Game of Pooks CodeChef Solution | CodeChef Problem Solution 2022

Game of Pooks CodeChef Solution | CodeChef Problem Solution 2022

We have found a new chess character — pook. It has the qualities of both a rook and a pawn. Specifically, treating the chessboard to be an N×N$N\times N$ grid where (i,j)$(i,j)$ denotes the intersection of the i$i$-th row and the j$j$-th column, a pook placed at square (x,y)$(x,y)$ threatens the following squares:

• (i,y)$(i,y)$ for every 1≤i≤N$1\le i\le N$
• (x,i)$(x,i)$ for every 1≤i≤N$1\le i\le N$
• (x+1,y−1)$(x+1,y-1)$, if x<N$x<N$ and y≥2$y\ge 2$
• (x+1,y+1)$(x+1,y+1)$, if x<N$x<N$ and y<N$y<N$

Find the maximum number of pooks that can be placed on an empty N×N$N\times N$ chessboard such that none of them threaten each other.

Solution Click Below:-  CLICK HERE

Input Format

• The first line of input will contain a single integer T$T$, denoting the number of test cases. Then the test cases follow.

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• Each test case consists of a single line of input, containing a single integer N$N$.

Output Format

For each test case, output in a single line the maximum number of pooks that can be placed on the chessboard such that they don't threaten each other.

Constraints

• 1≤T≤105$1\le T\le {10}^5$
• 1≤N≤109$1\le N\le {10}^9$

Sample Input 1 

3
1
2
3

Sample Output 1 

1
1
2

Explanation

Test case 1$1$: There is a single square, so we have a single pook.

Test case 2$2$: We can only place one pook. No matter where the first is placed, placing a second will lead to one of the two being threatened.

Test case 3$3$: Placing 2$2$ pooks on a 3×3$3\times 3$ grid is easy — for example, place one at (1,2)$(1,2)$ and another at (3,3)$(3,3)$. It can be shown that placing three is not possible.

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