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