[Solution] The Attack of Queen solution codechef

The Attack of Queen solution codechef – Chef has started developing interest in playing chess, and was learning how the Queen moves.

[Solution] The Attack of Queen solution codechef

Chef has an empty N×NN×N chessboard. He places a Queen at (X,Y)(X,Y) and wonders – What are the number of cells that are under attack by the Queen?

Notes:

  • The top-left cell is (1,1)(1,1), the top-right cell is (1,N)(1,N), the bottom-left cell is (N,1)(N,1) and the bottom-right cell is (N,N)(N,N).
  • The Queen can be moved any number of unoccupied cells in a straight line vertically, horizontally, or diagonally.
  • The cell on which the Queen is present, is not said to be under attack by the Queen.

Input Format

  • The first line contains a single integer TT – the number of test cases. Then the test cases follow.
  • The first and only line of each test case contains three integers NNXX and YY, as described in the problem statement.

Output Format

For each test case, output in a single line, the total number of cells that are under attack by the Queen.

[Solution] The Attack of Queen solution codechef

  • 1T1041≤T≤104
  • 1N1061≤N≤106
  • 1X,YN1≤X,Y≤N

Sample Input 1 

5
1 1 1
3 2 2
3 2 1
2 2 2
150 62 41

Sample Output 1 

0
8
6
3
527

The Attack of Queen solution Explanation

Test case 1: The only cell on the board is (1,1)(1,1). Since Queen stands on this cell, it is not under attack.

Test case 2: The Queen can attack the following cells: {(1,1),(1,2),(1,3),(2,1),(2,3),(3,1),(3,2),(3,3)}{(1,1),(1,2),(1,3),(2,1),(2,3),(3,1),(3,2),(3,3)}.

Test case 3: The Queen can attack the following cells: {(1,1),(1,2),(2,2),(2,3),(3,1),(3,2)}{(1,1),(1,2),(2,2),(2,3),(3,1),(3,2)}.

Test case 4: The Queen can attack the following cells: {(1,1),(1,2),(2,1)}{(1,1),(1,2),(2,1)}.

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