 # POOK Editorial

Setter and Editorialist : Yashodhan Agnihotri

1121

None.

# PROBLEM:

Find the maximum number of pooks on an N x N chessboard such that none of them threaten each other. A Pook has the properties of both, a pawn and a rook.

# EXPLANATION:

We will see 4 cases here. The three cases of N = 1,2,3 need to be handled separately while N \geq 4 will follow the answer of the N-Queen Problem. Since we can place atmost N unthreatening rooks on a N x N chessboard, therefore as a Pook has all the properties of Rooks, we would be able to place atmost N pooks as well.
The answer for the N-Queen problem for N greater than 4 is N queens, therefore our answer will also be the same here.

N = 1

Since there is just one square, we can place 1 pook in it.

N = 2

Here, we can place just 1 pook, since all the other three squares will be threatened by it.

N = 3

Here, however you place the pooks, you cannot place more than 2 pooks on the board.

N >= 4

Here, the answer is same as the N-Queen Problem i.e N pooks.

# SOLUTIONS:

Setter's Solution
``````#include<bits/stdc++.h>
using namespace std;

int main() {
int t;
cin >> t;
while (t--) {
int n;
cin >> n;
if (n == 2 || n == 3)
cout << n - 1 << "\n";
else
cout << n << "\n";
}
return 0;
}
``````

For doubts, please leave them in the comment section, I’ll address them.

1 Like

on what position can we put pook, for n=4, i can figure out only 3 position.

1 Like

considering a 4*4 grid (0 based indexing) , these are the following index
(1,0) (3,1) (0,2) (2,3) .

1 Like
``````  n = 3       n = 4        n = 5           n = 6            n = 7             n = 8
2           4            5               6                7                 8

p * *      * p * *     p * * * *      * p * * * *      p * * * * * *      * p * * * * * *
* * p      * * * p     * * p * *      * * * p * *      * * p * * * *      * * * p * * * *
* * *      p * * *     * * * * p      * * * * * p      * * * * p * *      * * * * * p * *
* * p *     * p * * *      p * * * * *      * * * * * * p      * * * * * * * p
* * * p *      * * p * * *      * p * * * * *      p * * * * * * *
* * * * p *      * * * p * * *      * * p * * * * *
* * * * * p *      * * * * p * * *
* * * * * * p *``````
7 Likes

got it