Algorithms and Data Structures

  • Profound Academy

    • Status
      • 1
        Implementation
      • 2
        Bitwise operations
      • 3
        Prefix Sums
      • 4
        Sliding window / Two pointers
      • 5
        Modular Arithmetic
      • 6
        Number Theory
      • 7
        Binary Search
      • 8
        Basic Sorting
      • 9
        Greedy Algorithms
      • 10
        Basic Dynamic Programming
      • 11
        Recursion
      • 12
        Linked LIst
      • 13
        Queue & Stack
      • 14
        Binary tree + BST
      • 15
        Divide & Conquer + Advanced Sorting
      • 16
        Heap
      • 17
        Hashing
      • 18
        Graph Representation

    • Fill the grid

    Given a grid, you are asked to fill it with L-shaped trominos except for a single cell (r, c). That one cell needs to be empty.
    An L-shaped tromino is a figure obtained by removing a single cell from a square.
    In case it’s not possible to fill the grid, the program should print Impossible.
     
    L-shaped tromino
    L-shaped tromino

    Input

    The first line of the input contains a single integer n (1 ≤ n ≤ 9).
    The second line contains the coordinates of the empty cell (r, c) (1 ≤ r, c ≤ ) where r is the row of the empty cell and c is the column.

    Output

    The program should print rows that contain numbers separated by a space. Each number should represent a single L-shaped tromino. The removed cell should be marked with a 0. The trominos should be indexed from 1 to . In case there are many solutions, the program can output any of those.

    Examples

    Input
    Output
    2 1 1
    0 1 3 3 1 1 4 3 2 4 4 5 2 2 5 5
     

    Constraints

    Time limit: 1 seconds

    Memory limit: 512 MB

    Output limit: 10 MB

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