Your brute force is too slow — it's an optimization problem

If you wrote a loop over itertools.permutations, itertools.combinations, or a product of choices to find the best option, and it grinds to a halt as the input grows, you don't have a performance bug — you have an optimization problem. The fix is not a faster loop; it's to model the problem and hand it to a solver like quicopt, which prunes the search instead of enumerating it.

Recognize the pattern

The naive code almost always looks like one of these:

# ordering / sequencing  -> exponential (n!)
for order in itertools.permutations(items): ...

# pick a subset          -> exponential (2^n)
for pick in itertools.product([0, 1], repeat=n): ...

# split / allocate       -> exponential or a coarse grid
for a in range(N):
    for b in range(N - a): ...

Each of these is a known problem with a compact model. Instead of enumerating, you declare variables, constraints and an objective, and call solve().

The fix, concretely

Assigning N workers to N tasks by trying every permutation is O(n!). As a MILP it is a few lines and comes back proven optimal:

assignment.py

from ortools.math_opt.python import mathopt
from quicopt import Client
cost = [[9,11,14,11,7],[6,15,13,13,10],[12,13,6,8,8],[11,9,10,12,9],[7,12,14,10,14]]
N = len(cost)
model = mathopt.Model(name="assignment")
x = [[model.add_binary_variable(name=f"x_{w}_{t}") for t in range(N)] for w in range(N)]
for w in range(N):
    model.add_linear_constraint(sum(x[w][t] for t in range(N)) == 1)
for t in range(N):
    model.add_linear_constraint(sum(x[w][t] for w in range(N)) == 1)
model.minimize(sum(cost[w][t] * x[w][t] for w in range(N) for t in range(N)))
print(Client("https://try.quicoptapi.pgi.fz-juelich.de").solve(model).display)

$ python assignment.py

├── status:     optimal
├── feasible:   true
├── objective:  38.0
├── x:          x_0_0=0, x_0_1=0, x_0_2=0, x_0_3=0, x_0_4=1, x_1_0=1, …  (25 variables)
└── solve_time: 0.0117 s

Find your problem

Your brute force looks like…	It's probably…	Guide
permutations of stops / a tour	Traveling salesman	TSP
routes for several vehicles	Vehicle routing	VRP
matching A's to B's one-to-one	Assignment	Assignment
pick items under a budget/limit	Knapsack	Knapsack
fewest sets/options covering everything	Set cover	Set cover
pack items into fewest bins	Bin packing	Bin packing
split jobs across machines/workers	Scheduling	Scheduling · Shifts
color / assign without conflicts	Graph coloring	Graph coloring
split a graph in two	Max-cut	Max-cut
divide a budget / resources	Allocation	Resource allocation

Browse every guide by problem class: Guides
Set up the client and solve your first model: Getting started

Not sure which one fits?

Tell us what you're optimizing — paste your slow loop — and we'll point you at the right model.

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Frequently asked questions

How do I know it's an optimization problem?

If you're looping over permutations, combinations, or a product of choices to find the best one, and it slows to a crawl as inputs grow, it's an optimization problem — a solver prunes that search instead of walking it.

Won't a solver be overkill for small inputs?

No — the model is a few lines and solves the small cases instantly too. The difference is it keeps working when the input grows past what brute force can handle.

Is quicopt free to use?

Yes — pip install quicopt and your first call sets up a free key, no license.