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master > master: code py - pollard rho mit 2 modi

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This commit is contained in:
RD
2022-07-01 13:47:32 +02:00
parent 3c965eda7b
commit de238fede9
5 changed files with 124 additions and 13 deletions
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3
code/python/src/algorithms/pollard_rho/__init__.py
View File

@@ -12,5 +12,6 @@ from src.algorithms.pollard_rho.algorithms import *;
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
__all__ = [
'pollard_rho_algorithm',
'pollard_rho_algorithm_linear',
'pollard_rho_algorithm_exponential',
];

65
code/python/src/algorithms/pollard_rho/algorithms.py
View File

@@ -18,14 +18,71 @@ from src.algorithms.pollard_rho.display import *;
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
__all__ = [
'pollard_rho_algorithm',
'pollard_rho_algorithm_linear',
'pollard_rho_algorithm_exponential',
];
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# METHOD pollard's rho algorithm
# METHOD pollard's rho algorithm - with linear grwoth
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
def pollard_rho_algorithm(
def pollard_rho_algorithm_linear(
n: int,
x_init: int = 2,
verbose: bool = False,
):
steps = [];
success = False;
f = lambda _: fct(_, n=n);
d = 1;
x = y = x_init;
steps.append(Step(x=x));
k = 0;
k_next = 1;
while True:
# aktualisiere x: x = f(x_prev):
x = f(x);
# aktualisiere y: y = f(f(y_prev)):
y = f(f(y));
# ggT berechnen:
d = math.gcd(abs(x-y), n);
steps.append(Step(x=x, y=y, d=d));
# Abbruchkriterien prüfen:
if d == 1: # weitermachen, solange d == 1
k += 1;
continue;
elif d == n: # versagt
success = False;
break;
else:
success = True;
break;
if verbose:
repr = display_table_linear(steps=steps);
print('');
print('\x1b[1mEuklidescher Algorithmus\x1b[0m');
print('');
print(repr);
print('');
if success:
print('\x1b[1mBerechneter Faktor:\x1b[0m');
print('');
print(f'd = \x1b[1m{d}\x1b[0m.');
else:
print('\x1b[91mKein (Prim)faktor erkannt!\x1b[0m');
print('');
return d;
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# METHOD pollard's rho algorithm - with exponential grwoth
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
def pollard_rho_algorithm_exponential(
n: int,
x_init: int = 2,
verbose: bool = False,
@@ -64,7 +121,7 @@ def pollard_rho_algorithm(
break;
if verbose:
repr = display_table(steps=steps);
repr = display_table_exponential(steps=steps);
print('');
print('\x1b[1mEuklidescher Algorithmus\x1b[0m');
print('');

29
code/python/src/algorithms/pollard_rho/display.py
View File

@@ -16,14 +16,37 @@ from src.models.pollard_rho import *;
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
__all__ = [
'display_table',
'display_table_linear',
'display_table_exponential',
];
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# METHOD display table
# METHOD display table - linear
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
def display_table(steps: List[Step]) -> str:
def display_table_linear(steps: List[Step]) -> str:
table = pd.DataFrame({
'i': [i for i in range(len(steps))],
'x': [step.x for step in steps],
'y': [step.y or '-' for step in steps],
'd': [step.d or '-' for step in steps],
}) \
.reset_index(drop=True);
# benutze pandas-Dataframe + tabulate, um schöner darzustellen:
repr = tabulate(
table,
headers=['i', 'x(i)', 'y(i) = x(2i)', 'gcd(|x - y|,n)'],
showindex=False,
colalign=('right', 'right', 'right', 'center'),
tablefmt='simple',
);
return repr;
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# METHOD display table - exponential
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
def display_table_exponential(steps: List[Step]) -> str:
table = pd.DataFrame({
'i': [i for i in range(len(steps))],
'x': [step.x for step in steps],