master > master: code py - hirschberg
This commit is contained in:
parent
53b2066e0d
commit
14a882e9d3
@ -16,6 +16,7 @@ from src.local.maths import *;
|
||||
from src.graphs.graph import *;
|
||||
from src.graphs.tarjan import *;
|
||||
from src.travel.naive import *;
|
||||
from src.string_alignment.hirschberg import *;
|
||||
|
||||
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
# GLOBAL CONSTANTS/VARIABLES
|
||||
@ -28,16 +29,22 @@ from src.travel.naive import *;
|
||||
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
def enter():
|
||||
## Beispiel aus Seminarblatt 8
|
||||
tsp_naive_algorithm(
|
||||
dist = np.asarray([
|
||||
[0, 7, 2, 5],
|
||||
[7, 0, 5, 6],
|
||||
[2, 5, 0, 5],
|
||||
[2, 7, 4, 0],
|
||||
], dtype=float),
|
||||
optimise=max,
|
||||
verbose=True,
|
||||
# ## Beispiel für Seminarwoche 9 (Blatt 8):
|
||||
# tsp_naive_algorithm(
|
||||
# dist = np.asarray([
|
||||
# [0, 7, 4, 3],
|
||||
# [7, 0, 5, 6],
|
||||
# [2, 5, 0, 5],
|
||||
# [2, 7, 4, 0],
|
||||
# ], dtype=float),
|
||||
# optimise=min,
|
||||
# verbose=True,
|
||||
# );
|
||||
## Beispiel für Seminarwoche 10 (Blatt 9):
|
||||
hirschberg_algorithm_full(
|
||||
X = 'ACGAAG',
|
||||
Y = 'AGAT',
|
||||
verbose = True,
|
||||
);
|
||||
return;
|
||||
|
||||
|
0
code/python/src/string_alignment/__init__.py
Normal file
0
code/python/src/string_alignment/__init__.py
Normal file
411
code/python/src/string_alignment/hirschberg.py
Normal file
411
code/python/src/string_alignment/hirschberg.py
Normal file
@ -0,0 +1,411 @@
|
||||
#!/usr/bin/env python3
|
||||
# -*- coding: utf-8 -*-
|
||||
|
||||
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
# IMPORTS
|
||||
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
from __future__ import annotations;
|
||||
from src.local.typing import *;
|
||||
from src.local.maths import *;
|
||||
|
||||
|
||||
|
||||
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
# EXPORTS
|
||||
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
__all__ = [
|
||||
'hirschberg_algorithm',
|
||||
'hirschberg_algorithm_full',
|
||||
];
|
||||
|
||||
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
# CONSTANTS / SETUP
|
||||
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
class Directions(Enum):
|
||||
UNSET = -1;
|
||||
DIAGONAL = 1;
|
||||
HORIZONTAL = 0;
|
||||
VERTICAL = 2;
|
||||
|
||||
def gap_penalty(x: str):
|
||||
return 1;
|
||||
|
||||
def missmatch_penalty(x: str, y: str):
|
||||
return 0 if x == y else 1;
|
||||
|
||||
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
# METHOD hirschberg_algorithm
|
||||
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
def hirschberg_algorithm(
|
||||
X: str,
|
||||
Y: str,
|
||||
verbose: bool = False,
|
||||
) -> Tuple[str, str]:
|
||||
Costs, Moves = hirschberg_match_matrix(X = '-' + X, Y = '-' + Y);
|
||||
path = reconstruct_optimal_path(Moves=Moves);
|
||||
word_x, word_y = reconstruct_words(X = '-' + X, Y = '-' + Y, Moves=Moves, path=path);
|
||||
if verbose:
|
||||
L = len(word_x);
|
||||
costs_repr, moves_repr = display_cost_matrix(Costs=Costs, path=path, X = '-' + X, Y = '-' + Y);
|
||||
print('');
|
||||
print('\x1b[1mAlignment:\x1b[0m');
|
||||
print(f' {word_y}');
|
||||
print(f' {L*"-"}');
|
||||
print(f' {word_x}');
|
||||
print('');
|
||||
print(costs_repr);
|
||||
print('');
|
||||
print(moves_repr);
|
||||
return word_x, word_y;
|
||||
|
||||
def hirschberg_algorithm_full(
|
||||
X: str,
|
||||
Y: str,
|
||||
depth: int = 0,
|
||||
verbose: bool = False,
|
||||
) -> Tuple[str, str]:
|
||||
n = len(Y);
|
||||
if n > 1:
|
||||
n = int(np.ceil(n/2));
|
||||
|
||||
# bilde linke Hälfte vom horizontalen Wort:
|
||||
Y1 = Y[:n];
|
||||
X1 = X;
|
||||
|
||||
# bilde rechte Hälfte vom horizontalen Wort (und kehre h. + v. um):
|
||||
Y2 = Y[n:][::-1];
|
||||
X2 = X[::-1];
|
||||
|
||||
# Löse Teilprobleme:
|
||||
Costs1, Moves1 = hirschberg_match_matrix(X = '-' + X1, Y = '-' + Y1);
|
||||
Costs2, Moves2 = hirschberg_match_matrix(X = '-' + X2, Y = '-' + Y2);
|
||||
path1, path2 = reconstruct_optimal_path_halves(
|
||||
Costs1=Costs1,
|
||||
Costs2=Costs2,
|
||||
Moves1=Moves1,
|
||||
Moves2=Moves2,
|
||||
);
|
||||
word_x_1, word_y_1 = reconstruct_words(X = '-' + X1, Y = '-' + Y1, Moves=Moves1, path=path1);
|
||||
word_x_2, word_y_2 = reconstruct_words(X = '-' + X2, Y = '-' + Y2, Moves=Moves2, path=path2);
|
||||
|
||||
if verbose:
|
||||
L = len(word_x_1) + len(word_x_2);
|
||||
costs_repr, moves_repr = display_cost_matrix_halves(
|
||||
Costs1 = Costs1,
|
||||
Costs2 = Costs2,
|
||||
path1 = path1,
|
||||
path2 = path2,
|
||||
X1 = '-' + X1,
|
||||
X2 = '-' + X2,
|
||||
Y1 = '-' + Y1,
|
||||
Y2 = '-' + Y2,
|
||||
);
|
||||
print('');
|
||||
print(f'\x1b[1mRekursionstiefe: {depth}\x1b[0m')
|
||||
print('');
|
||||
print('\x1b[1mAlignment:\x1b[0m');
|
||||
print(f' {word_y_1} {word_y_2[::-1]}');
|
||||
print(f' {(L+1)*"-"}');
|
||||
print(f' {word_x_1} {word_x_2[::-1]}');
|
||||
print('');
|
||||
print(moves_repr);
|
||||
|
||||
coord = path1[-1];
|
||||
m = coord[0];
|
||||
word_x_1, word_y_1 = hirschberg_algorithm_full(X=X[:m], Y=Y[:n], depth=depth+1, verbose=True);
|
||||
word_x_2, word_y_2 = hirschberg_algorithm_full(X=X[m:], Y=Y[n:], depth=depth+1, verbose=True);
|
||||
word_x = word_x_1 + word_x_2;
|
||||
word_y = word_y_1 + word_y_2;
|
||||
else:
|
||||
word_x, word_y = hirschberg_algorithm(X=X, Y=Y, verbose=False);
|
||||
if depth == 0:
|
||||
L = len(word_x);
|
||||
print('');
|
||||
print('\x1b[1mAlignment:\x1b[0m');
|
||||
print(f' {word_y}');
|
||||
print(f' {L*"-"}');
|
||||
print(f' {word_x}');
|
||||
print('');
|
||||
return word_x, word_y;
|
||||
|
||||
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
# METHODS cost matrix + optimal paths
|
||||
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
def hirschberg_match_matrix(
|
||||
X: str,
|
||||
Y: str,
|
||||
) -> Tuple[NDArray[(Any, Any), int], NDArray[(Any, Any), Directions]]:
|
||||
'''
|
||||
Berechnet Hirschberg-Costs-Matrix (ohne Rekursion).
|
||||
|
||||
Annahmen:
|
||||
- X[0] = gap
|
||||
- Y[0] = gap
|
||||
'''
|
||||
m = len(X); # display vertically
|
||||
n = len(Y); # display horizontally
|
||||
Costs = np.full(shape=(m, n), dtype=int, fill_value=0);
|
||||
Moves = np.full(shape=(m, n), dtype=Directions, fill_value=Directions.UNSET);
|
||||
|
||||
# zuerst 0. Spalte und 0. Zeile ausfüllen:
|
||||
for i, x in list(enumerate(X))[1:]:
|
||||
update_cost_matrix(Costs, Moves, x, '', i, 0);
|
||||
|
||||
for j, y in list(enumerate(Y))[1:]:
|
||||
update_cost_matrix(Costs, Moves, '', y, 0, j);
|
||||
|
||||
# jetzt alle »inneren« Werte bestimmen:
|
||||
for i, x in list(enumerate(X))[1:]:
|
||||
for j, y in list(enumerate(Y))[1:]:
|
||||
update_cost_matrix(Costs, Moves, x, y, i, j);
|
||||
return Costs, Moves;
|
||||
|
||||
def update_cost_matrix(
|
||||
Costs: NDArray[(Any, Any), int],
|
||||
Moves: NDArray[(Any, Any), Directions],
|
||||
x: str,
|
||||
y: str,
|
||||
i: int,
|
||||
j: int,
|
||||
):
|
||||
'''
|
||||
Schrittweise Funktion zur Aktualisierung vom Eintrag `(i,j)` in der Kostenmatrix.
|
||||
|
||||
Annahme:
|
||||
- alle »Vorgänger« von `(i,j)` in der Matrix sind bereits optimiert.
|
||||
|
||||
@inputs
|
||||
- `Costs` - bisher berechnete Kostenmatrix
|
||||
- `Moves` - bisher berechnete optimale Schritte
|
||||
- `i`, `x` - Position und Wert in String `X` (»vertical« dargestellt)
|
||||
- `j`, `y` - Position und Wert in String `Y` (»horizontal« dargestellt)
|
||||
'''
|
||||
|
||||
# nichts zu tun, wenn (i, j) == (0, 0):
|
||||
if i == 0 and j == 0:
|
||||
Costs[0, 0] = 0;
|
||||
return;
|
||||
|
||||
################################
|
||||
# NOTE: Berechnung von möglichen Moves wie folgt.
|
||||
#
|
||||
# Fall 1: (i-1,j-1) ---> (i,j)
|
||||
# ==> Stringvergleich ändert sich wie folgt:
|
||||
# s1 s1 x
|
||||
# ---- ---> ------
|
||||
# s2 s2 y
|
||||
#
|
||||
# Fall 2: (i,j-1) ---> (i,j)
|
||||
# ==> Stringvergleich ändert sich wie folgt:
|
||||
# s1 s1 GAP
|
||||
# ---- ---> -------
|
||||
# s2 s2 y
|
||||
#
|
||||
# Fall 3: (i-1,j) ---> (i,j)
|
||||
# ==> Stringvergleich ändert sich wie folgt:
|
||||
# s1 s1 x
|
||||
# ---- ---> -------
|
||||
# s2 s2 GAP
|
||||
#
|
||||
# Diese Fälle berücksichtigen wir:
|
||||
################################
|
||||
edges = [];
|
||||
if i > 0 and j > 0:
|
||||
edges.append((
|
||||
Directions.DIAGONAL,
|
||||
Costs[i-1, j-1] + missmatch_penalty(x, y),
|
||||
));
|
||||
if j > 0:
|
||||
edges.append((
|
||||
Directions.HORIZONTAL,
|
||||
Costs[i, j-1] + gap_penalty(y),
|
||||
));
|
||||
if i > 0:
|
||||
edges.append((
|
||||
Directions.VERTICAL,
|
||||
Costs[i-1, j] + gap_penalty(x),
|
||||
));
|
||||
|
||||
if len(edges) > 0:
|
||||
# Sortiere nach Priorität (festgelegt in Enum):
|
||||
edges = sorted(edges, key=lambda x: x[0].value);
|
||||
# Wähle erste Möglichkeit mit minimalen Kosten:
|
||||
index = np.argmin([ cost for _, cost in edges]);
|
||||
Moves[i, j], Costs[i, j] = edges[index];
|
||||
return;
|
||||
|
||||
def reconstruct_words(
|
||||
X: str,
|
||||
Y: str,
|
||||
Moves: NDArray[(Any, Any), Directions],
|
||||
path: List[Tuple[int, int]],
|
||||
) -> Tuple[str, str]:
|
||||
word_x = '';
|
||||
word_y = '';
|
||||
for (i, j) in path:
|
||||
x = X[i];
|
||||
y = Y[j];
|
||||
match Moves[i, j]:
|
||||
case Directions.DIAGONAL:
|
||||
word_x += x;
|
||||
word_y += y;
|
||||
case Directions.HORIZONTAL:
|
||||
word_x += '-';
|
||||
word_y += y;
|
||||
case Directions.VERTICAL:
|
||||
word_x += x;
|
||||
word_y += '-';
|
||||
return word_x, word_y;
|
||||
|
||||
def reconstruct_optimal_path(
|
||||
Moves: NDArray[(Any, Any), Directions],
|
||||
coord: Optional[Tuple[int, int]] = None,
|
||||
) -> List[Tuple[int, int]]:
|
||||
'''
|
||||
Liest Matrix mit optimalen Schritten den optimalen Pfad aus,
|
||||
angenfangen von Endkoordinaten.
|
||||
'''
|
||||
if coord is None:
|
||||
m, n = Moves.shape;
|
||||
(i, j) = (m-1, n-1);
|
||||
else:
|
||||
(i, j) = coord;
|
||||
path = [(i, j)];
|
||||
while (i, j) != (0, 0):
|
||||
match Moves[i, j]:
|
||||
case Directions.DIAGONAL:
|
||||
(i, j) = (i - 1, j - 1);
|
||||
case Directions.HORIZONTAL:
|
||||
(i, j) = (i, j - 1);
|
||||
case Directions.VERTICAL:
|
||||
(i, j) = (i - 1, j);
|
||||
case _:
|
||||
break;
|
||||
path.append((i, j));
|
||||
return path[::-1];
|
||||
|
||||
def reconstruct_optimal_path_halves(
|
||||
Costs1: NDArray[(Any, Any), int],
|
||||
Costs2: NDArray[(Any, Any), int],
|
||||
Moves1: NDArray[(Any, Any), Directions],
|
||||
Moves2: NDArray[(Any, Any), Directions],
|
||||
) -> Tuple[List[Tuple[int, int]], List[Tuple[int, int]]]:
|
||||
(m, n1) = Costs1.shape;
|
||||
(m, n2) = Costs2.shape;
|
||||
info = [
|
||||
(
|
||||
Costs1[i, n1-1] + Costs2[m-1-i, n2-1],
|
||||
(i, n1-1),
|
||||
(m-1-i, n2-1),
|
||||
)
|
||||
for i in range(m)
|
||||
];
|
||||
index = np.argmin([ cost for cost, _, _ in info ]);
|
||||
path1 = reconstruct_optimal_path(Moves1, coord=info[index][1]);
|
||||
path2 = reconstruct_optimal_path(Moves2, coord=info[index][2]);
|
||||
return path1, path2;
|
||||
|
||||
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
# AUXILIARY METHODS
|
||||
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|
||||
|
||||
def represent_cost_matrix(
|
||||
Costs: NDArray[(Any, Any), int],
|
||||
path: List[Tuple[int, int]],
|
||||
X: str,
|
||||
Y: str,
|
||||
pad: bool = False,
|
||||
) -> Tuple[NDArray[(Any, Any), Any], NDArray[(Any, Any), Any]]:
|
||||
m = len(X); # display vertically
|
||||
n = len(Y); # display horizontally
|
||||
|
||||
# erstelle string-Array:
|
||||
if pad:
|
||||
table = np.full(shape=(3 + m + 3, 3 + n + 1), dtype=object, fill_value='');
|
||||
else:
|
||||
table = np.full(shape=(3 + m, 3 + n), dtype=object, fill_value='');
|
||||
|
||||
# topmost rows:
|
||||
table[0, 3:(3+n)] = [str(j) for j in range(n)];
|
||||
table[1, 3:(3+n)] = [y for y in Y];
|
||||
table[2, 3:(3+n)] = '--';
|
||||
# leftmost columns:
|
||||
table[3:(3+m), 0] = [str(i) for i in range(m)];
|
||||
table[3:(3+m), 1] = [x for x in X];
|
||||
table[3:(3+m), 2] = '|';
|
||||
|
||||
if pad:
|
||||
table[-3, 3:(3+n)] = '--';
|
||||
table[3:(3+m), -1] = '|';
|
||||
|
||||
table_costs = table.copy();
|
||||
table_moves = table.copy();
|
||||
table_costs[3:(3+m), 3:(3+n)] = Costs;
|
||||
table_moves[3:(3+m), 3:(3+n)] = '.';
|
||||
for (i, j) in path:
|
||||
# table_costs[3 + i, 3 + j] = f'\x1b[92;1m{table_costs[3 + i, 3 + j]}\x1b[0m';
|
||||
table_moves[3 + i, 3 + j] = '@';
|
||||
|
||||
return table_costs, table_moves;
|
||||
|
||||
def display_cost_matrix(
|
||||
Costs: NDArray[(Any, Any), int],
|
||||
path: List[Tuple[int, int]],
|
||||
X: str,
|
||||
Y: str,
|
||||
) -> Tuple[str, str]:
|
||||
'''
|
||||
Zeigt Kostenmatrix + optimalen Pfad.
|
||||
|
||||
@inputs
|
||||
- `Costs` - Kostenmatrix
|
||||
- `Moves` - Kodiert die optimalen Schritte
|
||||
- `X`, `Y` - Strings
|
||||
|
||||
@returns
|
||||
- eine 'printable' Darstellung der Matrix mit den Strings X, Y + Indexes.
|
||||
'''
|
||||
table_costs, table_moves = represent_cost_matrix(Costs=Costs, path=path, X=X, Y=Y);
|
||||
# benutze pandas-Dataframe, um schöner darzustellen:
|
||||
costs_repr = pd.DataFrame(table_costs).to_string(index=False, header=False);
|
||||
moves_repr = pd.DataFrame(table_moves).to_string(index=False, header=False);
|
||||
return costs_repr, moves_repr;
|
||||
|
||||
def display_cost_matrix_halves(
|
||||
Costs1: NDArray[(Any, Any), int],
|
||||
Costs2: NDArray[(Any, Any), int],
|
||||
path1: List[Tuple[int, int]],
|
||||
path2: List[Tuple[int, int]],
|
||||
X1: str,
|
||||
X2: str,
|
||||
Y1: str,
|
||||
Y2: str,
|
||||
) -> Tuple[str, str]:
|
||||
'''
|
||||
Zeigt Kostenmatrix + optimalen Pfad für Schritt im D & C Hirschberg-Algorithmus
|
||||
|
||||
@inputs
|
||||
- `Costs1`, `Costs2` - Kostenmatrizen
|
||||
- `Moves1`, `Moves2` - Kodiert die optimalen Schritte
|
||||
- `X1`, `X2`, `Y1`, `Y2` - Strings
|
||||
|
||||
@returns
|
||||
- eine 'printable' Darstellung der Matrix mit den Strings X, Y + Indexes.
|
||||
'''
|
||||
table_costs1, table_moves1 = represent_cost_matrix(Costs=Costs1, path=path1, X=X1, Y=Y1, pad=True);
|
||||
table_costs2, table_moves2 = represent_cost_matrix(Costs=Costs2, path=path2, X=X2, Y=Y2, pad=True);
|
||||
|
||||
# merge Taellen:
|
||||
table_costs = np.concatenate([table_costs1, table_costs2[::-1, ::-1]], axis=1);
|
||||
table_moves = np.concatenate([table_moves1, table_moves2[::-1, ::-1]], axis=1);
|
||||
|
||||
# benutze pandas-Dataframe, um schöner darzustellen:
|
||||
costs_repr = pd.DataFrame(table_costs).to_string(index=False, header=False);
|
||||
moves_repr = pd.DataFrame(table_moves).to_string(index=False, header=False);
|
||||
|
||||
return costs_repr, moves_repr;
|
Loading…
x
Reference in New Issue
Block a user