For positive ? the number of executions of count = count + 1 is representative of the complexity, as the other lines of code don’t execute significantly more times. The recurrence relation can use the first iteration of the outer loop: that represents ? iterations of the inner loop. The loop continues for ?/2, and … Read more
Distributed Computing Economics written by Jim Gray in 2003 is a good start. See this quote: From this we conclude that one dollar equates to = 1 $ ≈ 1 GB sent over the WAN ≈ 10 Tops (tera cpu operations) ≈ 8 hours of cpu time ≈ 1 GB disk space ≈ 10 M … Read more
In big-O notation only the most significant term counts, and constant coefficients are ignored: O[n(n-1)/2] = O[n²/2 + n/2] = O[n²/2] = O(n²) 2 solved Why efficiency of selection sort or Bubble or Insertion sort is said to be n^2 and not as n(n-1)/2
There will be exactly n iterations of the first loop. There will be exactly n(n+1)/2 iterations of the second loop. Inside of the second loop there is roughly 1/3 of n/2 long loops, 1/3 of j long loops and 1/3 of 2 long loops. If we look only at the first of the three possible … Read more
Assuming that T(n) doesn’t suddenly become negative at some value of n, we can give a lower bound for the left hand side if we neglect the first term: We define a new function S(n) such that: We can immediately see that it has terms (ignoring off-by-one etc.). Thus if we keep expanding: At this … Read more
f(N) is the sum of all integers which are less or equals to N. f(N) = N + f(N-1) = N + N-1 + N-2 + … + 2 + 1 = N*(N+1) / 2 0 solved Figuring out the complexity of the code
For the first method, it is n*n = n^2. Since there are two loops, for each loop O(n) is n since you are going through each item in an array. Second one is a constant o(1). 1 solved How to calculate Big-O? [closed]