return -

C program to demonstrate pointer to array, C program to demonstrate Pointer...

C program to demonstrate Pointer to array: void p2a(int *); void main() {                 int x=10, *a,**b;                 int arr[5];                 a=&x;//po

C program for sorting, C Program for SORTING # include stdio.h> void...

C Program for SORTING # include stdio.h> void main() {           char a;           int *p;           int i,j,temp;           clrscr();           p=&i;

Luminous jewels, Problem : Luminous Jewels - Polishing Necklace Byteland c...

Problem : Luminous Jewels - Polishing Necklace Byteland county is very famous for luminous jewels. Luminous jewels are used in making beautiful necklaces. A necklace consists of v

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