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Clumsy Factorial

Difficulty: Medium

Problem Description

The factorial of a positive integer n is the product of all positive integers less than or equal to n. We make a clumsy factorial using the integers in decreasing order by swapping out the multiply operations for a fixed rotation of operations with multiply '*', divide '/', add '+', and subtract '-' in this order. Given an integer n, return the clumsy factorial of n.

Key Insights

  • The operations are applied in a fixed rotation: multiply, divide, add, and subtract.
  • Multiplication and division are processed left to right before addition and subtraction.
  • Division is floor division, meaning any fractional results are truncated.
  • The sequence of operations continues until all integers from n down to 1 are used.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

The solution involves simulating the clumsy factorial calculation by iterating through the numbers from n down to 1 and applying the operations in their fixed order. We maintain a variable to hold the current result and apply the operations sequentially based on the index of the current number. The algorithm processes each number with the appropriate operation, storing intermediate results as we go.

Code Solutions

def clumsy(n: int) -> int:
    if n == 0:
        return 0
    result = 0
    current = n
    operation = 0  # 0: *, 1: /, 2: +, 3: -
    
    while current > 0:
        if operation == 0:  # Multiply
            result = current * (result if result != 0 else 1)
        elif operation == 1:  # Divide
            result = result // current
        elif operation == 2:  # Add
            result += current
        elif operation == 3:  # Subtract
            result -= current
        
        current -= 1
        operation = (operation + 1) % 4  # Rotate operation
    
    return result
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