Download CSE 3358 Note Set 1

CSE 3358
NOTE SET 3
Data Structures and Algorithms
Objectives



Properties of Big-O
Standard Complexities
Finding Complexity from an algorithm
Big – O: Transitivity
If f(n) is O(g(n)) and g(n) is O(h(n)),
then f(n) is O(h(n)).
Big – O: Addition
If f(n) is O(h(n)) and g(n)
is O(h(n)), then f(n) + g(n) is O(h(n)).
Big – O
The function ank is O(nk).
Big – O
The function nk is O(nk+j)
for any positive j.
Standard Complexities
Execution times on a computer executing 1
million ops/sec (1 sec = 106 µsec)
Class
Big – O
n=10
O(1)
1 µsec
O(lg n)
3 µsec
O(n)
10 µsec
No name
O(n lg n)
33 µsec
Quadratic
O(n2)
10 µsec
Cubic
O(n3)
1 msec
Exponential
O(2n)
10 msec
Constant
Logarithmic
Linear
n=103
n=105
Determining Complexity

How can we determine the complexity of a
particular algorithm?
int sum(int* arr, int size)
{
int sum = 0;
for (int i = 0; i < size; i++)
sum += arr[i];
return sum;
}
int sum(int* arr, int size)
{
int sum = 0;
for (int i = 0; i < size; i++)
sum += arr[i];
return sum;
}