## Algorithm

Problem Name: 1006. Clumsy Factorial

The factorial of a positive integer `n` is the product of all positive integers less than or equal to `n`.

• For example, `factorial(10) = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1`.

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.

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

However, these operations are still applied using the usual order of operations of arithmetic. We do all multiplication and division steps before any addition or subtraction steps, and multiplication and division steps are processed left to right.

Additionally, the division that we use is floor division such that `10 * 9 / 8 = 90 / 8 = 11`.

Given an integer `n`, return the clumsy factorial of `n`.

Example 1:

```Input: n = 4
Output: 7
Explanation: 7 = 4 * 3 / 2 + 1
```

Example 2:

```Input: n = 10
Output: 12
Explanation: 12 = 10 * 9 / 8 + 7 - 6 * 5 / 4 + 3 - 2 * 1
```

Constraints:

• `1 <= n <= 104`

## Code Examples

### #1 Code Example with Javascript Programming

```Code - Javascript Programming```

``````
const clumsy = function(N) {
const ops = ["*", "/", "+", "-"];
const arr = [];
arr.push(N);
for (let i = N - 1, idx = 0; i > 0; i--, idx++) {
let op = ops[idx % 4];
let arrIdx = arr.length - 1  <  0 ? 0 : arr.length - 1;
switch (op) {
case "*":
arr[arrIdx] *= i;
break;
case "/":
arr[arrIdx] = Math.floor(arr[arrIdx] / i);
break;
case "+":
arr[0] += i;
break;
case "-":
arr.push(i);
break;
}
}

let res = arr[0];
for (let i = 1; i  <  arr.length; i++) {
res -= arr[i];
}
return res;
};
``````
Copy The Code &

Input

cmd
n = 4

Output

cmd
7

### #2 Code Example with Python Programming

```Code - Python Programming```

``````
class Solution:
def clumsy(self, N: int) -> int:
if N <= 2:
return N
if N <= 4:
return N + 3
if N % 4 == 0:
return N + 1
elif N % 4 <= 2:
return N + 2
else:
return N - 1
``````
Copy The Code &

Input

cmd
n = 4

Output

cmd
7