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So Tom, Dick & Harry showed up for an interview at the new grocery delivery startup.
There was a whiteboard, a laptop & a notebook, so they could use whatever makes them comfortable.
Tom's interview: The chief data scientist John Doe (JD) walked in.
JD. Lets talk about groceries.
Tom. Ok
You walk into a grocery store with a grocery bag and some cash, to buy groceries for a week.
1. your bag can hold ten pounds.
2. You have $100
3. You need about 2000 calories a day, so a weekly shopping trip is about 14,000 calories.
4. You must purchase at least 4 ounces of each grocery item.
Here's your dataset -
--- Calories Per Pound ---
Ham, 650 cals,
Lettuce, 70 cals
Cheese, 1670 cals
Tuna, 830 cals
Bread, 1300 cals
---- Price Per Pound ----
Ham, $4
Lettuce, $1.5
Cheese, $5
Tuna, $20
Bread, $1.20
Take your time, and list the number of ways you can buy your groceries.
JD walked out of the room.
Tom thought for a while.
Then he grabbed the laptop, opened up his favorite editor & wrote some code. When he was done -
The rest of the story is here
from ortools.linear_solver import pywraplp
def configure_variables(cfg, solver):
food = cfg['food']
minShop = cfg['minShop']
variable_list = [[]] * len(food)
for i in range(0, len(food)):
#you must buy at least minShop of each
variable_list[i] = solver.NumVar(minShop, solver.infinity(), str(food[i][0]))
return variable_list
def configure_constraints(cfg, solver, variable_list):
food = cfg['food']
maxWeight = cfg['maxWeight']
maxCost = cfg['maxCost']
minCals = cfg['minCals']
#Define the constraints
#Constraint 1: totalWeight<maxWeight
#ham + lettuce + cheese + tuna + bread <= maxWeight
constraint_list.append(solver.Constraint(0, maxWeight))
for i in range(0, len(food)):
#Constraint 2: totalPrice<=maxCost
constraint_list.append(solver.Constraint(0, maxCost))
for i in range(0, len(food)):
#Constraint 3: totalCalories>=minCals
constraint_list.append(solver.Constraint(minCals, minCals + 100))
for i in range(0, len(food)):
return constraint_list
def configure_objective(what, cfg, solver, variable_list, constraint_list):
food = cfg['food']
objective = solver.Objective()
if (what=='cost'):
# Define our objective: minimizing cost
for i in range(0, len(food)):
objective.SetCoefficient(variable_list[i], food[i][2])
# Define our objective: maximizing calories
for i in range(0, len(food)):
objective.SetCoefficient(variable_list[i], food[i][1])
# Define our objective: cutting on ham and cheese
for i in range(0, len(food)):
if (food[i][0] in ['ham','cheese']):
# Define our objective: cutting on ham, cheese and tuna
for i in range(0, len(food)):
if (food[i][0] in ['bread']):
# Define our objective: use all the money
for i in range(0, len(food)):
objective.SetCoefficient(variable_list[i], food[i][2])
return objective
def solve(solver):
result_status = solver.Solve()
return result_status
def print_solution(solver,result_status,variable_list,constraint_list):
if result_status == solver.OPTIMAL:
print('Successful solve.')
# The problem has an optimal solution.
print(('Problem solved in %f milliseconds' % solver.wall_time()))
# The objective value of the solution.
print(('Optimal objective value = %f' % solver.Objective().Value()))
# The value of each variable in the solution.
for variable in variable_list:
print(('%s = %f' % (, variable.solution_value())))
print(('Variable sum = %f' % var_sum));
print('Advanced usage:')
print(('Problem solved in %d iterations' % solver.iterations()))
for variable in variable_list:
print(('%s: reduced cost = %f' % (, variable.reduced_cost())))
activities = solver.ComputeConstraintActivities()
for i, constraint in enumerate(constraint_list):
print(('constraint %d: dual value = %f\n'
' activity = %f' %
(i, constraint.dual_value(), activities[constraint.index()])))
elif result_status == solver.INFEASIBLE:
print('No solution found.')
elif result_status == solver.POSSIBLE_OVERFLOW:
print('Some inputs are too large and may cause an integer overflow.')
def main(cfg, what):
solver = pywraplp.Solver('SolveSimpleSystem',pywraplp.Solver.GLOP_LINEAR_PROGRAMMING)
variable_list = configure_variables(cfg, solver)
constraint_list = configure_constraints(cfg, solver, variable_list)
objective = configure_objective(what, cfg, solver, variable_list, constraint_list)
result_status = solve(solver)
print_solution(solver, result_status, variable_list, constraint_list)
return {'variable_list':variable_list,
'constraint_list': constraint_list,
'result_status': result_status}
if __name__ == '__main__':
cfg = {'maxWeight': 10,
'maxCost': 100,
'minCals': 14000,
'minShop': 4/16.0, #16 ounces per pound
'food': [['ham',650, 4],