I'm tackling with VRPtw problem and struggling that the solver finds no solution with any data except for artificial small one.
The setting is as below.
There are several depots and locations to visit. Each locations have the time-window. Each vehicles have break time and work time. Also, the locations have some constraints and only the vehicles which satisfy that demand can visit there.
Based on this experiment setting, I wrote the code below.
As I wrote, it looks that it is working with small artificial data, but with real data, it never found the solution. I tried with 5 different data sets.
Although I set the 7200 sec time limit, previously I ran for longer than 10 hours and it was same.
The data's scale is 40~50 vehicles and 200~300 locations.
Does this code have a problem? If not, on what kind of order, should I change the approach(such as initialization, searching method and so on)?
(Edited to use integer for time matrix)
from dataclasses import dataclass
from typing import List, Tuple
from ortools.constraint_solver import pywrapcp
from ortools.constraint_solver import routing_enums_pb2
# TODO: Refactor
BIG_ENOUGH = 100000000
TIME_DIMENSION = 'Time'
TIME_LIMIT = 7200
#dataclass
class DataSet:
time_matrix: List[List[int]]
locations_num: int
vehicles_num: int
vehicles_break_time_window: List[Tuple[int, int, int]]
vehicles_work_time_windows: List[Tuple[int, int]]
location_time_windows: List[Tuple[int, int]]
vehicles_depots_indices: List[int]
possible_vehicles: List[List[int]]
def execute(data: DataSet):
manager = pywrapcp.RoutingIndexManager(data.locations_num,
data.vehicles_num,
data.vehicles_depots_indices,
data.vehicles_depots_indices)
routing_parameters = pywrapcp.DefaultRoutingModelParameters()
routing_parameters.solver_parameters.trace_propagation = True
routing_parameters.solver_parameters.trace_search = True
routing = pywrapcp.RoutingModel(manager, routing_parameters)
def time_callback(source_index, dest_index):
from_node = manager.IndexToNode(source_index)
to_node = manager.IndexToNode(dest_index)
return data.time_matrix[from_node][to_node]
transit_callback_index = routing.RegisterTransitCallback(time_callback)
routing.SetArcCostEvaluatorOfAllVehicles(transit_callback_index)
routing.AddDimension(
transit_callback_index,
BIG_ENOUGH,
BIG_ENOUGH,
False,
TIME_DIMENSION)
time_dimension = routing.GetDimensionOrDie(TIME_DIMENSION)
# set time window for locations start time
# set condition restrictions
possible_vehicles = data.possible_vehicles
for location_idx, time_window in enumerate(data.location_time_windows):
index = manager.NodeToIndex(location_idx + data.vehicles_num)
time_dimension.CumulVar(index).SetRange(time_window[0], time_window[1])
routing.SetAllowedVehiclesForIndex(possible_vehicles[location_idx], index)
solver = routing.solver()
for i in range(data.vehicles_num):
routing.AddVariableMinimizedByFinalizer(
time_dimension.CumulVar(routing.Start(i)))
routing.AddVariableMinimizedByFinalizer(
time_dimension.CumulVar(routing.End(i)))
# set work time window for vehicles
for vehicle_index, work_time_window in enumerate(data.vehicles_work_time_windows):
start_index = routing.Start(vehicle_index)
time_dimension.CumulVar(start_index).SetRange(work_time_window[0],
work_time_window[0])
end_index = routing.End(vehicle_index)
time_dimension.CumulVar(end_index).SetRange(work_time_window[1],
work_time_window[1])
# set break time for vehicles
node_visit_transit = {}
for n in range(routing.Size()):
if n >= data.locations_num:
node_visit_transit[n] = 0
else:
node_visit_transit[n] = 1
break_intervals = {}
for v in range(data.vehicles_num):
vehicle_break = data.vehicles_break_time_window[v]
break_intervals[v] = [
solver.FixedDurationIntervalVar(vehicle_break[0],
vehicle_break[1],
vehicle_break[2],
True,
'Break for vehicle {}'.format(v))
]
time_dimension.SetBreakIntervalsOfVehicle(
break_intervals[v], v, node_visit_transit
)
search_parameters = pywrapcp.DefaultRoutingSearchParameters()
search_parameters.first_solution_strategy = (
routing_enums_pb2.FirstSolutionStrategy.PATH_CHEAPEST_ARC)
search_parameters.local_search_metaheuristic = (
routing_enums_pb2.LocalSearchMetaheuristic.GREEDY_DESCENT)
search_parameters.time_limit.seconds = TIME_LIMIT
search_parameters.log_search = True
solution = routing.SolveWithParameters(search_parameters)
return solution
if __name__ == '__main__':
data = DataSet(
time_matrix=[[0, 0, 4, 5, 5, 6],
[0, 0, 6, 4, 5, 5],
[1, 3, 0, 6, 5, 4],
[2, 1, 6, 0, 5, 4],
[2, 2, 5, 5, 0, 6],
[3, 2, 4, 4, 6, 0]],
locations_num=6,
vehicles_num=2,
vehicles_depots_indices=[0, 1],
vehicles_work_time_windows=[(720, 1080), (720, 1080)],
vehicles_break_time_window=[(720, 720, 15), (720, 720, 15)],
location_time_windows=[(735, 750), (915, 930), (915, 930), (975, 990)],
possible_vehicles=[[0], [1], [0], [1]]
)
solution = execute(data)
if solution is not None:
print("solution is found")
Related
I am trying to perform the following operation in Polars.
For value in column B which is below 80 will be scaled between 1 and 4, where as for anything above 80, will be set as 5.
df_pandas = pd.DataFrame(
{
"A": [1, 2, 3, 4, 5, 6, 7, 8, 9, 10],
"B": [50, 300, 80, 12, 105, 78, 66, 42, 61.5, 35],
}
)
test_scaler = MinMaxScaler(feature_range=(1,4)) # from sklearn.preprocessing
df_pandas.loc[df_pandas['B']<80, 'Test'] = test_scaler.fit_transform(df_pandas.loc[df_pandas['B']<80, "B"].values.reshape(-1,1))
df_pandas = df_pandas.fillna(5)
This is what I did with Polars:
# dt is a dictionary
dt = df.filter(
pl.col('B')<80
).to_dict(as_series=False)
below_80 = list(dt.keys())
dt_scale = list(
test_scaler.fit_transform(
np.array(dt['B']).reshape(-1,1)
).reshape(-1) # reshape back to one dimensional
)
# reassign to dictionary dt
dt['B'] = dt_scale
dt_scale_df = pl.DataFrame(dt)
dt_scale_df
dummy = df.join(
dt_scale_df, how="left", on="A"
).fill_null(5)
dummy = dummy.rename({"B_right": "Test"})
Result:
A
B
Test
1
50.0
2.727273
2
300.0
5.000000
3
80.0
5.000000
4
12.0
1.000000
5
105.0
5.000000
6
78.0
4.000000
7
66.0
3.454545
8
42.0
2.363636
9
61.5
3.250000
10
35.0
2.045455
Is there a better approach for this?
Alright, I have got 3 examples for you that should help you from which the last should be preferred.
Because you only want to apply your scaler to a part of a column, we should ensure we only send that part of the data to the scaler. This can be done by:
window function over a partition
partition_by
when -> then -> otherwise + min_max expression
Window function over partititon
This requires a python function that will be applied over the partitions. In the function itself we then have to check in which partition we are and deal with it accordingly.
df = pl.from_pandas(df_pandas)
min_max_sc = MinMaxScaler((1, 4))
def my_scaler(s: pl.Series) -> pl.Series:
if s.len() > 0 and s[0] > 80:
out = (s * 0 + 5)
else:
out = pl.Series(min_max_sc.fit_transform(s.to_numpy().reshape(-1, 1)).flatten())
# ensure all types are the same
return out.cast(pl.Float64)
df.with_column(
pl.col("B").apply(my_scaler).over(pl.col("B") < 80).alias("Test")
)
partition_by
This partitions the the original dataframe to a dictionary holding the different partitions. We then only modify the partitions as needed.
parts = (df
.with_column((pl.col("B") < 80).alias("part"))
.partition_by("part", as_dict=True)
)
parts[True] = parts[True].with_column(
pl.col("B").map(
lambda s: pl.Series(min_max_sc.fit_transform(s.to_numpy().reshape(-1, 1)).flatten())
).alias("Test")
)
parts[False] = parts[False].with_column(
pl.lit(5.0).alias("Test")
)
pl.concat([df for df in parts.values()]).select(pl.all().exclude("part"))
when -> then -> otherwise + min_max expression
This one I like best. We can make function that creates a polars expression that is the min_max scaling function you need. This will have best performance.
def min_max_scaler(col: str, predicate: pl.Expr):
x = pl.col(col)
x_min = x.filter(predicate).min()
x_max = x.filter(predicate).max()
# * 3 + 1 to set scale between 1 - 4
return (x - x_min) / (x_max - x_min) * 3 + 1
predicate = pl.col("B") < 80
df.with_column(
pl.when(predicate)
.then(min_max_scaler("B", predicate))
.otherwise(5).alias("Test")
)
this is my first time creating a FFN to train it to translate French to English using word prediction:
Input are two arrays of size 2 x window_size + 1 from source language and window_size target language. And the label of size 1
For e.g for window_size = 2:
["je","mange", "la", "pomme","avec"]
and
["I", "eat"]
So the input of size [5] and [2] after concatenating => 7
Label: "the" (refering to "la" in French)
The label is changed to one-hot-encoding before comparing with yHat
I'm using unique index for each word ( 1 to len(vocab) ) and train using the index (not the words)
The output of the FFN is a probability of the size of the vocab of the target language
The problem is that the FFN doesn't learn and the accuracy stays at 0.
When I print the size of y_final (target probability) and yHat (Model Hypo) they have different dimensions:
yHat.size()=[512, 7, 10212]
with 64 batch_size, 7 is the concatenated input size and 10212 size of target vocab, while
y_final.size()= [512, 10212]
And over all the forward method I have these sizes:
torch.Size([512, 5, 32])
torch.Size([512, 5, 64])
torch.Size([512, 5, 64])
torch.Size([512, 2, 256])
torch.Size([512, 2, 32])
torch.Size([512, 2, 64])
torch.Size([512, 2, 64])
torch.Size([512, 7, 64])
torch.Size([512, 7, 128])
torch.Size([512, 7, 10212])
Since the accuracy augments when yHat = y_final then I thought that it is never the case because they don't even have the same shapes (2D vs 3D). Is this the problem ?
Please refer to the code and if you need any other info please tell me.
The code is working fine, no errors.
trainingData = TensorDataset(encoded_source_windows, encoded_target_windows, encoded_labels)
# print(trainingData)
batchsize = 512
trainingLoader = DataLoader(trainingData, batch_size=batchsize, drop_last=True)
def ffnModel(vocabSize1,vocabSize2, learningRate=0.01):
class ffNetwork(nn.Module):
def __init__(self):
super().__init__()
self.embeds_src = nn.Embedding(vocabSize1, 256)
self.embeds_target = nn.Embedding(vocabSize2, 256)
# input layer
self.inputSource = nn.Linear(256, 32)
self.inputTarget = nn.Linear(256, 32)
# hidden layer 1
self.fc1 = nn.Linear(32, 64)
self.bnormS = nn.BatchNorm1d(5)
self.bnormT = nn.BatchNorm1d(2)
# Layer(s) afer Concatenation:
self.fc2 = nn.Linear(64,128)
self.output = nn.Linear(128, vocabSize2)
self.softmaaax = nn.Softmax(dim=0)
# forward pass
def forward(self, xSource, xTarget):
xSource = self.embeds_src(xSource)
xSource = F.relu(self.inputSource(xSource))
xSource = F.relu(self.fc1(xSource))
xSource = self.bnormS(xSource)
xTarget = self.embeds_target(xTarget)
xTarget = F.relu(self.inputTarget(xTarget))
xTarget = F.relu(self.fc1(xTarget))
xTarget = self.bnormT(xTarget)
xCat = torch.cat((xSource, xTarget), dim=1)#dim=128 or 1 ?
xCat = F.relu(self.fc2(xCat))
print(xCat.size())
xCat = self.softmaaax(self.output(xCat))
return xCat
# creating instance of the class
net = ffNetwork()
# loss function
lossfun = nn.CrossEntropyLoss()
# lossfun = nn.NLLLoss()
optimizer = torch.optim.Adam(net.parameters(), lr=learningRate)
return net, lossfun, optimizer
def trainModel(vocabSize1,vocabSize2, learningRate):
# number of epochs
numepochs = 64
# create a new Model instance
net, lossfun, optimizer = ffnModel(vocabSize1,vocabSize2, learningRate)
# initialize losses
losses = torch.zeros(numepochs)
trainAcc = []
# loop over training data batches
batchAcc = []
batchLoss = []
for epochi in range(numepochs):
#Switching on training mode
net.train()
# loop over training data batches
batchAcc = []
batchLoss = []
for A, B, y in tqdm(trainingLoader):
# forward pass and loss
final_y = []
for i in range(y.size(dim=0)):
yy = [0] * target_vocab_length
yy[y[i]] = 1
final_y.append(yy)
final_y = torch.tensor(final_y)
yHat = net(A, B)
loss = lossfun(yHat, final_y)
################
print("\n yHat.size()")
print(yHat.size())
print("final_y.size()")
print(final_y.size())
# backprop
optimizer.zero_grad()
loss.backward()
optimizer.step()
# loss from this batch
batchLoss.append(loss.item())
print(f'batchLoss: {loss.item()}')
#Accuracy calculator:
matches = torch.argmax(yHat) == final_y # booleans (false/true)
matchesNumeric = matches.float() # convert to numbers (0/1)
accuracyPct = 100 * torch.mean(matchesNumeric) # average and x100
batchAcc.append(accuracyPct) # add to list of accuracies
print(f'accuracyPct: {accuracyPct}')
trainAcc.append(np.mean(batchAcc))
losses[epochi] = np.mean(batchLoss)
return trainAcc,losses,net
trainAcc,losses,net = trainModel(len(source_vocab),len(target_vocab), 0.01)
print(trainAcc)
I have a single trained classifier tested on 2 related multiclass classification tasks. As each trial of the classification tasks are related, the 2 sets of predictions constitute paired data. I would like to run a paired permutation test to find out if the difference in classification accuracy between the 2 prediction sets is significant.
So my data consists of 2 lists of predicted classes, where each prediction is related to the prediction in the other test set at the same index.
Example:
actual_classes = [1, 3, 6, 1, 22, 1, 11, 12, 9, 2]
predictions1 = [1, 3, 6, 1, 22, 1, 11, 12, 9 10] # 90% acc.
predictions2 = [1, 3, 7, 10, 22, 1, 7, 12, 2, 10] # 50% acc.
H0: There is no significant difference in classification accuracy.
How do I go about running a paired permutation test to test significance of the difference in classification accuracy?
I have been thinking about this and I'm going to post a proposed solution and see if someone approves or explains why I'm wrong.
actual_classes = [1, 3, 6, 1, 22, 1, 11, 12, 9, 2]
predictions1 = [1, 3, 6, 1, 22, 1, 11, 12, 9 10] # 90% acc.
predictions2 = [1, 3, 7, 10, 22, 1, 7, 12, 2, 10] # 50% acc.
paired_predictions = [[1,1], [3,3], [6,7], [1,10], [22,22], [1,1], [11,7], [12,12], [9,2], [10,10]]
actual_test_statistic = predictions1 - predictions2 # 90%-50%=40 # 0.9-0.5=0.4
all_simulations = [] # empty list
for number_of_iterations:
shuffle(paired_predictions) # only shuffle between pairs, not within
simulated_predictions1 = paired_predictions[first prediction of each pair]
simulated_predictions2 = paired_predictions[second prediction of each pair]
simulated_accuracy1 = proportion of times simulated_predictions1 equals actual_classes
simulated_accuracy2 = proportion of times simulated_predictions2 equals actual_classes
all_simulations.append(simulated_accuracy1 - simulated_accuracy2) # Put the simulated difference in the list
p = count(absolute(all_simulations) > absolute(actual_test_statistic ))/number_of_iterations
If you have any thoughts, let me know in the comments. Or better still, provide your own corrected version in your own answer. Thank you!
I am new to constraint programming and OR-Tools. A brief about the problem. There are 8 positions, for each position I need to decide which move of type A (move_A) and which move of type B (move_B) should be selected such that the value achieved from the combination of the 2 moves (at each position) is maximized. (This is only a part of the bigger problem though). And I want to use AddElement approach to do the sub setting.
Please see the below attempt
from ortools.sat.python import cp_model
model = cp_model.CpModel()
# value achieved from combination of different moves of type A
# (moves_A (rows)) and different moves of type B (moves_B (columns))
# for e.g. 2nd move of type A and 3rd move of type B will give value = 2
value = [
[ -1, 5, 3, 2, 2],
[ 2, 4, 2, -1, 1],
[ 4, 4, 0, -1, 2],
[ 5, 1, -1, 2, 2],
[ 0, 0, 0, 0, 0],
[ 2, 1, 1, 2, 0]
]
# 6 moves of type A
num_moves_A = len(value)
# 5 moves of type B
num_moves_B = len(value[0])
num_positions = 8
type_move_A_position = [model.NewIntVar(0, num_moves_A - 1, f"move_A[{i}]") for i in range(num_positions)]
type_move_B_position = [model.NewIntVar(0, num_moves_B - 1, f"move_B[{i}]") for i in range(num_positions)]
value_position = [model.NewIntVar(0, 10, f"value_position[{i}]") for i in range(num_positions)]
# I am getting an error when I run the below
objective_terms = []
for i in range(num_positions):
model.AddElement(type_move_B_position[i], value[type_move_A_position[i]], value_position[i])
objective_terms.append(value_position[i])
The error is as follows:
Traceback (most recent call last):
File "<ipython-input-65-3696379ce410>", line 3, in <module>
model.AddElement(type_move_B_position[i], value[type_move_A_position[i]], value_position[i])
TypeError: list indices must be integers or slices, not IntVar
In MiniZinc the below code would have worked
var int: obj = sum(i in 1..num_positions ) (value [type_move_A_position[i], type_move_B_position[i]])
I know in OR-Tools we will have to create some intermediary variables to store results first, so the above approach of minizinc will not work. But I am struggling to do so.
I can always create a 2 matrix of binary binary variables one for num_moves_A * num_positions and the other for num_moves_B * num_positions, add re;evant constraints and achieve the purpose
But I want to learn how to do the same thing via AddElement constraint
Any help on how to re-write the AddElement snippet is highly appreciated. Thanks.
AddElement is 1D only.
The way it is translated from minizinc to CP-SAT is to create an intermediate variable p == index1 * max(index2) + index2 and use it in an element constraint with a flattened matrix.
Following Laurent's suggestion (using AddElement constraint):
from ortools.sat.python import cp_model
model = cp_model.CpModel()
# value achieved from combination of different moves of type A
# (moves_A (rows)) and different moves of type B (moves_B (columns))
# for e.g. 2 move of type A and 3 move of type B will give value = 2
value = [
[-1, 5, 3, 2, 2],
[2, 4, 2, -1, 1],
[4, 4, 0, -1, 2],
[5, 1, -1, 2, 2],
[0, 0, 0, 0, 0],
[2, 1, 1, 2, 0],
]
min_value = min([min(i) for i in value])
max_value = max([max(i) for i in value])
# 6 moves of type A
num_moves_A = len(value)
# 5 moves of type B
num_moves_B = len(value[0])
# number of positions
num_positions = 5
# flattened matrix of values
value_flat = [value[i][j] for i in range(num_moves_A) for j in range(num_moves_B)]
# flattened indices
flatten_indices = [
index1 * len(value[0]) + index2
for index1 in range(len(value))
for index2 in range(len(value[0]))
]
type_move_A_position = [
model.NewIntVar(0, num_moves_A - 1, f"move_A[{i}]") for i in range(num_positions)
]
model.AddAllDifferent(type_move_A_position)
type_move_B_position = [
model.NewIntVar(0, num_moves_B - 1, f"move_B[{i}]") for i in range(num_positions)
]
model.AddAllDifferent(type_move_B_position)
# below intermediate decision variable is created which
# will store index corresponding to the selected move of type A and
# move of type B for each position
# this will act as index in the AddElement constraint
flatten_index_num = [
model.NewIntVar(0, len(flatten_indices), f"flatten_index_num[{i}]")
for i in range(num_positions)
]
# another intermediate decision variable is created which
# will store value corresponding to the selected move of type A and
# move of type B for each position
# this will act as the target in the AddElement constraint
value_position_index_num = [
model.NewIntVar(min_value, max_value, f"value_position_index_num[{i}]")
for i in range(num_positions)
]
objective_terms = []
for i in range(num_positions):
model.Add(
flatten_index_num[i]
== (type_move_A_position[i] * len(value[0])) + type_move_B_position[i]
)
model.AddElement(flatten_index_num[i], value_flat, value_position_index_num[i])
objective_terms.append(value_position_index_num[i])
model.Maximize(sum(objective_terms))
# Solve
solver = cp_model.CpSolver()
status = solver.Solve(model)
solver.ObjectiveValue()
for i in range(num_positions):
print(
str(i)
+ "--"
+ str(solver.Value(type_move_A_position[i]))
+ "--"
+ str(solver.Value(type_move_B_position[i]))
+ "--"
+ str(solver.Value(value_position_index_num[i]))
)
The below version uses AddAllowedAssignments constraint to achieve the same purpose (per Laurent's alternate approach) :
from ortools.sat.python import cp_model
model = cp_model.CpModel()
# value achieved from combination of different moves of type A
# (moves_A (rows)) and different moves of type B (moves_B (columns))
# for e.g. 2 move of type A and 3 move of type B will give value = 2
value = [
[-1, 5, 3, 2, 2],
[2, 4, 2, -1, 1],
[4, 4, 0, -1, 2],
[5, 1, -1, 2, 2],
[0, 0, 0, 0, 0],
[2, 1, 1, 2, 0],
]
min_value = min([min(i) for i in value])
max_value = max([max(i) for i in value])
# 6 moves of type A
num_moves_A = len(value)
# 5 moves of type B
num_moves_B = len(value[0])
# number of positions
num_positions = 5
type_move_A_position = [
model.NewIntVar(0, num_moves_A - 1, f"move_A[{i}]") for i in range(num_positions)
]
model.AddAllDifferent(type_move_A_position)
type_move_B_position = [
model.NewIntVar(0, num_moves_B - 1, f"move_B[{i}]") for i in range(num_positions)
]
model.AddAllDifferent(type_move_B_position)
value_position = [
model.NewIntVar(min_value, max_value, f"value_position[{i}]")
for i in range(num_positions)
]
tuples_list = []
for i in range(num_moves_A):
for j in range(num_moves_B):
tuples_list.append((i, j, value[i][j]))
for i in range(num_positions):
model.AddAllowedAssignments(
[type_move_A_position[i], type_move_B_position[i], value_position[i]],
tuples_list,
)
model.Maximize(sum(value_position))
# Solve
solver = cp_model.CpSolver()
status = solver.Solve(model)
solver.ObjectiveValue()
for i in range(num_positions):
print(
str(i)
+ "--"
+ str(solver.Value(type_move_A_position[i]))
+ "--"
+ str(solver.Value(type_move_B_position[i]))
+ "--"
+ str(solver.Value(value_position[i]))
)
I've got a list of some integers, e.g. [1, 2, 3, 4, 5, 10]
And I've another integer (N). For example, N = 19.
I want to check if my integer can be represented as a sum of any amount of numbers in my list:
19 = 10 + 5 + 4
or
19 = 10 + 4 + 3 + 2
Every number from the list can be used only once. N can raise up to 2 thousand or more. Size of the list can reach 200 integers.
Is there a good way to solve this problem?
4 years and a half later, this question is answered by Jonathan.
I want to post two implementations (bruteforce and Jonathan's) in Python and their performance comparison.
def check_sum_bruteforce(numbers, n):
# This bruteforce approach can be improved (for some cases) by
# returning True as soon as the needed sum is found;
sums = []
for number in numbers:
for sum_ in sums[:]:
sums.append(sum_ + number)
sums.append(number)
return n in sums
def check_sum_optimized(numbers, n):
sums1, sums2 = [], []
numbers1 = numbers[:len(numbers) // 2]
numbers2 = numbers[len(numbers) // 2:]
for sums, numbers_ in ((sums1, numbers1), (sums2, numbers2)):
for number in numbers_:
for sum_ in sums[:]:
sums.append(sum_ + number)
sums.append(number)
for sum_ in sums1:
if n - sum_ in sums2:
return True
return False
assert check_sum_bruteforce([1, 2, 3, 4, 5, 10], 19)
assert check_sum_optimized([1, 2, 3, 4, 5, 10], 19)
import timeit
print(
"Bruteforce approach (10000 times):",
timeit.timeit(
'check_sum_bruteforce([1, 2, 3, 4, 5, 6, 7, 8, 9, 10], 200)',
number=10000,
globals=globals()
)
)
print(
"Optimized approach by Jonathan (10000 times):",
timeit.timeit(
'check_sum_optimized([1, 2, 3, 4, 5, 6, 7, 8, 9, 10], 200)',
number=10000,
globals=globals()
)
)
Output (the float numbers are seconds):
Bruteforce approach (10000 times): 1.830944365834205
Optimized approach by Jonathan (10000 times): 0.34162875449254027
The brute force approach requires generating 2^(array_size)-1 subsets to be summed and compared against target N.
The run time can be dramatically improved by simply splitting the problem in two. Store, in sets, all of the possible sums for one half of the array and the other half separately. It can now be determined by checking for every number n in one set if the complementN-n exists in the other set.
This optimization brings the complexity down to approximately: 2^(array_size/2)-1+2^(array_size/2)-1=2^(array_size/2 + 1)-2
Half of the original.
Here is a c++ implementation using this idea.
#include <bits/stdc++.h>
using namespace std;
bool sum_search(vector<int> myarray, int N) {
//values for splitting the array in two
int right=myarray.size()-1,middle=(myarray.size()-1)/2;
set<int> all_possible_sums1,all_possible_sums2;
//iterate over the first half of the array
for(int i=0;i<middle;i++) {
//buffer set that will hold new possible sums
set<int> buffer_set;
//every value currently in the set is used to make new possible sums
for(set<int>::iterator set_iterator=all_possible_sums1.begin();set_iterator!=all_possible_sums1.end();set_iterator++)
buffer_set.insert(myarray[i]+*set_iterator);
all_possible_sums1.insert(myarray[i]);
//transfer buffer into the main set
for(set<int>::iterator set_iterator=buffer_set.begin();set_iterator!=buffer_set.end();set_iterator++)
all_possible_sums1.insert(*set_iterator);
}
//iterator over the second half of the array
for(int i=middle;i<right+1;i++) {
set<int> buffer_set;
for(set<int>::iterator set_iterator=all_possible_sums2.begin();set_iterator!=all_possible_sums2.end();set_iterator++)
buffer_set.insert(myarray[i]+*set_iterator);
all_possible_sums2.insert(myarray[i]);
for(set<int>::iterator set_iterator=buffer_set.begin();set_iterator!=buffer_set.end();set_iterator++)
all_possible_sums2.insert(*set_iterator);
}
//for every element in the first set, check if the the second set has the complemenent to make N
for(set<int>::iterator set_iterator=all_possible_sums1.begin();set_iterator!=all_possible_sums1.end();set_iterator++)
if(all_possible_sums2.find(N-*set_iterator)!=all_possible_sums2.end())
return true;
return false;
}
Ugly and brute force approach:
a = [1, 2, 3, 4, 5, 10]
b = []
a.size.times do |c|
b << a.combination(c).select{|d| d.reduce(&:+) == 19 }
end
puts b.flatten(1).inspect