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The Sieve of Eratosthenes: Empirical Analysis and Visualization of Various Approaches
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| import time | |
| import matplotlib.pyplot as plt | |
| def naive_sieve(m: int): | |
| BA = [True] * m | |
| for i, k in zip(range(2, m + 1), range(len(BA))): | |
| if BA[k] is False: continue | |
| for j in range(2, i): | |
| if i % j == 0: | |
| BA[k] = False | |
| f = k + j | |
| while f < len(BA): | |
| BA[f] = False | |
| f += j | |
| break | |
| return [i for i,j in zip(range(2, m + 1), BA) if j is True] | |
| def suboptimal_sieve(m: int): | |
| BA = [True] * m | |
| for i, k in zip(range(2, m + 1), range(2, len(BA))): | |
| if BA[k] is False: continue | |
| for j in range(i**2, m, i): | |
| BA[j] = False | |
| return [i for i,j in zip(range(2, m + 1), BA[2:]) if j is True] | |
| def fast_sieve(m: int): | |
| BA = [True] * m | |
| rtm = int(m**(1/2)) + 1 | |
| for i in range(2, len(BA)): | |
| if BA[i]: | |
| yield i | |
| if i < rtm: | |
| f = i | |
| while f < len(BA): | |
| BA[f] = False | |
| f += i | |
| def pidelport_sieve(limit): | |
| a = [True] * limit | |
| a[0] = a[1] = False | |
| for (i, isprime) in enumerate(a): | |
| if isprime: | |
| yield i | |
| for n in range(i*i, limit, i): | |
| a[n] = False | |
| def visualize_performance(): | |
| yt_naive = [] | |
| yt_suboptimal = [] | |
| yt_fast = [] | |
| yt_pidelport = [] | |
| xd = [x for x in range(100, 4501, 100)] | |
| for dt in xd: | |
| for f in [ | |
| [naive_sieve, yt_naive], | |
| [suboptimal_sieve, yt_suboptimal], | |
| [fast_sieve, yt_fast], | |
| [pidelport_sieve, yt_pidelport] | |
| ]: | |
| t1 = time.time() | |
| f[0](dt) | |
| t2 = time.time() | |
| f[1].append(t2-t1) | |
| fig = plt.figure() | |
| gs = fig.add_gridspec(1, 2) | |
| line, box = gs.subplots(sharey=False) | |
| # Line graph | |
| line.plot(xd, yt_naive, label="Naive SOE") | |
| line.plot(xd, yt_suboptimal, label="Suboptimal SOE") | |
| line.plot(xd, yt_fast, label="Fast SOE") | |
| line.plot(xd, yt_pidelport, label="Pi Delport's SOE") | |
| line.set(xlabel="\nRange of Primes Computed", ylabel="Time Taken (Seconds)\n") | |
| line.set_title("Benchmark per Range") | |
| line.legend() | |
| # Box plot | |
| box.boxplot([yt_naive, yt_suboptimal, yt_fast, yt_pidelport]) | |
| box.set(xlabel="\nSOE Algorithms", xticklabels=["Naive", "Suboptimal", "Fast", "Pi Delport's"]) | |
| box.set_title("Average Benchmark Duration") | |
| plt.suptitle("Performance Comparison of \nVarious Implementations of the Sieve of Eratosthenes") | |
| plt.show() | |
| if __name__ == '__main__': | |
| visualize_performance() |
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