My question is very simple. I wrote this program for pure entertainment. It takes a numerical input and finds the length of every Collatz Sequence up to and including that number. I want to make it faster algorithmically or mathematically (i.e. I know I could make it faster by running multiple versions parallel or by writing it in C++, but where's the fun in that?). Any and all help is welcome, thanks! EDIT: Code further optimized with the help of dankal444 from matplotlib import pyplot as plt import numpy as np import numba as nb # Get Range to Check top_range = int(input('Top Range: ')) @nb.njit('int64[:](int_)') def collatz(top_range): # Initialize mem mem = np.zeros(top_range + 1, dtype = np.int64) for start in range(2, top_range + 1): # If mod4 == 1: (3x + 1)/4 if start % 4 == 1: mem[start] = mem[(start + (start >> 1) + 1) // 2] + 3 # If 4mod == 3: 3(3x + 1) + 1 and continue elif start % 4 == 3: num = start + (start >> 1) + 1 num += (num >> 1) + 1 count = 4 while num >= start: if num % 2: num += (num >> 1) + 1 count += 2 else: num //= 2 count += 1 mem[start] = mem[num] + count # If 4mod == 2 or 0: x/2 else: mem[start] = mem[(start // 2)] + 1 return mem mem = collatz(top_range) # Plot each starting number with the length of it's sequence plt.scatter([*range(1, len(mem) + 1)], mem, color = 'black', s = 1) plt.show() Continue reading...
