I’d like to add my own input to the potential solution here.

Solution 1 – Building on NoDakker’s Solution

In the first provided example, the input file’s numbers cleanly cover the span of 1-6. NoDakker’s approach relies on an arithmetic sequence, n * (n + 1) / 2 to determine the rightmost edge of our constructed data pyramid. This approach has to make the assumption that any input file will contain a contiguous, ascending set of numbered keys. For example: 1, 2, 3, 4, 5, 6, and so on.

This is a solid approach if that constraint is honored by our input file’s keys. We can further optimize their solution by storing those edges in a dictionary preemptively instead of re-computing them at each iteration of the main loop:

edges = {}

for n in range(100):
    edges[(n**n + n) / 2] = n    

Then, in the main loop, we can lookup our current key in O(1) time and place it in our message_words array using :

for line in lines:
    number = int(line.split()[0])

    if number in edges:
        message_words[edges[number]] = line.split()[1]

This version is only slightly more optimal. Both solutions are O(n), where n is the number of lines in our input file. Our loop to calculate the arithmetic sequence is O(100), or any other arbitrary input other than 100, which simplifies to O(1). So you might see that we don’t get a ton of value by moving it out, but if we want to squeeze performance out of our code, we perform this O(1) operation once instead of n times. O(1) is still technically better than O(100).

Solution 2 – A non-contiguous set of input keys

However, since our problem statement is vague, there is a possibility that we will be given a non-contiguous set of input keys. Imagine a scenario where our provided words are mapped to a set of numbers like such: 1,4,8,12,16… Our current logic breaks down because it relies on referencing the given key to our set of possible edges.

The problem simply states that with our given set of input keys, we construct a pyramid and use its rightmost edges to decode our message. In this case, it becomes necessary to adjust our solution to accommodate any possible set of input keys.

I believe this will require some form of sorting, which increases our time complexity to O(nlogn) in the worst case, using Python’s sorted() method. I’ve provided this solution below.

def decode(input_file):
    with open(input_file, "r") as f:
        data = f.readlines()

    word_dict = {}

    for line in data:
        num, word = int(line.split()[0]), line.split()[1]
        word_dict[num] = word

    sorted_index = sorted(word_dict.keys())

    message = ""
    i, level = 0, 0

    while i < len(sorted_index):
        message += word_dict[sorted_index[i]] + " "
        level += 1
        i += level + 1

    return message[:-1]  # Remove trailing space

In this solution, we map our input keys and values to a dictionary, word_dict. Next, we pull the keys out of our dictionary and use Python’s sorted() method to arrange them in ascending order. We are then able to construct our decoded message irrespective of the original input keys by iterating on a separate arithmetic variable, i, which gets incremented by the equation i_n = i_n-1 + pyramid_level + 1.

As NoDakker stated, the output of this equation is still gibberish, and I’d be interested in hearing more perspectives on the most optimal solution for this puzzle.

I’m a very curious person, so to know the actual answer, i loaded the huge input into excel and sorted it by numbers. i manually high-lighted the end numbers of line in pyramid upto 10 words. It went something like " young system present student lot experiment strong crease sun company".

Logically looking at the data 1 has word young, so output should defo start with young.

here is the answer I did manage to crack it
def decode(message_file):
# Read the content of the file
with open(message_file, ‘r’) as file:
lines = file.readlines()

# Initialize an empty dictionary to store the words corresponding to each number
decoded_dict = {}

# Loop through each line in the file
for line in lines:
    # Split the line into number and word if it contains whitespace
    if ' ' in line:
        num, word = line.split(maxsplit=1)  # Split only once
        # Convert the number to an integer
        num = int(num)
        # Store the word in the dictionary with the number as key
        decoded_dict[num] = word.strip()  # Strip any leading/trailing whitespace from the word

# Initialize an empty list to store the decoded words
decoded_words = []

# Loop through the numbers starting from 1
for i in range(1, len(lines) + 1):
    # If the number is in the decoded_dict, add the corresponding word to the decoded_words list
    if i in decoded_dict:
        decoded_words.append(decoded_dict[i])

# Join the decoded words into a string
decoded_message = ' '.join(decoded_words)

return decoded_message

Test the function with the provided file

decoded_message = decode(file_path)
print(decoded_message)