test.py

from pulp import LpInteger
from pulp import LpMaximize
from pulp import LpProblem
from pulp import LpVariable


def maximize_score(A_total, B_total, C_total, D_total):
    prob = LpProblem("MaximizeScore", LpMaximize)

    # Define helper function to create variables for single-resource conversions
    def resource_vars(name_prefix):
        # Returns variables for 10-set, 4-set, and single-unit usage
        return (
            LpVariable(f"{name_prefix}_10", lowBound=0, cat=LpInteger),
            LpVariable(f"{name_prefix}_4", lowBound=0, cat=LpInteger),
            LpVariable(f"{name_prefix}_1", lowBound=0, cat=LpInteger),
        )

    # Variables for combinations
    x1 = LpVariable("combo1", lowBound=0, cat=LpInteger)  # A3+B3+C3+D3 = 30 points
    x2 = LpVariable("combo2", lowBound=0, cat=LpInteger)  # A2+B2+C2+D2 = 18 points
    x3 = LpVariable("combo3", lowBound=0, cat=LpInteger)  # A1+B1+C1+D1 = 8 points
    x4 = LpVariable("combo4", lowBound=0, cat=LpInteger)  # A1+D1 = 5 points
    x5 = LpVariable("combo5", lowBound=0, cat=LpInteger)  # A1+C2 = 8 points
    x6 = LpVariable("combo6", lowBound=0, cat=LpInteger)  # D1+B2 = 8 points

    # Resource conversion variables
    A_10, A_4, A_1 = resource_vars("A")
    B_10, B_4, B_1 = resource_vars("B")
    C_10, C_4, C_1 = resource_vars("C")
    D_10, D_4, D_1 = resource_vars("D")

    # Objective function
    # Combos:
    # x1: 30 pts, x2: 18 pts, x3: 8 pts, x4: 5 pts, x5: 8 pts, x6: 8 pts
    # Resource conversions:
    # Each 10-same-resource: 30 pts, each 4-same-resource: 10 pts, each single: 1 pt
    prob += (
        30 * x1
        + 18 * x2
        + 8 * x3
        + 5 * x4
        + 8 * x5
        + 8 * x6
        + 30 * (A_10 + B_10 + C_10 + D_10)
        + 10 * (A_4 + B_4 + C_4 + D_4)
        + (A_1 + B_1 + C_1 + D_1)
    )

    # Constraints for resource usage:
    # A resource
    prob += (
        3 * x1 + 2 * x2 + 1 * x3 + 1 * x4 + 1 * x5 + 0 * x6 + 10 * A_10 + 4 * A_4 + A_1 <= A_total
    )
    # B resource
    prob += (
        3 * x1 + 2 * x2 + 1 * x3 + 0 * x4 + 0 * x5 + 2 * x6 + 10 * B_10 + 4 * B_4 + B_1 <= B_total
    )
    # C resource
    prob += (
        3 * x1 + 2 * x2 + 1 * x3 + 0 * x4 + 2 * x5 + 0 * x6 + 10 * C_10 + 4 * C_4 + C_1 <= C_total
    )
    # D resource
    prob += (
        3 * x1 + 2 * x2 + 1 * x3 + 1 * x4 + 0 * x5 + 1 * x6 + 10 * D_10 + 4 * D_4 + D_1 <= D_total
    )

    # Solve the problem
    prob.solve()

    # Extract results
    result = {
        "Status": prob.status,
        "Objective": prob.objective.value(),
        "combo1": x1.varValue,
        "combo2": x2.varValue,
        "combo3": x3.varValue,
        "combo4": x4.varValue,
        "combo5": x5.varValue,
        "combo6": x6.varValue,
        "A_10": A_10.varValue,
        "A_4": A_4.varValue,
        "A_1": A_1.varValue,
        "B_10": B_10.varValue,
        "B_4": B_4.varValue,
        "B_1": B_1.varValue,
        "C_10": C_10.varValue,
        "C_4": C_4.varValue,
        "C_1": C_1.varValue,
        "D_10": D_10.varValue,
        "D_4": D_4.varValue,
        "D_1": D_1.varValue,
    }
    return result


def print_solution(result):
    if result["Status"] != 1:
        print("No optimal solution found.")
        return

    print("Optimal solution found!")
    print(f"Total Score: {result['Objective']:.0f}")
    print("\nCombinations chosen (and their scoring):")
    combo_info = {
        "combo1": ("A3 + B3 + C3 + D3 => 30 pts", 30),
        "combo2": ("A2 + B2 + C2 + D2 => 18 pts", 18),
        "combo3": ("A1 + B1 + C1 + D1 => 8 pts", 8),
        "combo4": ("A1 + D1 => 5 pts", 5),
        "combo5": ("A1 + C2 => 8 pts", 8),
        "combo6": ("D1 + B2 => 8 pts", 8),
    }

    for combo in combo_info:
        qty = result[combo]
        if qty > 0:
            desc, pts = combo_info[combo]
            total_pts = pts * qty
            print(f"  {combo} x{int(qty)}: {desc}, total {total_pts} pts")

    print("\nSingle-resource conversions (and their scoring):")
    print("  10 of the same resource = 30 pts")
    print("   4 of the same resource = 10 pts")
    print("   1 of the same resource = 1 pt")
    for res in ["A", "B", "C", "D"]:
        used_10 = int(result[f"{res}_10"]) if result[f"{res}_10"] else 0
        used_4 = int(result[f"{res}_4"]) if result[f"{res}_4"] else 0
        used_1 = int(result[f"{res}_1"]) if result[f"{res}_1"] else 0
        if used_10 or used_4 or used_1:
            score_10 = used_10 * 30
            score_4 = used_4 * 10
            score_1 = used_1 * 1
            total_res_score = score_10 + score_4 + score_1
            print(
                f"  {res}: 10-sets={used_10} (=>{score_10} pts), 4-sets={used_4} (=>{score_4} pts), singles={used_1} (=>{score_1} pts), total {total_res_score} pts"
            )


results = maximize_score(17, 13, 16, 12)
print_solution(results)