java - Building a summation from analyzing code? -

i have midterm tomorrow, , supposed able analyze code. thing don't understand @ all. given this:

consider java method comparing 2 strings. method has 2 inputs , should use 2 variables express running time. let n length of a , let m length of b. can express running time function of n and/or m. if assume without loss of generality n < m.

  private static int comparestrings ( string , string b) {        int = 0;         while ( < . length () && < b. length ( ) ) {             if (a . charat ( ) < b. charat ( ) ) return −1;             if (a . charat ( ) > b. charat ( ) ) return 1;             ++;        }        if (a . length () < b. length ( ) ) return −1;         if (a . length () > b. length ( ) ) return 1;   } 

a) express worst case running time of method sum.

b) simplify sum , state big-oh bound.

the notation need in :

n Σ i= 1 

i don't understand how build sum out of code, or it's running time. step step instructions great. problem given practice problem , not homework. want understand this!!!

the worst case run time o(n).

why?
1. because assume n < m , algorithm compares characters long there characters remaining in both strings [characters yet compared].

naturally condition fails hold when there no more characters in shortest string, a.

2. because worst case must occur when while loop not interrupted return.

this can coincide case in evaluate n times.

the stipulation a substring of b such a[0] == b[0] also.

cost sum of

• evaluating while condition
• the cost of 2 comparisons, etc. in body of loop
• incrementing i

it bounded above nc + k c worst case cost of while loop body, k cost of operations evaluated once (such return statement), , n has agreed-upon significance.

if allow n rise without bound can see fits definition of o(n).