This document discusses the binary search algorithm. It begins by introducing the authors and topic, which is binary search. It then defines binary search as an algorithm that finds a target value within a sorted array by repeatedly dividing the search space in half. The document goes on to explain how binary search works by comparing the middle element of the array to the target on each iteration and eliminating half of the remaining elements. It provides an example to demonstrate this process. Finally, it notes that binary search has better time complexity than linear search since it narrows the search space faster with each comparison.

2. Rokibul Alam
CSE 01205989
Team Member’s
Md. Tohidul Alam
CSE 01205984
Antar Hossain
CSE 01205975
2
Md Isma Azam Bappy
CSE 01205994

3. Our topic
Binary Search
Algorithm

4. What is Binary
search?
In computer science, Binary search,
also known as ------
* half-interval search,
*logarithmic search,
*binary chop,
Binary search is a search algorithm
that finds the position of a target
value within a sorted array.

5. How Binary search work
It work only for Sorted Array.
At each level the Array is halved and the key is search in
any one of the half while the other half is rejected.
Best case occurs when we the key we are looking for is
Present in the middle of the array.
Worst case occurs when the key is not present.
Lets see a Example how Binary search Works

6. How Binary Search Work
value -4 2 7 10 15 20 22 25 30 36
Index 0 1 2 3 4 5 6 7 8 9
min max
Here,
min=0 and Max=9
Now,
Mid=(min+max)/2;
=(0+9)/2
= 4.5 we get floor value 4 here
mid
Example: Searching the array below for the value 20.
Now,
Compare index[mid] with 20
here,
index[4] = 15, Where 15<20
Now Ignore the ( left side ) from mid.

7. How Binary Search Work
min max
Here,
min= 5 and Max = 9
Now,
Mid=(min+max)/2;
=(5+9)/2
= 7
Example: Searching the array below for the value 20.
Now,
Compare index[mid] with 20
mid
Here,
Index[7] = 25, Where 25>20
Now Ignore the ( Right side ) from mid.
value 20 22 25 30 36
Index 5 6 7 8 9

8. How Binary Search Work
min max
Here,
min= 5 and Max= 6
Now,
Mid=(min+max)/2;
=(5+6)/2
= 5
Example: Searching the array below for the value 20.
Now,
Compare index[mid] with 20
mid
Here,
Index[5] = 20 => Where 20 ==20
At last we get our Target value (20) from this array
value 20 22
Index 5 6

9. Flow Chart of Binary Search Start
Lb=0
Ub = size of array
Lb<=Ub?
yes
No
Mid=(Lb+Ub)/2
Key Not Found!
Array[mid]==key?Key Is Found
yes
Array [mid] > key?
yes
Lb=mid+1
No
Ub=mid-1

10. Pseudo Code:

11. Why Binary search is more
Better then Linear search.
1.Linear search follows sequence and Binary search doesn’t follow.
2.Linear search starts searching from the starting to ending point. Binary searching starts from
middle point.
3.Space complexity of Linear Search is O(1) and Binary Search is O(logn). In this case Binary
Search is better than Linear Search.

12. Let’s see the Binary Search Code In
(C program)