from pulp import *

# Create the problem
prob = LpProblem("Hospital Staffing", LpMinimize)

# Create a list of doctors
doctors = [i for i in range(50)]  # Choosing value big enough

# Create a list of days
days = ["Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday", "Sunday"]

# Define the demand for each day of the week
req_doctors = {"Monday": 16, "Tuesday": 12, "Wednesday": 18, "Thursday": 13, "Friday": 15, "Saturday": 9, "Sunday": 7}

# Create the decision variables
# Each doctor i starts their 3-day shift on day j
x = LpVariable.dicts("Doctors", (range(len(doctors)), range(7)), 0, 1, LpBinary)

# Set the objective function
prob += lpSum(x[i][j] for i in range(len(doctors)) for j in range(7))

# Minimum number of doctors for each day
# For each day of the week, we count doctor as available not only on the start day of their shift but also on the two next days
for j in range(7):
    prob += lpSum(x[i][(j-k)%7] for i in range(len(doctors)) for k in range(3)) >= req_doctors[days[j]]

# Doctor can only start their 3-day work shift once in a week
for i in range(len(doctors)):
    prob += lpSum(x[i][j] for j in range(7)) <= 1

# Solve the problem
prob.solve()

print("Status:", LpStatus[prob.status])

work_schedule = {day: [] for day in days}

for i in range(len(doctors)):
    for j in range(7):
        if x[i][j].varValue > 0:
            for k in range(3):
                work_day = days[(j + k) % 7]
                work_schedule[work_day].append("Doctor " + str(i))

for day in days:
    print(day + ":")
    for doctor in work_schedule[day]:
        print(doctor)
    print()

print("Total number of doctors = ", value(prob.objective))