Difficult Python Question 3 — Hollow Triangle Of Letters

Write a function that takes in a string, and prints the following hollow triangular pattern. If there are insufficient characters to make a perfect triangle, simply use * characters in their place.

string = “abcdefghijkl” (length=12)

Here, this string can form a perfect triangle by itself

   a
  b l
 c   k
defghij

string = “abcdefghijk” (length=11)

Here, there are insufficient letters to form a perfect triangle, so * characters are used to fill it up.

   a
  b *
 c   k
defghij

string = “abcdefghij” (length=10)

   a
  b *
 c   *
defghij

string = “abcdefghi” (length=9)

   a
  b *
 c   *
defghi*

string = “abcdefgh” (length=8)

Here, this string can form a perfect triangle by itself

  a
 b h
cdefg

string = “abcdefghijklmnop” (length=16)

This string too can form a perfect triangle by itself.

    a
   b p
  c   o
 d     n
efghijklm

string = “abcdefghijklmno” (length=15)

    a
   b *
  c   o
 d     n
efghijklm

Some Hints:

1. Notice that strings with lengths that are multiples of 4 make perfect triangles (no * needed)
2. Add the needed * characters to your string first
3. Try to find a relationship between the length of the string and the height of the triangle
4. Split your function into 3 parts — 1 to print the first line, 1 to print the last line, and 1 to print all the middle lines

The Logic Behind The Solution

Let’s split the solution into a couple of steps

1. Adding the additional * to our string
2. Finding the height of our hollow triangle
3. Establishing patterns to print our triangle
4. Printing the first line
5. Printing the 2nd line to the 2nd last line
6. Printing the last line

1) Adding the additional * to our string

Here, we know that strings with a length that is a multiple of 4 will make a perfect triangle. As such, we want to add enough * characters behind our string such that its length becomes a multiple of 4.

Let’s say we have a string "abcdefghi" which has a length of 9. To make its length a multiple of 4, we would need to add 3 * characters. Now let’s say we have a string "abcdefghijk" which has a length of 11 characters. To make its length a multiple of 4, we would need to add only 1 * character.

Hence, to determine how many * to add, we can use the modulo % operator, which gives us the remainder when one number is divided by another, and we arrive at this formula 4 — len(string) % 4). At the end of this step, our string should have 0 to 4 * characters added behind to make its length a multiple of 4.

2) Finding the height of our hollow triangle

Let’s list down some string lengths and their corresponding triangle height

string length of 8 -> triangle height of 3
string length of 12 -> triangle height of 4
string length of 16 -> triangle height of 5

Here, we can see this relationship:

triangle height = string length // 4 + 1

3) Establishing patterns to print our triangle

Let’s say we have a string "abcdefghijklmno*" after we’ve added the necessary * characters. Our triangle with height of 5:

    a
   b *
  c   o
 d     n
efghijklm

Observable patterns:

    a          4 spaces + string[0]
   b *         3 spaces + string[1] + 1 spaces + string[-1]
  c   o        2 spaces + string[2] + 3 spaces + string[-2]
 d     n       1 spaces + string[3] + 5 spaces + string[-3]
efghijklm      string[4: -4+1]

Based on the patterns here, we can split the function into 3 parts:

4) Printing the first line

    a          4 spaces + string[0]

The first line consists of (height-1) spaces and the first character (character at index 0), and we simply need to print this once.

5) Printing the 2nd line to the 2nd last line

   b *         3 spaces + string[1] + 1 spaces + string[-1]
  c   o        2 spaces + string[2] + 3 spaces + string[-2]
 d     n       1 spaces + string[3] + 5 spaces + string[-3]

Here, we need a for loop that loops height-2 times (minus the 1st and last line). For each line, we need to print:

• height-i-1 spaces
• string[i]
• i*2-1 spaces
• string[-i]

6) Printing the last line

efghijklm      string[4: -4+1]

The last line consists of all characters that we haven’t printed — in this case it would be the slice from 4 to -3.

The Code Solution

def hollow_triangle(string):
    if len(string) % 4 > 0:
        string += "*" * (4-len(string)%4)

    height = len(string) // 4 + 1

    print(" "*(height-1) + string[0])
    
    for i in range(1, height-1):
        print(" "*(height-i-1), end="")
        print(string[i], end="")
        print(" "*(2*i-1), end="")
        print(string[-1])

    print(string[i+1:-i])

The Code Solution (Comments Added)

def hollow_triangle(string):

    # step 1 - adding * to string
    if len(string) % 4 > 0:
        string += "*" * (4-len(string)%4)

    # step 2 - finding height of triangle
    height = len(string) // 4 + 1

    # step 4 - printing first line
    print(" "*(height-1) + string[0])
    

    # step 5 - printing 2nd to 2nd last line
    for i in range(1, height-1):
        print(" "*(height-i-1), end="")
        print(string[i], end="")
        print(" "*(2*i-1), end="")
        print(string[-1])

    # step 6 - printing last line
    print(string[i+1:-i])

Conclusion

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