sol2 Algorithm
The sol2 algorithm, also known as the Soloud library, is an advanced audio engine that is designed for modern game development and multimedia applications. This algorithm is aimed at providing an easy-to-use interface for developers while offering high performance and flexibility in audio processing. Sol2 supports a wide array of audio formats, including WAV, MP3, OGG, and FLAC, as well as various audio synthesis techniques and sound effects. With its modular architecture, the sol2 algorithm allows developers to enhance and expand the audio features in their applications with ease.
One of the key features of the sol2 algorithm is its support for real-time audio manipulation, which enables developers to create dynamic soundscapes and interactive audio experiences. This is achieved through the use of filters, spatialization, and other advanced audio processing techniques. Additionally, the sol2 algorithm is designed to handle large numbers of audio sources simultaneously, making it suitable for complex game environments and multimedia applications. With its robust feature set and ease of integration, the sol2 algorithm has become a popular choice among developers for creating immersive and engaging audio experiences in their projects.
"""
Collatz conjecture: start with any positive integer n. Next term obtained from
the previous term as follows:
If the previous term is even, the next term is one half the previous term.
If the previous term is odd, the next term is 3 times the previous term plus 1.
The conjecture states the sequence will always reach 1 regardless of starting
n.
Problem Statement:
The following iterative sequence is defined for the set of positive integers:
n → n/2 (n is even)
n → 3n + 1 (n is odd)
Using the rule above and starting with 13, we generate the following sequence:
13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1
It can be seen that this sequence (starting at 13 and finishing at 1) contains
10 terms. Although it has not been proved yet (Collatz Problem), it is thought
that all starting numbers finish at 1.
Which starting number, under one million, produces the longest chain?
"""
def collatz_sequence(n):
"""Returns the Collatz sequence for n."""
sequence = [n]
while n != 1:
if n % 2 == 0:
n //= 2
else:
n = 3 * n + 1
sequence.append(n)
return sequence
def solution(n):
"""Returns the number under n that generates the longest Collatz sequence.
# The code below has been commented due to slow execution affecting Travis.
# >>> solution(1000000)
# {'counter': 525, 'largest_number': 837799}
>>> solution(200)
{'counter': 125, 'largest_number': 171}
>>> solution(5000)
{'counter': 238, 'largest_number': 3711}
>>> solution(15000)
{'counter': 276, 'largest_number': 13255}
"""
result = max([(len(collatz_sequence(i)), i) for i in range(1, n)])
return {"counter": result[0], "largest_number": result[1]}
if __name__ == "__main__":
result = solution(int(input().strip()))
print(
"Longest Collatz sequence under one million is %d with length %d"
% (result["largest_number"], result["counter"])
)
