master > master: code py - refactoring

- umbenennungen
- verbesseungen der Darstellungen
- enums zur beseren Steuerung der versch. Modi
- refactoring des Algorithmus
- Verwendung von tabulator

code/python/src/graphs/graph.py

@@ -7,7 +7,7 @@
 
 from __future__ import annotations;
 
-from src.local.typing import *;
+from src.thirdparty.types import *;
 
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 # EXPORTS

code/python/src/graphs/tarjan.py

@@ -6,12 +6,8 @@
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
 from __future__ import annotations;
-from enum import Enum;
-from dataclasses import dataclass;
-from dataclasses import field
-from platform import node;
 
-from src.local.typing import *;
+from src.thirdparty.types import *;
 
 from src.core.log import *;
 from src.stacks.stack import *;

code/python/src/hirschberg/__init__.py

@@ -0,0 +1,20 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# IMPORTS
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+from src.hirschberg.algorithms import *;
+from src.hirschberg.constants import *;
+from src.hirschberg.display import *;
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# EXPORTS
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+__all__ = [
+    'hirschberg_algorithm',
+    'VerboseMode',
+    'DisplayOptions',
+];

code/python/src/hirschberg/algorithms.py

@@ -0,0 +1,152 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# IMPORTS
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+from src.thirdparty.types import *;
+from src.thirdparty.maths import *;
+
+from src.hirschberg.constants import *;
+from src.hirschberg.display import *;
+from src.hirschberg.matrix import *;
+from src.hirschberg.paths import *;
+from src.hirschberg.types import *;
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# EXPORTS
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+__all__ = [
+    'hirschberg_algorithm',
+    'simple_algorithm',
+];
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# METHOD hirschberg_algorithm
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+def simple_algorithm(
+    X:    str,
+    Y:    str,
+    verb: VerboseMode = VerboseMode.NONE,
+    show: List[DisplayOptions] = [],
+) -> Tuple[str, str]:
+    '''
+    Dieser Algorithmus berechnet die Edit-Distanzen + optimale Richtungen ein Mal.
+    Darus wird ein optimales Alignment direkt abgeleitet.
+    '''
+    Costs, Moves = compute_cost_matrix(X = '-' + X, Y = '-' + Y);
+    path = reconstruct_optimal_path(Moves=Moves);
+    word_x, word_y = reconstruct_words(X = '-' + X, Y = '-' + Y, moves=[Moves[coord] for coord in path], path=path);
+    if verb != VerboseMode.NONE:
+        repr = display_cost_matrix(Costs=Costs, path=path, X = '-' + X, Y = '-' + Y, verb=verb);
+        display = word_y + f'\n{"-"*len(word_x)}\n' + word_x;
+        print(f'\n{repr}\n\n\x1b[1mOptimales Alignment:\x1b[0m\n\n{display}\n');
+    return word_x, word_y;
+
+def hirschberg_algorithm(
+    X:    str,
+    Y:    str,
+    once: bool = False,
+    verb: VerboseMode = VerboseMode.NONE,
+    show: List[DisplayOptions] = [],
+) -> Tuple[str, str]:
+    '''
+    Der Hirschberg-Algorithmus berechnet nur die Edit-Distanzen (Kostenmatrix)
+    und weder speichert noch berechnet die Matrix der optimalen Richtungen.
+
+    Dies liefert eine Platz-effizientere Methode als die simple Methode.
+
+    Durch Rekursion wird eine Art Traceback durch die zugrunde liegende DP erreicht.
+    Daraus wird unmittelbar ein optimales Alignment bestimmt.
+    Des Weiteren werden Zeitkosten durch Divide-and-Conquer klein gehalten.
+    '''
+    # ggf. nur den simplen Algorithmus ausführen:
+    if once:
+        return simple_algorithm(X=X, Y=Y, verb=verb, show=show);
+
+    align = hirschberg_algorithm_step(X=X, Y=Y, depth=1, verb=verb, show=show);
+    word_x = align.as_string1();
+    word_y = align.as_string2();
+
+    # verbose output hier behandeln (irrelevant für Algorithmus):
+    if verb != VerboseMode.NONE:
+        if DisplayOptions.TREE in show:
+            display = align.astree(braces=True);
+        else:
+            display_x = align.as_string1(braces=True);
+            display_y = align.as_string2(braces=True);
+            display = display_y + f'\n{"-"*len(display_x)}\n' + display_x;
+        print(f'\n\x1b[1mOptimales Alignment:\x1b[0m\n\n{display}\n');
+
+    return word_x, word_y;
+
+def hirschberg_algorithm_step(
+    X:     str,
+    Y:     str,
+    depth: int = 0,
+    verb:  VerboseMode = VerboseMode.NONE,
+    show:  List[DisplayOptions] = [],
+) -> Alignment:
+    '''
+    Der rekursive Schritt der Hirschberg-Algorithmus teil eines der Wörter in zwei
+    und bestimmt eine entsprechende Aufteilung des zweiten Wortes in zwei,
+    die die Edit-Distanz minimiert.
+
+    Dies liefert uns Information über eine Stelle des optimalen Pfads durch die Kostenmatrix
+    sowie eine Aufteilung des Problems in eine linke und rechte Hälfte.
+    '''
+    n = len(Y);
+    if n == 1:
+        Costs, Moves = compute_cost_matrix(X = '-' + X, Y = '-' + Y);
+        path = reconstruct_optimal_path(Moves=Moves);
+        word_x, word_y = reconstruct_words(X = '-' + X, Y = '-' + Y, moves=[Moves[coord] for coord in path], path=path);
+
+        # verbose output hier behandeln (irrelevant für Algorithmus):
+        if verb != VerboseMode.NONE and (DisplayOptions.ATOMS in show):
+            repr = display_cost_matrix(Costs=Costs, path=path, X = '-' + X, Y = '-' + Y, verb=verb);
+            print(f'\n\x1b[1mRekursionstiefe: {depth}\x1b[0m\n\n{repr}')
+
+        return AlignmentBasic(word1=word_x, word2=word_y);
+    else:
+        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 = compute_cost_matrix(X = '-' + X1, Y = '-' + Y1);
+        Costs2, Moves2 = compute_cost_matrix(X = '-' + X2, Y = '-' + Y2);
+
+        # verbose output hier behandeln (irrelevant für Algorithmus):
+        if verb != VerboseMode.NONE:
+            path1, path2 = reconstruct_optimal_path_halves(Costs1=Costs1, Costs2=Costs2, Moves1=Moves1, Moves2=Moves2);
+            repr = display_cost_matrix_halves(
+                Costs1 = Costs1,
+                Costs2 = Costs2,
+                path1  = path1,
+                path2  = path2,
+                X1     =  '-' + X1,
+                X2     =  '-' + X2,
+                Y1     =  '-' + Y1,
+                Y2     =  '-' + Y2,
+                verb   = verb,
+            );
+            print(f'\n\x1b[1mRekursionstiefe: {depth}\x1b[0m\n\n{repr}')
+
+        # Koordinaten des optimalen Übergangs berechnen:
+        coord1, coord2 = get_optimal_transition(Costs1=Costs1, Costs2=Costs2);
+        p = coord1[0];
+        # Divide and Conquer ausführen:
+        align_left = hirschberg_algorithm_step(X=X[:p], Y=Y[:n], depth=depth+1, verb=verb, show=show);
+        align_right = hirschberg_algorithm_step(X=X[p:], Y=Y[n:], depth=depth+1, verb=verb, show=show);
+
+        # Resultate zusammensetzen:
+        return AlignmentPair(left=align_left, right=align_right);

code/python/src/hirschberg/constants.py

@@ -0,0 +1,51 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# IMPORTS
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+from src.thirdparty.types import *;
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# EXPORTS
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+__all__ = [
+    'VerboseMode',
+    'DisplayOptions',
+    'Directions',
+    'gap_penalty',
+    'missmatch_penalty',
+];
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# ENUMS
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+class VerboseMode(Enum):
+    NONE = -1;
+    COSTS = 0;
+    MOVES = 1;
+    COSTS_AND_MOVES = 2;
+
+class DisplayOptions(Enum):
+    TREE = 0;
+    ATOMS = 1;
+
+class Directions(Enum):
+    UNSET = -1;
+    # Prioritäten hier setzen
+    DIAGONAL = 0;
+    HORIZONTAL = 1;
+    VERTICAL = 2;
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# PENALTIES
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+def gap_penalty(x: str):
+    return 1;
+
+def missmatch_penalty(x: str, y: str):
+    return 0 if x == y else 1;

code/python/src/hirschberg/display.py

@@ -0,0 +1,123 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# IMPORTS
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+from src.thirdparty.types import *;
+from src.thirdparty.maths import *;
+
+from src.hirschberg.constants import *;
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# EXPORTS
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+__all__ = [
+    'represent_cost_matrix',
+    'display_cost_matrix',
+    'display_cost_matrix_halves',
+];
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# METHODS
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+def represent_cost_matrix(
+    Costs: np.ndarray, # NDArray[(Any, Any), int],
+    path: List[Tuple[int, int]],
+    X: str,
+    Y: str,
+    verb: VerboseMode,
+    pad: bool = False,
+) -> np.ndarray: # 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] = '|';
+
+    match verb:
+        case VerboseMode.MOVES:
+            table[3:(3+m), 3:(3+n)] = '.';
+            for (i, j) in path:
+                table[3 + i, 3 + j] = '*';
+        case VerboseMode.COSTS | VerboseMode.COSTS_AND_MOVES:
+            table[3:(3+m), 3:(3+n)] = Costs.copy();
+            if verb == VerboseMode.COSTS_AND_MOVES:
+                for (i, j) in path:
+                    table[3 + i, 3 + j] = f'\x1b[31;4;1m{table[3 + i, 3 + j]}\x1b[0m';
+
+    return table;
+
+def display_cost_matrix(
+    Costs: np.ndarray, # NDArray[(Any, Any), int],
+    path: List[Tuple[int, int]],
+    X: str,
+    Y: str,
+    verb: VerboseMode,
+) -> 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 = represent_cost_matrix(Costs=Costs, path=path, X=X, Y=Y, verb=verb);
+    # benutze pandas-Dataframe + tabulate, um schöner darzustellen:
+    repr = tabulate(pd.DataFrame(table), showindex=False, stralign='center', tablefmt='plain');
+    return repr;
+
+def display_cost_matrix_halves(
+    Costs1: np.ndarray, # NDArray[(Any, Any), int],
+    Costs2: np.ndarray, # NDArray[(Any, Any), int],
+    path1: List[Tuple[int, int]],
+    path2: List[Tuple[int, int]],
+    X1: str,
+    X2: str,
+    Y1: str,
+    Y2: str,
+    verb: VerboseMode,
+) -> 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.
+    '''
+    table1 = represent_cost_matrix(Costs=Costs1, path=path1, X=X1, Y=Y1, verb=verb, pad=True);
+    table2 = represent_cost_matrix(Costs=Costs2, path=path2, X=X2, Y=Y2, verb=verb, pad=True);
+
+    # merge Taellen:
+    table = np.concatenate([table1[:, :-1], table2[::-1, ::-1]], axis=1);
+
+    # benutze pandas-Dataframe + tabulate, um schöner darzustellen:
+    repr = tabulate(pd.DataFrame(table), showindex=False, stralign='center', tablefmt='plain');
+    return repr;

code/python/src/hirschberg/matrix.py

@@ -0,0 +1,127 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# IMPORTS
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+from src.thirdparty.types import *;
+from src.thirdparty.maths import *;
+
+from src.hirschberg.constants import *;
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# EXPORTS
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+__all__ = [
+    'compute_cost_matrix',
+    'update_cost_matrix',
+];
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# METHODS cost matrix + optimal paths
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+def compute_cost_matrix(
+    X: str,
+    Y: str,
+) -> Tuple[np.ndarray, np.ndarray]: # 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: np.ndarray, # NDArray[(Any, Any), int],
+    Moves: np.ndarray, # 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;

code/python/src/hirschberg/paths.py

@@ -0,0 +1,125 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# IMPORTS
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+from src.thirdparty.types import *;
+from src.thirdparty.maths import *;
+
+from src.hirschberg.constants import *;
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# EXPORTS
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+__all__ = [
+    'get_optimal_transition',
+    'reconstruct_optimal_path',
+    'reconstruct_optimal_path_halves',
+    'reconstruct_words',
+];
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# METHODS optimaler treffpunkt
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+def get_optimal_transition(
+    Costs1: np.ndarray, # NDArray[(Any, Any), int],
+    Costs2: np.ndarray, # NDArray[(Any, Any), int],
+) -> Tuple[Tuple[int, int], Tuple[int, int]]:
+    '''
+    Rekonstruiere »Treffpunkt«, wo die Gesamtkosten minimiert sind.
+    Dieser Punkt stellt einen optimal Übergang für den Rekursionsschritt dar.
+    '''
+    (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 ]);
+    coord1 = info[index][1];
+    coord2 = info[index][2];
+    return coord1, coord2;
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# METHODS reconstruction von words/paths
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+def reconstruct_optimal_path(
+    Moves: np.ndarray, # 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: np.ndarray, # NDArray[(Any, Any), int],
+    Costs2: np.ndarray, # NDArray[(Any, Any), int],
+    Moves1: np.ndarray, # NDArray[(Any, Any), Directions],
+    Moves2: np.ndarray, # NDArray[(Any, Any), Directions],
+) -> Tuple[List[Tuple[int, int]], List[Tuple[int, int]]]:
+    '''
+    Rekonstruiere optimale Pfad für Rekursionsschritt,
+    wenn horizontales Wort in 2 aufgeteilt wird.
+    '''
+    coord1, coord2 = get_optimal_transition(Costs1=Costs1, Costs2=Costs2);
+    path1 = reconstruct_optimal_path(Moves1, coord=coord1);
+    path2 = reconstruct_optimal_path(Moves2, coord=coord2);
+    return path1, path2;
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# METHODS reconstruction von words
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+def reconstruct_words(
+    X: str,
+    Y: str,
+    moves: List[Directions],
+    path: List[Tuple[int, int]],
+) -> Tuple[str, str]:
+    '''
+    Berechnet String-Alignment aus Path.
+    '''
+    word_x = '';
+    word_y = '';
+    for ((i, j), move) in zip(path, moves):
+        x = X[i];
+        y = Y[j];
+        match move:
+            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;

code/python/src/hirschberg/types.py

@@ -0,0 +1,107 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# IMPORTS
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+from __future__ import annotations;
+
+from src.thirdparty.types import *;
+from src.thirdparty.maths import *;
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# EXPORTS
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+__all__ = [
+    'Alignment',
+    'AlignmentBasic',
+    'AlignmentPair',
+];
+
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+# Class Alignments
+# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+class Alignment():
+    @property
+    def parts1(self) -> List[str]:
+        if isinstance(self, AlignmentBasic):
+            return [self.word1];
+        elif isinstance(self, AlignmentPair):
+            return self.left.parts1 + self.right.parts1;
+        return [];
+
+    @property
+    def parts2(self) -> List[str]:
+        if isinstance(self, AlignmentBasic):
+            return [self.word2];
+        elif isinstance(self, AlignmentPair):
+            return self.left.parts2 + self.right.parts2;
+        return [];
+
+    def astree(
+        self,
+        indent: str = '    ',
+        prefix: str = '',
+        braces: bool = False,
+        branch: str = '|____ ',
+    ) -> str:
+        return '\n'.join(list(self._astree_recursion(indent=indent, prefix=prefix, braces=braces, branch=branch)));
+
+    def _astree_recursion(
+        self,
+        depth: int = 0,
+        indent: str = '    ',
+        prefix: str = '',
+        braces: bool = False,
+        branch: str = '|____ ',
+    ) -> Generator[str, None, None]:
+        word1 = self.as_string1(braces=braces);
+        word2 = self.as_string2(braces=braces);
+        if isinstance(self, AlignmentBasic):
+            u = prefix + branch if depth > 0 else prefix;
+            yield f'{u}{word2}';
+            yield f'{" "*len(u)}{word1}';
+        elif isinstance(self, AlignmentPair):
+            u = prefix + branch if depth > 0 else prefix;
+            yield f'{u}{word2}';
+            yield f'{" "*len(u)}{word1}';
+            yield '';
+            yield from self.left._astree_recursion(
+                depth  = depth + 1,
+                indent = indent,
+                prefix = indent + prefix,
+                braces = braces,
+                branch = branch,
+            );
+            yield '';
+            yield from self.right._astree_recursion(
+                depth  = depth + 1,
+                indent = indent,
+                prefix = indent + prefix,
+                braces = braces,
+                branch = branch,
+            );
+        return;
+
+    def as_string1(self, braces: bool = False) -> Tuple[str, str]:
+        if braces:
+            return f'({")(".join(self.parts1)})';
+        return ''.join(self.parts1);
+
+    def as_string2(self, braces: bool = False,) -> Tuple[str, str]:
+        if braces:
+            return f'({")(".join(self.parts2)})';
+        return ''.join(self.parts2);
+
+@dataclass
+class AlignmentBasic(Alignment):
+    word1: str = field();
+    word2: str = field();
+
+@dataclass
+class AlignmentPair(Alignment):
+    left: Alignment = field();
+    right: Alignment = field();

code/python/src/stacks/stack.py

@@ -5,7 +5,7 @@
 # IMPORTS
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
-from src.local.typing import *;
+from src.thirdparty.types import *;
 
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 # EXPORTS

code/python/src/string_alignment/hirschberg.py

@@ -1,453 +0,0 @@
-#!/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_once',
-    'DisplayMode'
-];
-
-# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-# CONSTANTS / SETUP
-# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-class DisplayMode(Enum):
-    NONE = -1;
-    COSTS = 0;
-    MOVES = 1;
-    COSTS_AND_MOVES = 2;
-
-class Directions(Enum):
-    UNSET = -1;
-    # Prioritäten hier setzen
-    DIAGONAL = 0;
-    HORIZONTAL = 1;
-    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_once(
-    X: str,
-    Y: str,
-    mode: DisplayMode = DisplayMode.NONE,
-) -> Tuple[str, str]:
-    Costs, Moves = compute_cost_matrix(X = '-' + X, Y = '-' + Y);
-    path = reconstruct_optimal_path(Moves=Moves);
-    word_x, word_y = reconstruct_words(X = '-' + X, Y = '-' + Y, moves=[Moves[coord] for coord in path], path=path);
-    if mode != DisplayMode.NONE:
-        repr = display_cost_matrix(Costs=Costs, path=path, X = '-' + X, Y = '-' + Y, mode=mode);
-        print(f'\n{repr}');
-        print(f'\n\x1b[1mOptimales Alignment:\x1b[0m');
-        print('');
-        print(word_y);
-        print(len(word_x) * '-');
-        print(word_x);
-        print('');
-    return word_x, word_y;
-
-def hirschberg_algorithm(
-    X: str,
-    Y: str,
-    mode: DisplayMode = DisplayMode.NONE,
-) -> Tuple[str, str]:
-    alignments_x, alignments_y = hirschberg_algorithm_step(X=X, Y=Y, depth=1, mode=mode);
-    word_x = ''.join(alignments_x);
-    word_y = ''.join(alignments_y);
-    if mode != DisplayMode.NONE:
-        display_x = f'[{"][".join(alignments_x)}]';
-        display_y = f'[{"][".join(alignments_y)}]';
-        print(f'\n\x1b[1mOptimales Alignment:\x1b[0m');
-        print('');
-        print(display_y);
-        print(len(display_x) * '-');
-        print(display_x);
-        print('');
-    return word_x, word_y;
-
-def hirschberg_algorithm_step(
-    X: str,
-    Y: str,
-    depth: int = 0,
-    mode: DisplayMode = DisplayMode.NONE,
-) -> Tuple[List[str], List[str]]:
-    n = len(Y);
-    if n == 1:
-        Costs, Moves = compute_cost_matrix(X = '-' + X, Y = '-' + Y);
-        path = reconstruct_optimal_path(Moves=Moves);
-        word_x, word_y = reconstruct_words(X = '-' + X, Y = '-' + Y, moves=[Moves[coord] for coord in path], path=path);
-        # if verbose:
-        #     repr = display_cost_matrix(Costs=Costs, path=path, X = '-' + X, Y = '-' + Y);
-        #     print(f'\n\x1b[1mRekursionstiefe: {depth}\x1b[0m\n\n{repr}')
-        return [word_x], [word_y];
-    else:
-        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 = compute_cost_matrix(X = '-' + X1, Y = '-' + Y1);
-        Costs2, Moves2 = compute_cost_matrix(X = '-' + X2, Y = '-' + Y2);
-
-        if mode != DisplayMode.NONE:
-            path1, path2 = reconstruct_optimal_path_halves(Costs1=Costs1, Costs2=Costs2, Moves1=Moves1, Moves2=Moves2);
-            repr = display_cost_matrix_halves(
-                Costs1 = Costs1,
-                Costs2 = Costs2,
-                path1  = path1,
-                path2  = path2,
-                X1     =  '-' + X1,
-                X2     =  '-' + X2,
-                Y1     =  '-' + Y1,
-                Y2     =  '-' + Y2,
-                mode   = mode,
-            );
-            print(f'\n\x1b[1mRekursionstiefe: {depth}\x1b[0m\n\n{repr}')
-
-        # Koordinaten des optimalen Übergangs berechnen:
-        coord1, coord2 = get_optimal_transition(Costs1=Costs1, Costs2=Costs2);
-        p = coord1[0];
-        # Divide and Conquer ausführen:
-        alignments_x_1, alignments_y_1 = hirschberg_algorithm_step(X=X[:p], Y=Y[:n], depth=depth+1, verbose=verbose, mode=mode);
-        alignments_x_2, alignments_y_2 = hirschberg_algorithm_step(X=X[p:], Y=Y[n:], depth=depth+1, verbose=verbose, mode=mode);
-
-        # Resultate zusammensetzen:
-        alignments_x = alignments_x_1 + alignments_x_2;
-        alignments_y = alignments_y_1 + alignments_y_2;
-        if len(Y[:n]) <= 1 and len(Y[n:]) <= 1:
-            # falls linke + rechte Hälfte nur aus <= 1 Buchstsaben bestehen, bestehen Alignment aus nur einem Teil ---> führe zusammen:
-            alignments_x = [ ''.join(alignments_x) ];
-            alignments_y = [ ''.join(alignments_y) ];
-        return alignments_x, alignments_y;
-
-# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-# METHODS cost matrix + optimal paths
-# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-def compute_cost_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;
-
-# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-# METHODS optimaler treffpunkt
-# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-def get_optimal_transition(
-    Costs1: NDArray[(Any, Any), int],
-    Costs2: NDArray[(Any, Any), int],
-) -> Tuple[Tuple[int, int], Tuple[int, int]]:
-    '''
-    Rekonstruiere »Treffpunkt«, wo die Gesamtkosten minimiert sind.
-    Dieser Punkt stellt einen optimal Übergang für den Rekursionsschritt dar.
-    '''
-    (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 ]);
-    coord1 = info[index][1];
-    coord2 = info[index][2];
-    return coord1, coord2;
-
-# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-# METHODS reconstruction von words/paths
-# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-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]]]:
-    '''
-    Rekonstruiere optimale Pfad für Rekursionsschritt,
-    wenn horizontales Wort in 2 aufgeteilt wird.
-    '''
-    coord1, coord2 = get_optimal_transition(Costs1=Costs1, Costs2=Costs2);
-    path1 = reconstruct_optimal_path(Moves1, coord=coord1);
-    path2 = reconstruct_optimal_path(Moves2, coord=coord2);
-    return path1, path2;
-
-def reconstruct_words(
-    X: str,
-    Y: str,
-    moves: List[Directions],
-    path: List[Tuple[int, int]],
-) -> Tuple[str, str]:
-    word_x = '';
-    word_y = '';
-    for ((i, j), move) in zip(path, moves):
-        x = X[i];
-        y = Y[j];
-        match move:
-            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;
-
-# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-# AUXILIARY METHODS
-# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-def represent_cost_matrix(
-    Costs: NDArray[(Any, Any), int],
-    path: List[Tuple[int, int]],
-    X: str,
-    Y: str,
-    mode: DisplayMode,
-    pad: bool = False,
-) -> 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] = '|';
-
-    match mode:
-        case DisplayMode.MOVES:
-            table[3:(3+m), 3:(3+n)] = '.';
-            for (i, j) in path:
-                table[3 + i, 3 + j] = '*';
-        case DisplayMode.COSTS | DisplayMode.COSTS_AND_MOVES:
-            table[3:(3+m), 3:(3+n)] = Costs.copy();
-            if mode == DisplayMode.COSTS_AND_MOVES:
-                for (i, j) in path:
-                    table[3 + i, 3 + j] = f'{{{table[3 + i, 3 + j]}}}';
-
-    return table;
-
-def display_cost_matrix(
-    Costs: NDArray[(Any, Any), int],
-    path: List[Tuple[int, int]],
-    X: str,
-    Y: str,
-    mode: DisplayMode,
-) -> 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 = represent_cost_matrix(Costs=Costs, path=path, X=X, Y=Y, mode=mode);
-    # benutze pandas-Dataframe + tabulate, um schöner darzustellen:
-    repr = tabulate(pd.DataFrame(table), showindex=False, stralign='center', tablefmt='plain');
-    return 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,
-    mode: DisplayMode,
-) -> 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.
-    '''
-    table1 = represent_cost_matrix(Costs=Costs1, path=path1, X=X1, Y=Y1, mode=mode, pad=True);
-    table2 = represent_cost_matrix(Costs=Costs2, path=path2, X=X2, Y=Y2, mode=mode, pad=True);
-
-    # merge Taellen:
-    table = np.concatenate([table1[:, :-1], table2[::-1, ::-1]], axis=1);
-
-    # benutze pandas-Dataframe + tabulate, um schöner darzustellen:
-    repr = tabulate(pd.DataFrame(table), showindex=False, stralign='center', tablefmt='plain');
-    return repr;

code/python/src/thirdparty/types.py

@@ -5,6 +5,8 @@
 # IMPORTS
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
+from dataclasses import dataclass;
+from dataclasses import field;
 from enum import Enum;
 from types import TracebackType;
 from typing import Any;
@@ -25,6 +27,8 @@ from nptyping import NDArray;
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
 __all__ = [
+    'dataclass',
+    'field',
     'Enum',
     'TracebackType',
     'Any',

code/python/src/travel/naive.py

@@ -6,8 +6,8 @@
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
 from __future__ import annotations;
-from src.local.typing import *;
-from src.local.maths import *;
+from src.thirdparty.types import *;
+from src.thirdparty.maths import *;
 
 # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 # EXPORTS

code/python/tests/tests_graphs/test_tarjan.py

@@ -12,7 +12,7 @@ from pytest import lazy_fixture;
 from unittest import TestCase;
 from unittest.mock import patch;
 
-from src.local.typing import *;
+from src.thirdparty.types import *;
 from src.graphs.graph import *;
 from src.graphs.tarjan import *;