add project structure and Russll's method implementation

.gitignore

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+# Byte-compiled / optimized / DLL files
+__pycache__/
+*.py[cod]
+*$py.class
+
+# C extensions
+*.so
+
+vscode/
+
+# Distribution / packaging
+.Python
+build/
+develop-eggs/
+dist/
+downloads/
+eggs/
+.eggs/
+lib/
+lib64/
+parts/
+sdist/
+var/
+wheels/
+share/python-wheels/
+*.egg-info/
+.installed.cfg
+*.egg
+MANIFEST
+
+# PyInstaller
+#  Usually these files are written by a python script from a template
+#  before PyInstaller builds the exe, so as to inject date/other infos into it.
+*.manifest
+*.spec
+
+# Installer logs
+pip-log.txt
+pip-delete-this-directory.txt
+
+# Unit test / coverage reports
+htmlcov/
+.tox/
+.nox/
+.coverage
+.coverage.*
+.cache
+nosetests.xml
+coverage.xml
+*.cover
+*.py,cover
+.hypothesis/
+.pytest_cache/
+cover/
+
+# Translations
+*.mo
+*.pot
+
+# Django stuff:
+*.log
+local_settings.py
+db.sqlite3
+db.sqlite3-journal
+
+# Flask stuff:
+instance/
+.webassets-cache
+
+# Scrapy stuff:
+.scrapy
+
+# Sphinx documentation
+docs/_build/
+
+# PyBuilder
+.pybuilder/
+target/
+
+# Jupyter Notebook
+.ipynb_checkpoints
+
+# IPython
+profile_default/
+ipython_config.py
+
+# pyenv
+#   For a library or package, you might want to ignore these files since the code is
+#   intended to run in multiple environments; otherwise, check them in:
+# .python-version
+
+# pipenv
+#   According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control.
+#   However, in case of collaboration, if having platform-specific dependencies or dependencies
+#   having no cross-platform support, pipenv may install dependencies that don't work, or not
+#   install all needed dependencies.
+#Pipfile.lock
+
+# poetry
+#   Similar to Pipfile.lock, it is generally recommended to include poetry.lock in version control.
+#   This is especially recommended for binary packages to ensure reproducibility, and is more
+#   commonly ignored for libraries.
+#   https://python-poetry.org/docs/basic-usage/#commit-your-poetrylock-file-to-version-control
+#poetry.lock
+
+# pdm
+#   Similar to Pipfile.lock, it is generally recommended to include pdm.lock in version control.
+#pdm.lock
+#   pdm stores project-wide configurations in .pdm.toml, but it is recommended to not include it
+#   in version control.
+#   https://pdm.fming.dev/latest/usage/project/#working-with-version-control
+.pdm.toml
+.pdm-python
+.pdm-build/
+
+# PEP 582; used by e.g. github.com/David-OConnor/pyflow and github.com/pdm-project/pdm
+__pypackages__/
+
+# Celery stuff
+celerybeat-schedule
+celerybeat.pid
+
+# SageMath parsed files
+*.sage.py
+
+# Environments
+.env
+.venv
+env/
+venv/
+ENV/
+env.bak/
+venv.bak/
+
+# Spyder project settings
+.spyderproject
+.spyproject
+
+# Rope project settings
+.ropeproject
+
+# mkdocs documentation
+/site
+
+# mypy
+.mypy_cache/
+.dmypy.json
+dmypy.json
+
+# Pyre type checker
+.pyre/
+
+# pytype static type analyzer
+.pytype/
+
+# Cython debug symbols
+cython_debug/
+
+# PyCharm
+#  JetBrains specific template is maintained in a separate JetBrains.gitignore that can
+#  be found at https://github.com/github/gitignore/blob/main/Global/JetBrains.gitignore
+#  and can be added to the global gitignore or merged into this file.  For a more nuclear
+#  option (not recommended) you can uncomment the following to ignore the entire idea folder.
+#.idea/

main.py

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+import numpy as np
+from typing import Optional
+from enum import Enum
+
+# M constant
+M = 1_000_000
+
+
+class State(Enum):
+    SOLVED = 0
+    UNSOLVED = 1
+    UNAPPLICABLE = 2
+
+
+class Result:
+    solved: State
+    objective_function_value: Optional[np.int64]
+    solution: Optional[np.array]
+
+    def __init__(self,
+                 solved: State,
+                 objective_function_value: Optional[np.array] = None,
+                 solution: np.int64 = None):
+        self.solved = solved
+        self.objective_function_value = objective_function_value
+        self.solution = solution
+
+
+def NorthwestCorner(
+        S: np.array,
+        C: np.array,
+        D: np.array) -> Result:
+    # TODO Northwest corner method
+    pass
+
+
+def Vogel(
+        S: np.array,
+        C: np.array,
+        D: np.array) -> Result:
+    # TODO Vogel's method
+    pass
+
+
+def Russell(
+        S: np.array,
+        C: np.array,
+        D: np.array) -> Result:
+    selected = np.zeros(C.shape)
+    remaining_rows = np.ones(C.shape[0], dtype=bool)
+    remaining_cols = np.ones(C.shape[1], dtype=bool)
+    x_0 = np.zeros(C.shape)
+    while True:
+
+        mask = np.outer(remaining_rows, remaining_cols)
+
+        u = np.max(np.where(mask, C, -M), axis=1)
+        v = np.max(np.where(mask, C, -M), axis=0)
+        d = np.zeros(C.shape, dtype=np.int64)
+        for i in range(C.shape[0]):
+            for j in range(C.shape[1]):
+                if selected[i][j]:
+                    d[i][j] = M
+                else:
+                    d[i][j] = C[i][j] - u[i] - v[j]
+
+        i, j = np.unravel_index(np.argmin(d, axis=None), d.shape)
+
+        if (D[j] == 0):
+            break
+
+        if (S[i] >= D[j]):
+            x_0[i][j] = D[j]
+            S[i] -= D[j]
+            D[j] = 0
+            remaining_cols[j] = 0
+        else:
+            x_0[i][j] = S[i]
+            D[j] -= S[i]
+            S[i] = 0
+            remaining_rows[i] = 0
+        selected[i][j] = 1
+    return x_0
+
+
+def print_problem_statement(S, C, D) -> None:
+    # TODO print table
+    pass
+
+
+def solve(
+        S: np.array,
+        C: np.array,
+        D: np.array) -> int:
+
+    print_problem_statement(S, C, D)
+
+    if (np.sum(S) != np.sum(D)):
+        print("The problem is not balanced!")
+        return 1
+
+    result1 = NorthwestCorner(S, C, D)
+    result2 = Vogel(S, C, D)
+    result3 = Russell(S, C, D)
+
+    # TODO check for state (unappicable?)
+
+    print(result1.solution, result2.solution, result3.solution)
+    return 0
+
+
+if __name__ == "__main__":
+    C = np.array([
+        [16, 16, 13, 22, 17],
+        [14, 14, 13, 19, 15],
+        [19, 19, 20, 23, M],
+        [M, 0, M, 0, 0]
+    ], dtype=np.int64)
+
+    S = np.array([
+        50, 60, 50, 50
+    ])
+
+    D = np.array([
+        30, 20, 70, 30, 60
+    ])
+
+    print(Russell(S, C, D))