1. Searching: linear & binary
Lecture 02
Searching: linear & binary

2. How to solve a problem Hit and trial method Divide and conquer
Linear search
Divide and conquer
Recursion
Dynamic programming (optimization problems)
Longest common subsequence problem
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3. Hit and trial method: hitting on a problem randomly and see weather it is optimal solution or not
Linear search: one by one see all the elements/ items and find is it the value I am looking for.
Divide-and-conquer: Divide a problem into number of sub problems. Conquer the problem by solving it recursively. Combine the solutions of sub problems for original problem
Recursion: is an equation or inequality that describes a function in terms of its value on smaller inputs
Dynamic Programming: applies where sub problems overlap. It does not repeatedly solve a common sub problem. It solves a sub problem once and saves answer and constructs an optimal solution from computed information
LCS: comparing DNAs, file comparison (2 different versions of same file), screen display etc
Superior Uni- DSA2014 BSSE

4. Linear search
Linear search or sequential search is a method for finding particular value in a list that consists of checking every one of its elements, one at a time and in sequence, until the desired one is found.
The linear search is very simple and works on unsorted arrays of elements
Can be implemented as
Forward search
Recursive method
Searching in reverse order etc
Superior Uni- DSA2014 BSSE

5. Method of searching linear search intuitive approach
start at first item
is it the one I am looking for?
if not go to next item
repeat until found or all items checked
Array does not need to be sorted
Superior Uni- DSA2014 BSSE

6. Linear search analysis
Linear search looks at every element until it finds a match
The worst-case would be
the element is not found or
it is the last element in the array
for an array of length n, n comparisons would be required
Linear search is used for smaller number of elements
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7. Pseudo code
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8. Binary search
Binary search is another searching algorithm, used to search a specific value (or index of value) from the sorted array.
In binary search, we first compare the value to be searched with the item in the middle position of the array. If there's a match, we can return immediately. If the key is less than the middle key, then the item sought must lie in the lower half of the array; if it's greater than the item sought must lie in the upper half of the array
Superior Uni- DSA2014 BSSE

9. Method of searching Binary search takes a sorted array of length n:
looks at the middle element of array, if it equals search key
return array position -else-
If middle element is greater than search key
Changes upper bound of search area to [middle] – 1
Searches again looking at middle element in new bounds
If middle element is less than search key
Changes lower bound of search area to [middle] + 1
If the element is not found
returns a value outside of the range, or NIL.
Superior Uni- DSA2014 BSSE

10. Superior Uni- DSA2014 BSSE

11. Pseudo code
Superior Uni- DSA2014 BSSE

12. Binary Search
Binary search. Given value and sorted array a[], find index i such that a[i] = value, or report that no such index exists.
Invariant. Algorithm maintains a[lo]  value  a[hi].
Ex. Binary search for 33. 6 13 14 25 33 43 51 53 64 72 84 93 95 96 97 1 2 3 4 5 6 7 8 9 10 11 12 13 14 lo hi
Superior Uni- DSA2014 BSSE

13. Binary Search
Binary search. Given value and sorted array a[], find index i such that a[i] = value, or report that no such index exists.
Invariant. Algorithm maintains a[lo]  value  a[hi].
Ex. Binary search for 33. 6 13 14 25 33 43 51 53 64 72 84 93 95 96 97 1 2 3 4 5 6 7 8 9 10 11 12 13 14 lo
mid hi
Superior Uni- DSA2014 BSSE

14. Binary Search
Binary search. Given value and sorted array a[], find index i such that a[i] = value, or report that no such index exists.
Invariant. Algorithm maintains a[lo]  value  a[hi].
Ex. Binary search for 33. 6 13 14 25 33 43 51 53 64 72 84 93 95 96 97 1 2 3 4 5 6 7 8 9 10 11 12 13 14 lo hi
Superior Uni- DSA2014 BSSE

15. Binary Search
Binary search. Given value and sorted array a[], find index i such that a[i] = value, or report that no such index exists.
Invariant. Algorithm maintains a[lo]  value  a[hi].
Ex. Binary search for 33. 6 13 14 25 33 43 51 53 64 72 84 93 95 96 97 1 2 3 4 5 6 7 8 9 10 11 12 13 14 lo
mid hi
Superior Uni- DSA2014 BSSE

16. Binary Search
Binary search. Given value and sorted array a[], find index i such that a[i] = value, or report that no such index exists.
Invariant. Algorithm maintains a[lo]  value  a[hi].
Ex. Binary search for 33. 6 13 14 25 33 43 51 53 64 72 84 93 95 96 97 1 2 3 4 5 6 7 8 9 10 11 12 13 14 lo hi
Superior Uni- DSA2014 BSSE

17. Binary Search
Binary search. Given value and sorted array a[], find index i such that a[i] = value, or report that no such index exists.
Invariant. Algorithm maintains a[lo]  value  a[hi].
Ex. Binary search for 33. 6 13 14 25 33 43 51 53 64 72 84 93 95 96 97 1 2 3 4 5 6 7 8 9 10 11 12 13 14 lo
mid hi
Superior Uni- DSA2014 BSSE

18. Binary Search
Binary search. Given value and sorted array a[], find index i such that a[i] = value, or report that no such index exists.
Invariant. Algorithm maintains a[lo]  value  a[hi].
Ex. Binary search for 33. 6 13 14 25 33 43 51 53 64 72 84 93 95 96 97 1 2 3 4 5 6 7 8 9 10 11 12 13 14
lo hi
Superior Uni- DSA2014 BSSE

19. Binary Search
Binary search. Given value and sorted array a[], find index i such that a[i] = value, or report that no such index exists.
Invariant. Algorithm maintains a[lo]  value  a[hi].
Ex. Binary search for 33. 6 13 14 25 33 43 51 53 64 72 84 93 95 96 97 1 2 3 4 5 6 7 8 9 10 11 12 13 14
lo hi mid
Superior Uni- DSA2014 BSSE

20. Binary Search
Binary search. Given value and sorted array a[], find index i such that a[i] = value, or report that no such index exists.
Invariant. Algorithm maintains a[lo]  value  a[hi].
Ex. Binary search for 33. 6 13 14 25 33 43 51 53 64 72 84 93 95 96 97 1 2 3 4 5 6 7 8 9 10 11 12 13 14
lo hi mid
Superior Uni- DSA2014 BSSE

21. Binary search analysis
Logarithmic: problem size reduced to half
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22. Binary or linear
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23. Binary or linear
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24. https://groups.yahoo.com/neo/groups/BSSE3_DSA_Superi orUni/info
Group URL
orUni/info
Superior Uni- DSA2014 BSSE