c34026b101
note: done using ```sh git grep -l "2010-2024 Google" | xargs sed -i 's/2010-2024 Google/2010-2025 Google/' ```
96 lines
2.9 KiB
Python
Executable File
96 lines
2.9 KiB
Python
Executable File
#!/usr/bin/env python3
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# Copyright 2010-2025 Google LLC
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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"""We are trying to group items in equal sized groups.
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Each item has a color and a value. We want the sum of values of each group to
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be as close to the average as possible.
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Furthermore, if one color is an a group, at least k items with this color must
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be in that group."""
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from ortools.linear_solver import pywraplp
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# Data
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max_quantities = [
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["N_Total", 1944],
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["P2O5", 1166.4],
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["K2O", 1822.5],
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["CaO", 1458],
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["MgO", 486],
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["Fe", 9.7],
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["B", 2.4],
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]
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chemical_set = [
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["A", 0, 0, 510, 540, 0, 0, 0],
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["B", 110, 0, 0, 0, 160, 0, 0],
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["C", 61, 149, 384, 0, 30, 1, 0.2],
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["D", 148, 70, 245, 0, 15, 1, 0.2],
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["E", 160, 158, 161, 0, 10, 1, 0.2],
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]
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NUM_PRODUCTS = len(max_quantities)
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ALL_PRODUCTS = range(NUM_PRODUCTS)
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NUM_SETS = len(chemical_set)
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ALL_SETS = range(NUM_SETS)
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# Model
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max_set = [
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min(max_quantities[q][1] / chemical_set[s][q + 1] for q in ALL_PRODUCTS
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if chemical_set[s][q + 1] != 0.0) for s in ALL_SETS
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]
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solver = pywraplp.Solver("chemical_set_lp",
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pywraplp.Solver.GLOP_LINEAR_PROGRAMMING)
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set_vars = [solver.NumVar(0, max_set[s], f"set_{s}") for s in ALL_SETS]
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epsilon = solver.NumVar(0, 1000, "epsilon")
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for p in ALL_PRODUCTS:
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solver.Add(
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sum(chemical_set[s][p + 1] * set_vars[s]
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for s in ALL_SETS) <= max_quantities[p][1])
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solver.Add(
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sum(chemical_set[s][p + 1] * set_vars[s]
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for s in ALL_SETS) >= max_quantities[p][1] - epsilon)
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solver.Minimize(epsilon)
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print(f"Number of variables = {solver.NumVariables()}")
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print(f"Number of constraints = {solver.NumConstraints()}")
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result_status = solver.Solve()
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# The problem has an optimal solution.
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assert result_status == pywraplp.Solver.OPTIMAL
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assert solver.VerifySolution(1e-7, True)
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print(f"Problem solved in {solver.wall_time()} milliseconds")
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# The objective value of the solution.
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print(f"Optimal objective value = {solver.Objective().Value()}")
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for s in ALL_SETS:
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print(f" {chemical_set[s][0]} = {set_vars[s].solution_value()}", end=" ")
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print()
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for p in ALL_PRODUCTS:
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name = max_quantities[p][0]
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max_quantity = max_quantities[p][1]
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quantity = sum(set_vars[s].solution_value() * chemical_set[s][p + 1]
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for s in ALL_SETS)
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print(f"{name}: {quantity} out of {max_quantity}")
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