Package g3501_3600.s3537_fill_a_special_grid

Class Solution

  • All Implemented Interfaces:
    
public final class Solution

    3537 - Fill a Special Grid.

    Medium

    You are given a non-negative integer n representing a <code>2<sup>n</sup> x 2<sup>n</sup></code> grid. You must fill the grid with integers from 0 to <code>2<sup>2n</sup> - 1</code> to make it special. A grid is special if it satisfies all the following conditions:

    • All numbers in the top-right quadrant are smaller than those in the bottom-right quadrant.

    • All numbers in the bottom-right quadrant are smaller than those in the bottom-left quadrant.

    • All numbers in the bottom-left quadrant are smaller than those in the top-left quadrant.

    • Each of its quadrants is also a special grid.

    Return the special <code>2<sup>n</sup> x 2<sup>n</sup></code> grid.

    Note: Any 1x1 grid is special.

    Example 1:

    Input: n = 0

    Output: [0]

    Explanation:

    The only number that can be placed is 0, and there is only one possible position in the grid.

    Example 2:

    Input: n = 1

    Output: [3,0,2,1]

    Explanation:

    The numbers in each quadrant are:

    • Top-right: 0

    • Bottom-right: 1

    • Bottom-left: 2

    • Top-left: 3

    Since 0 &lt; 1 &lt; 2 &lt; 3, this satisfies the given constraints.

    Example 3:

    Input: n = 2

    Output: [15,12,3,0,14,13,2,1,11,8,7,4,10,9,6,5]

    Explanation:

    The numbers in each quadrant are:

    • Top-right: 3, 0, 2, 1

    • Bottom-right: 7, 4, 6, 5

    • Bottom-left: 11, 8, 10, 9

    • Top-left: 15, 12, 14, 13

    • max(3, 0, 2, 1) &lt; min(7, 4, 6, 5)

    • max(7, 4, 6, 5) &lt; min(11, 8, 10, 9)

    • max(11, 8, 10, 9) &lt; min(15, 12, 14, 13)

    This satisfies the first three requirements. Additionally, each quadrant is also a special grid. Thus, this is a special grid.

    Constraints:

    • 0 &lt;= n &lt;= 10

    • Nested Class Summary

      Nested Classes 
      Modifier and Type Class Description

    • Field Summary

      Fields 
      Modifier and Type Field Description

    • Constructor Summary

      Constructors 
      Constructor Description
      Solution()

    • Enum Constant Summary

      Enum Constants 
      Enum Constant Description

    • Method Summary

      Modifier and Type Method Description
      final Array<IntArray> specialGrid(Integer n)

      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait