, 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:-

Write a c program to add two complex numbers, #include stdio.h   struct  c...

#include stdio.h   struct  complex   {   float real;   float imag;   };   struct complex complexadd(struct complex,struct  complex);   void main()     {          Date: 26

I need app design team wanted to new check-in app, New App Production compa...

New App Production company is seeking an organized and highly accomplished design team to prepare the first (and potentially more) of my companies' App concepts, intended completel

Pebble merchant problem, There is a pebble merchant. He sells the pebbles, ...

There is a pebble merchant. He sells the pebbles, that are used for shining the floor. His main duty is to take the length of the room’s sides. But he sometimes mistakes doing that

How can one "reopen" std::cin & std::cout in binary mode?, A: It is impleme...

A: It is implementation dependent. Verify with your compiler's documentation. For instance, assume you wish to do binary I/O using std::cin & std::cout. Unluckily there is no st

Virtual constructor, Is it possible to have Virtual Constructor? If yes, ho...

Is it possible to have Virtual Constructor? If yes, how? If not, Why not possible?

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

Draw a picture using line - c program, Draw a picture using line: void...

Draw a picture using line: void main(void) {     int   driver = DETECT,mode;     int   x[10],y[10];     int   x_center = 360, y_center = 180, rad = 100;     int

Loops, how do i print out invalid input?

how do i print out invalid input?

#Class objects, make use of class objects two calculate average

make use of class objects two calculate average

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