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;
};
Input
Output
#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
Input
Output