#1006

Medium

auto_awesomeStack-based state management

LeetCode Problem Workspace

Clumsy Factorial

Compute the clumsy factorial of a number using a fixed rotation of multiply, divide, add, and subtract operations efficiently.

math stack simulation

Problem Statement

Given a positive integer n, compute its clumsy factorial by applying a sequence of operations to the integers from n down to 1. The sequence uses multiply '*', divide '/', add '+', and subtract '-' repeatedly, following the usual arithmetic precedence: all multiplication and division are done left to right before addition and subtraction.

Return the final result after applying the clumsy operation rotation. For example, n = 4 produces 7 because the operations are applied as 4 * 3 / 2 + 1, and n = 10 produces 12 because the operations are applied as 10 * 9 / 8 + 7 - 6 * 5 / 4 + 3 - 2 * 1.

Examples

Example 1

Input: n = 4

Output: 7

7 = 4 * 3 / 2 + 1

Example 2

Input: n = 10

Output: 12

12 = 10 * 9 / 8 + 7 - 6 * 5 / 4 + 3 - 2 * 1

Constraints

1 <= n <= 104

Solution Approach

Stack-based Simulation

Use a stack to process the sequence of operations while iterating from n down to 1. Push the initial number, then for each subsequent number, apply the next operation in the rotation and update the stack to preserve correct precedence. Multiplication and division update the top of the stack, addition and subtraction push new values.

Operation Rotation Management

Track the operation rotation using a counter or modulo approach to ensure the order '*', '/', '+', '-' repeats correctly. This ensures each number is combined properly, and arithmetic order is maintained for left-to-right multiply/divide before addition/subtraction.

Final Aggregation

After processing all numbers, sum all values in the stack to compute the final clumsy factorial result. This guarantees that intermediate multiplication and division steps are fully resolved and addition/subtraction steps are aggregated correctly.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

Time complexity is O(n) because each number from n to 1 is processed once, and each stack operation is O(1). Space complexity is O(n) in the worst case due to storing intermediate results in the stack.

What Interviewers Usually Probe

Check if the candidate respects left-to-right multiplication/division precedence before addition/subtraction.
Look for efficient stack usage to avoid recalculating intermediate results multiple times.
Observe whether the rotation of operations is correctly implemented and cycled through.

Common Pitfalls or Variants

Common pitfalls

Failing to apply multiplication and division left to right before addition and subtraction.
Incorrectly handling the operation rotation, especially after the first cycle.
Attempting recursive factorial computation without considering operation order, leading to wrong results.

Follow-up variants

Compute clumsy factorial for a subset of numbers with custom operation sequences.
Implement the clumsy factorial using recursion instead of stack simulation.
Optimize space by using variables instead of a stack to track intermediate results.

FAQ

What exactly is the clumsy factorial pattern?

The clumsy factorial uses a fixed operation rotation of '*', '/', '+', '-' applied to numbers from n down to 1 while respecting left-to-right multiplication and division before addition and subtraction.

Can I implement clumsy factorial without a stack?

Yes, but careful management of intermediate results and operation order is required to maintain correct arithmetic precedence.

What are common mistakes when computing clumsy factorial?

Common errors include misapplying operation order, breaking the operation rotation, and mishandling subtraction in the middle of the sequence.

How do I handle division in clumsy factorial?

Division should be integer division and applied immediately in left-to-right order before any addition or subtraction steps.

Is clumsy factorial useful in coding interviews?

Yes, it tests stack-based state management, simulation of operation sequences, and precise handling of arithmetic order.

terminal

Solution

Solution 1: Stack + Simulation

The calculation process of clumsy factorial can be seen as a simulation of a stack.

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class Solution:
    def clumsy(self, n: int) -> int:
        k = 0
        stk = [n]
        for x in range(n - 1, 0, -1):
            if k == 0:
                stk.append(stk.pop() * x)
            elif k == 1:
                stk.append(int(stk.pop() / x))
            elif k == 2:
                stk.append(x)
            else:
                stk.append(-x)
            k = (k + 1) % 4
        return sum(stk)

Continue Practicing

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