Abstract / Summary

Given a number n compute its factorial applying operations in the order multiplication division addition subtraction repeating for every four numbers.

Note

The full problem description, including helpful examples, can be found on LeetCode.

This problem is ranked as

and has an acceptance rate of about 59% (60k+ submissions).

Typical patterns to solve this problem:

• Math
• Simulation
• Stack

Every single line of code was written by me, 100% from scratch, between August 2023 and August 2024.
However, two years later I set up this website and used various AI tools to generate most of the walkthrough / explanations below.

See this dedicated page for more details.

Overview

The provided Solution class implements a single method clumsy that computes the “clumsy factorial” of a positive integer n. The algorithm builds a textual arithmetic expression by interleaving the numbers from n down to 1 with a repeating sequence of operators *, //, +, -. The constructed expression is then handed to Python’s built-in eval function, which evaluates it and returns the numeric result.

Core Logic

The method begins by creating an infinite cyclic iterator over the four operators.

ops = cycle(["*", "//", "+", "-"])

itertools.cycle yields each operator in turn and automatically wraps around, eliminating the need for manual index management or modulo arithmetic.

Next, a generator expression produces a series of string fragments, each consisting of a number followed by the next operator from the cycle. The numbers are generated in descending order from n to 2.

"".join(str(i) + next(ops) for i in range(n, 1, -1))

The join call concatenates these fragments into a single continuous string. Finally, the literal "1" is appended to the end of the expression, guaranteeing that the last number is always present without an accompanying operator.

expression = "".join(str(i) + next(ops) for i in range(n, 1, -1)) + "1"

The complete expression is then evaluated with eval, which parses and computes the result using Python’s native arithmetic semantics.

return eval(expression)

Edge-Case Handling

When n equals 1, the range(n, 1, -1) iterator produces no values, so the generator yields an empty string. The concatenation step therefore results in just "1", and eval("1") correctly returns 1. This implicit handling means the method works for the smallest valid input without requiring a separate conditional branch.

The use of the floor-division operator // ensures that intermediate division results are truncated toward negative infinity, matching the specification of the clumsy factorial problem, which expects integer division behavior. Because the expression is built as a string, the order of operations follows Python’s standard precedence rules, automatically applying multiplication and division before addition and subtraction.

Performance Characteristics

The implementation leverages several built-in facilities that contribute to efficient execution.

• itertools.cycle provides O(1) amortized time for each next call, avoiding the overhead of manual modulo calculations.
• The generator expression feeds directly into str.join, which pre-allocates the final string size based on the total length of the fragments, resulting in a single memory allocation for the complete expression.
• Delegating the arithmetic to eval allows the heavy lifting to be performed by CPython’s optimized bytecode interpreter, which executes the expression in compiled form rather than interpreting a Python-level loop. This reduces interpreter overhead compared to a manual implementation that would iterate and apply each operator step by step.

Overall, the method runs in linear time with respect to n due to the single pass that constructs the expression, and the evaluation step operates on a string whose length is also linear in n. The combination of generator-based construction, efficient string joining, and native evaluation yields a concise solution with minimal Python-level control flow.

Imagine you have a big box of numbered blocks starting from a number like ten and counting down all the way to one. This piece of code is like a magical machine that takes those blocks and lines them up in a row. It then reaches into a special bag that knows a secret pattern, which is to multiply, then divide, then add, and then subtract. The machine goes down the line of blocks and uses that pattern to snap them together in a specific order, just like following a recipe to build a tower. It keeps repeating that cycle for every single block until it reaches the very last one, which is the number one. When it finishes, all the blocks are connected into one big math problem that the computer solves to find a final treasure number.

Several LLMs ranked my code quality on a scale from 1 (very poor) to 10 (outstanding):

not analyzed yet

I wrote a basic crawler to find other solutions to that problem.
Obviously, I did that after I solved the problem myself.

In general, AlgoMonster and WalkCCC solutions are high-quality and always worth a look.
I haven't checked most of the other solutions, but they might be helpful as well.

And of course, the LeetCode forum is always a good place (or even the best) to look for alternative approaches.

(click on a column header to sort the table)

	author
author	solutions
www	AlgoMonster	C++	Python		Java			TS
	WalkCCC	C++	Python		Java
	leetcode.ca	C++	Python		Java	Go		TS
	LeetcodeHelp	C++	Python		Java
	Progiez	C++	Python		Java
github	black-shadows	C++
	charles-wangkai				Java
	everthis			JS
	fsq	C++
	Garvit244		Python
	halfrost					Go
	JoshCrozier			JS
	lkwq007		Python
	suxrobGM						C#
AlgoMonster	C++, Python, Java, TypeScript
WalkCCC	C++, Python, Java
leetcode.ca	C++, Go, Java, Python, TypeScript
LeetcodeHelp	C++, Java, Python
Progiez	C++, Java, Python
black-shadows	C++, C++
charles-wangkai	Java
everthis	JavaScript
fsq	C++
Garvit244	Python
halfrost	Go
JoshCrozier	JavaScript
lkwq007	Python
suxrobGM	C#

There are a few extra pages giving you some insights into my setup:

• Tech Stack - my development environment and tools
• AI - how AI helped me create this website (NOT solving the problems)
• Progress - progression over time
• Quality - code quality