searching & sorting
DESCRIPTION
Searching & Sorting. Linear Search. I'm thinking of a number between 1 and 100 You try to guess it I'll give too low/too high hints. Linear Search. I'm thinking of a number between 1 and 100 You try to guess it I'll give too low/too high hints Method #1 – Linear Search 1, 2, 3…. - PowerPoint PPT PresentationTRANSCRIPT
Searching & Sorting
Algorithms
• Step by step recipe to do a task…
Algorithms
• Step by step recipe to do a task where:– Operations are computable– Operations are unambiguous– Operations are well ordered– Finite number of operations
Linear Search
• I'm thinking of a number between 1 and 100– You try to guess it– I'll give too low/too high hints
Linear Search
• I'm thinking of a number between 1 and 100– You try to guess it– I'll give too low/too high hints
• Method #1 – Linear Search– 1, 2, 3….
Linear Search Algorithm
• In pseudocode:
Binary Search
• Method #2 – Binary Search– Pick middle of remaining search space– Too high? Eliminate middle and above– Too low? Eliminate middle and below
Algorithm
Binary Search
Searching for 5:Location: 1 2 3 4 5 6 Value:
Step minLocation maxLocation middleLocation middleValue1 1 6 (1 + 6) / 2
= 3.5 = 3
4
Binary Search
Searching for 5:Location: 1 2 3 4 5 6 Value:
Step minLocation maxLocation middleLocation middleValue1 1 6 (1 + 6) / 2
= 3.5 = 3
4
Binary Search
Searching for 5:Location: 1 2 3 4 5 6 Value:
Step minLocation maxLocation middleLocation middleValue1 1 6 (1 + 6) / 2
= 3.5 = 3
4
2 4 (one more than old middleLocation)
6 (unchanged)
(4 + 6) / 2= 5
7 (value at location 5)This is too big, need to search lower
Binary Search
Searching for 5:Location: 1 2 3 4 5 6 Value:
Step minLocation maxLocation middleLocation middleValue1 1 6 (1 + 6) / 2
= 3.5 = 3
4
2 4 (one more than old middleLocation)
6 (unchanged)
(4 + 6) / 2= 5
7 (value at location 5)This is too big, need to search lower
Binary Search
Searching for 5:Location: 1 2 3 4 5 6 Value:
Step minLocation maxLocation middleLocation middleValue1 1 6 (1 + 6) / 2
= 3.5 = 3
4
2 4 (one more than old middleLocation)
6 (unchanged)
(4 + 6) / 2= 5
7 (value at location 5)This is too big, need to search lower
3 4 (unchanged)
4 (one less than old middleLocation)
(4 + 4) / 2= 8 / 2= 4
5 Found it!!!
Binary Search
Searching for 5:Location: 1 2 3 4 5 6 Value:
Step minLocation maxLocation middleLocation middleValue1 1 6 (1 + 6) / 2
= 3.5 = 3
4
2 4 (one more than old middleLocation)
6 (unchanged)
(4 + 6) / 2= 5
7 (value at location 5)This is too big, need to search lower
3 4 (unchanged)
4 (one less than old middleLocation)
(4 + 4) / 2= 8 / 2= 4
5 Found it!!!
Binary Search
Searching for 6:Location: 1 2 3 4 5 6 Value:
Step minLocation maxLocation middleLocation middleValue1 1 6 (1 + 6) / 2
= 3.5 = 3
4 (value at location 3)too small, need to search higher
Binary Search
Searching for 6:Location: 1 2 3 4 5 6 Value:
Step minLocation maxLocation middleLocation middleValue1 1 6 (1 + 6) / 2
= 3.5 = 3
4 (value at location 3)too small, need to search higher
2 4 (one more than old middleLocation)
6 (unchanged)
(4 + 6) / 2= 10 / 2= 5
7(value at location 5)too big, need to search lower
Binary Search
Searching for 6:Location: 1 2 3 4 5 6 Value:
Step minLocation maxLocation middleLocation middleValue1 1 6 (1 + 6) / 2
= 3.5 = 3
4 (value at location 3)too small, need to search higher
2 4 (one more than old middleLocation)
6 (unchanged)
(4 + 6) / 2= 10 / 2= 5
7(value at location 5)too big, need to search lower
Binary Search
Searching for 6:Location: 1 2 3 4 5 6 Value:
Step minLocation maxLocation middleLocation middleValue1 1 6 (1 + 6) / 2
= 3.5 = 3
4 (value at location 3)too small, need to search higher
2 4 (one more than old middleLocation)
6 (unchanged)
(4 + 6) / 2= 10 / 2= 5
7(value at location 5)too big, need to search lower
3 4 (unchanged)
4 (one less than old middleLocation)
(4 + 4) / 2= 8 / 2= 4
5 (value at location 3)too small, need to search higher
Binary Search
Searching for 6:Location: 1 2 3 4 5 6 Value:
Step minLocation maxLocation middleLocation middleValue1 1 6 (1 + 6) / 2
= 3.5 = 3
4 (value at location 3)too small, need to search higher
2 4 (one more than old middleLocation)
6 (unchanged)
(4 + 6) / 2= 10 / 2= 5
7(value at location 5)too big, need to search lower
3 4 (unchanged)
4 (one less than old middleLocation)
(4 + 4) / 2= 8 / 2= 4
5 (value at location 3)too small, need to search higher
Binary Search
Searching for 6:Location: 1 2 3 4 5 6 Value:
Step minLocation maxLocation middleLocation middleValue1 1 6 (1 + 6) / 2
= 3.5 = 3
4 (value at location 3)too small, need to search higher
2 4 (one more than old middleLocation)
6 (unchanged)
(4 + 6) / 2= 10 / 2= 5
7(value at location 5)too big, need to search lower
3 4 (unchanged)
4 (one less than old middleLocation)
(4 + 4) / 2= 8 / 2= 4
5 (value at location 3)too small, need to search higher
4 5 (one more than old middleLocation)
4(unchanged)
minLocation > maxLocation - we have nothing left to check - value is not there!
Basic Sorts
Sorting
• How do we sort?
Selection Sort
• A human algorithm:
Selection Sort
• In a computer:http://computerscience.chemeketa.edu/cs160Reader/Algorithms/SelectionSort2.html
Insertion Sort
• For a human:
Selection Sort
• In a computer:http://computerscience.chemeketa.edu/cs160Reader/Algorithms/InsertionSort2.html