add project structure and Russll's method implementation

main.py

@@ -0,0 +1,128 @@
+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))