java - Worst case Analysis On a loop -


I have written this loop but I am having trouble analyzing the complexity of time in its worst condition. 

 for  (int i = 0)   
; I and lieutenant; Primenzas Size () - 1; I ++) {Prime = Prime. Zest (I); If (prime; <= factor) {if (factor% prime == 0) {factor = factor / prime; divisors.add (prime); I = 0; } If break (factor & lieutenant; = 3); } And break; The most important scenario: the factor is the key. 
 That's why we'll always  brake  directions. 
 and the cycle will be implemented  primeNumbers.size ()  bar.  
 Now we should evaluate  primeNumbers.size () . This is =  O (n / ln n) .  
 We ensure that the number of calculations will be reduced in the  form (if factor% prime == 0)  statement. 
 If we go there then it will mean that  factor = p * m . So we  O (p / Ln (p) + m / ln (m))  =  O ((p * ln (m) + m / ln (p)) / (ln ( m) * ln (p)))  & lt;  O ((p * m) / (ln (m) * ln (p)))  & lt;  O ((p * m) / (ln (m) + ln (p)))  =  O (p * m / ln (m * p))  = < Code> O (n / lnn) . >> By dividing this way we reduce the number of calculations.

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