Normally, 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 instead make a clumsy factorial: using the integers in decreasing order, we swap out the multiply operations for a fixed rotation of operations: 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 equals 11. This guarantees the result is an integer.
Implement the clumsy function as defined above: given an integer N, it returns the clumsy factorial of N.
Example 1:
Input:
4
Output:
7
Explanation:
7 = 4 * 3 / 2 + 1
Example 2:
Input:
10
Output:
12
Explanation:
12 = 10 * 9 / 8 + 7 - 6 * 5 / 4 + 3 - 2 * 1
Note:
1 <= N <= 10000-2^31 <= answer <= 2^31 - 1(The answer is guaranteed to fit within a 32-bit integer.)
Thoughts:
- Split into chunks of size 4, then deal with case 3 or 2 or 1
- The first chunk has a positive sign, then negative starting from the second trunk, including the remaining (3, 2, or 1) part
- if n < 4, the sign is positive
class Solution {
/**
* @param Integer $N
* @return Integer
*/
function clumsy($n) {
$r = 0;
$f = 0;
$first_positive_chunk_set = false;
if($n >= 4){
$r = floor($n*($n-1)/($n-2)) + $n-3;
$n -= 4;
$first_positive_chunk_set = true;
}
while(floor($n / 4) >= 1){
$r -= floor($n*($n-1)/($n-2)) - $n+3;
$n -= 4;
}
if($n >= 3){
$r -= floor($n*($n-1)/($n-2)) ;
$n -= 3;
}
if($n >= 2){
$r -= $n*($n-1) ;
$n -= 2;
}
if($n >= 1){
$r -= $n ;
$n -= 1;
}
return $first_positive_chunk_set?$r:-$r;
}
}
Another Solution Inspired by Other
- Base on math
- Other than that(short), this solution is hard to read and understand.
class Solution {
/**
* @param Integer $N
* @return Integer
*/
function clumsy($n) {
if ($n<5){
return $n+3*($n>2);
}
return $n+2-3*($n%4==3)-($n%4==0);
}
}