1. CS 280 Data Structures Professor John Peterson

2. Log Complexity int j = n; while (j > 0) { System.out.println(j); j = j / 2; /* Integer division! */ } What would this print for n = 10? 100?

3. Example public void r(int i) { if (i == 0) return; System.out.print(i) r(i-1); r(i-1); } r(n)

4. Example: 2 N public void r(int i) { if (i == 0) return; System.out.print(i) r(i-1); r(i-1); } r(n)

5. Dominating Terms The big idea behind Big-O notation is that when you add complexities, one term may dominate the other. That is, once n has reached some value, one complexity is ALWAYS bigger than another. Example: O(n 2 ) + O(n) = O(n 2 + n) = O(n 2 )

6. A Complexity Ladder O(1) O(log(n)) O(n) O(n log(n)) O(n 2 ) O(2 n ) There are lots more complexities “between the cracks” but these are the ones that we’ll be seeing this term.

7. Insertion Sort Complexity What is the complexity of insertion sort? insertionSort(array A) for i <- 1 to length[A]-1 do value <- A[i] j <- i-1 while j >= 0 and A[j] > value do A[j + 1] = A[j]; j <- j-1 A[j+1] <- value