Clumsy Factorial - Practice Coding Problems

Clumsy Factorial - Problem

The Clumsy Factorial Challenge

Imagine taking the traditional factorial operation and giving it a twist! While a regular factorial multiplies all numbers from n down to 1, the clumsy factorial uses a rotating pattern of operations.

🎯 The Pattern: Starting from n and going down, we cycle through operations in this order:
* → / → + → - → * → / → + → - → ...

For example: clumsy(10) = 10 * 9 / 8 + 7 - 6 * 5 / 4 + 3 - 2 * 1

Important: We follow standard order of operations (multiplication and division before addition and subtraction), and division is floor division (rounds down).

Goal: Given an integer n, calculate and return the clumsy factorial result.

Input & Output

example_1.py — Small Number

$ Input: n = 4

› Output: 7

💡 Note: clumsy(4) = 4 * 3 / 2 + 1 = 12 / 2 + 1 = 6 + 1 = 7

example_2.py — Medium Number

$ Input: n = 10

› Output: 12

💡 Note: clumsy(10) = 10 * 9 / 8 + 7 - 6 * 5 / 4 + 3 - 2 * 1 = 90/8 + 7 - 30/4 + 3 - 2 = 11 + 7 - 7 + 3 - 2 = 12

example_3.py — Edge Case

$ Input: n = 1

› Output: 1

💡 Note: For n = 1, there are no operations to perform, so clumsy(1) = 1

Visualization

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Understanding the Visualization

Compute Several Examples

Calculate clumsy factorial for n = 5, 6, 7, 8, 9, 10... to see the pattern

Notice the Pattern

Results follow a predictable cycle based on n mod 4

Verify the Formula

Test the pattern on more values to confirm it holds

Apply Direct Calculation

Use O(1) formula instead of O(n) simulation

Key Takeaway

🎯 Key Insight: Mathematics often hides elegant patterns in seemingly complex problems - look for cycles and repetitions!

Time & Space Complexity

Time Complexity

⏱️

O(1)

Direct pattern calculation without loops

✓ Linear Growth

Space Complexity

O(1)

Only using constant extra variables

✓ Linear Space

Constraints

1 ≤ n ≤ 10⁴
Division is floor division (rounds down)
Standard order of operations applies (* and / before + and -)

Asked in

f Facebook 15 G Google 8 a Amazon 5 ⊞ Microsoft 3

The optimal solution recognizes that clumsy factorial follows a mathematical pattern based on n mod 4, allowing O(1) direct calculation instead of simulation. For n ≥ 5: when n%4 = 0 return n+1, when n%4 ∈ {1,2} return n+2, when n%4 = 3 return n-1.

Common Approaches

Approach	Time	Space	Notes
✓ Mathematical Pattern Recognition (Optimal)	O(1)	O(1)	Recognize the mathematical pattern to avoid simulation entirely
Simulation with Stack	O(n)	O(n)	Simulate the calculation using a stack to handle operator precedence

Mathematical Pattern Recognition (Optimal) — Algorithm Steps

Handle base cases (n ≤ 4) directly
For n ≥ 5, recognize the pattern: result ≈ n + 1
Apply pattern based on n mod 4:
- If n % 4 ∈ {1,2}: return n + 2
- If n % 4 ∈ {3,0}: return n - 1 and n + 1 respectively

Visualization

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Step-by-Step Walkthrough

Calculate Examples

Compute clumsy factorial for several values

Identify Pattern

Notice the relationship between input n and result

Group by Modulo

Pattern repeats every 4 values (n mod 4)

Apply Formula

Use direct calculation based on pattern

Code -

solution.c — C

#include <stdio.h>

int clumsy(int n) {
    // Base cases
    if (n <= 0) return 0;
    if (n == 1) return 1;
    if (n == 2) return 2;
    if (n == 3) return 6;
    if (n == 4) return 7;
    
    // Pattern recognition for n >= 5
    int remainder = n % 4;
    
    switch (remainder) {
        case 0: return n + 1;
        case 1: return n + 2;
        case 2: return n + 2;
        case 3: return n - 1;
        default: return 0;
    }
}

int main() {
    int n;
    scanf("%d", &n);
    printf("%d\n", clumsy(n));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(1)

Direct pattern calculation without loops

✓ Linear Growth

Space Complexity

O(1)

Only using constant extra variables

✓ Linear Space

Constraints

1 ≤ n ≤ 10⁴
Division is floor division (rounds down)
Standard order of operations applies (* and / before + and -)

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Input & Output

Visualization

Time & Space Complexity

Related Problems

Constraints

Common Approaches

Mathematical Pattern Recognition (Optimal) — Algorithm Steps

Visualization

Code -

Time & Space Complexity

Constraints

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