Solution for Designer Door Mat Problem

Problem

We need to print a door mat design pattern given two inputs n (rows) and m (columns).
- The pattern must have WELCOME centered in the middle row.
- The top half and bottom half must be symmetric with motifs made of .|..
- The total width m is guaranteed to be 3 * n.

My Approach

1. Top Half:

   • For each row before the middle, the motif count grows as (2 * height + 1).
   • Each line is padded with - on both sides to keep the width = m.

2. Middle Row:

   • Simply print WELCOME centered with dashes.

3. Bottom Half:

   • Mirror the top half.
   • Motif count decreases as (2 * ((n-1) - height) + 1).

4. Symmetry Guarantee:

   • By controlling motif counts in both halves, the design is symmetric around the middle.

Code

# Enter your code here. Read input from STDIN. Print output to STDOUT
n, m = map(int, input().split())

dash = '-'
center = '.|.'
welcome = 'WELCOME'

dash_mul_top = 3 * (n // 2)
dash_mul_bottom = 3

for height in range(0, n):
    if height < n // 2:
        # Top half
        print(dash * dash_mul_top, end="")
        print(center * (2 * height + 1), end="")
        print(dash * dash_mul_top, end="")
        dash_mul_top -= 3
        print()

    elif height == n // 2:
        # Middle row
        dash_mul_middle = (m - len(welcome)) // 2
        print(dash * dash_mul_middle, end="")
        print(welcome, end="")
        print(dash * dash_mul_middle, end="")
        print()

    else:
        # Bottom half
        print(dash * dash_mul_bottom, end="")
        print(center * (2 * ((n - 1) - height) + 1), end="")
        print(dash * dash_mul_bottom, end="")
        dash_mul_bottom += 3
        print()

Example

Input:

7 21

Output:

---------.|.---------
------.|..|..|.------
---.|..|..|..|..|.---
-------WELCOME-------
---.|..|..|..|..|.---
------.|..|..|.------
---------.|.---------

Complexity Analysis

• Time Complexity:

  • We print exactly n lines, and each line is of length m.
  • Complexity = O(n * m) (printing dominates).

• Space Complexity:

  • Only a few counters and string multiplications are used.
  • No extra storage proportional to n or m.
  • Complexity = O(1) auxiliary space.

✅ The solution is clean, efficient, and guaranteed to run within constraints.