1. Data structure –
is the scheme of organizing related information

2. A linear data structure traverses the data elements sequentially, in which only one data element can directly be reached. (Ex: Arrays, Linked Lists)
Non-Linear data structure: The data items are not arranged in a sequential structure. (Ex: Trees, Graphs)
Hierarchical structure - a structure of data having several levels arranged in a treelike structure.

3. Data structure –
is the scheme of organizing related information

4. Direct access:
called “Random access”
is faster than serial access
Serial access:
called “sequential access”
from the begin to the required information

5. Big O notation
Big O notation describes the asymptotic behavior of functions.
Big O notation tells you how fast a function grows or declines.
CPU (time) usage
memory usage
disk usage
network usage
Time complexity

6. Basic operations:
one arithmetic operation (e.g., +, *).
one assignment (e.g. x := 0)
one test (e.g., x = 0)
one read
one write

7. Notation names O(1) constant O(log(n)) logarithmic O(n log n)
O((log(n))c) polylogarithmic
O(n) linear
O(n2) quadratic
O(n3) cubic
O(nc) polynomial
O(cn) exponential (non polynomial)
O(2n) exponential

8. Algorithmic run time expansion

9. 2n
n3/2
5n2
100n

10. N
log2N
Nlog2N N2 N3 2N 2 1 4 8 3 24 64
512
256 16
4096
65536

11. If
f(n) = 8 log(n) + 5(log(n))3 + 7n + 3 n2 + 6 n3
then
f(n) = O(n3).

12. Sequence of statements
...
statement k;
total time = time(statement 1) + time(statement 2) time(statement k)

13. If-Then-Else
if (cond) then
block 1 (sequence of statements)
else
block 2 (sequence of statements)
end if;
max(time(block 1), time(block 2))

14. Loops
for I in 1 .. N loop
sequence of statements
end loop;
O(N)

15. Nested loops
for I in 1 .. N loop
for J in 1 .. M loop
sequence of statements
end loop;
O(N * M).

16. (1) for (int i=0; i<n-1; i++)
(2) for (int j=n-1; j>i; j--)
(3) if (a[j-1]>a[j]) {
(4) temp=a[j-1];
(5) a[j-1]=a[j];
(6) a[j]=temp; }
O(n-i)
O(1)
O(n2)

17. Linear search
A linear search sequentially moves through your list looking for a matching value.
1. The element is found, i.e. a[i] = x.
2. The entire array has been scanned, and no match was found.
i=0;
while (i<n && a[i]≠x) i++;
O(n)

18. There are three conditions: А[mid]==key A[mid]<key A[mid]>key
Binary Search
The key idea is to inspect a middle element and to compare it with the search argument key.
There are three conditions:
А[mid]==key
A[mid]<key
A[mid]>key

19. Example:
А[10], key=16.
left= 0
right= 9
mid = 4
16>A[mid]
left= 5
mid = 7
16<A[mid]
right= 6
mid = 5
16=A[mid]

20. Binary Search int search_bin(int a[],int left, int right,int key)
{int mid;
int midval;
while (left <=right) {
mid=( left +right)/2;
midval=a[mid];
if (midval==key) return mid;
else if (key<midval) right=mid-1;
else left =mid+1; }
return -1;