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Algorithms
- 1. ProgramBy :- EmanEl-ma’asarawi2/24/20111
- 2. What is Program?Howto make program?How to think about the program?Steps for making a good project.2/24/20112
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- 5. list ofinstruction to achieve specific task.ProgramI/P instructionProcessing instructionO/P instruction2/24/20115
- 6. Programming ToolboxesH/WS/WOsCompiler Texteditor Idea wareAlgorithmDSProgramming MethodologiesStructure DesignOop S/W ConceptsInformation hidingData encapsulationData abstraction2/24/20116
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- 9. DS cont…A datastructure can be viewed as consisting of a set of algorithms for performing operations on the data it stores.2/24/20119
- 10. Variable:- data storage locationthat has a value that can change during program execution. Constant:- fixed value that can’t change.2/24/201110
- 11. Applications of DataStructureDSLinearNon-LinearSequentialLinkedLinkedqueuesGraphsTreeLinkedstackslinkedlistsqueuearraystack2/24/201111
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- 13. 1-Array Is adata structure where all elements are stored in contiguous memoryn210Individual elementsArray 2/24/201113
- 14. Random accessFixed sizeLessefficient used on data stored in arrayArray propertiesArray sizeElement size1-in bytes2-the number of elementData type of array2/24/201114
- 15. Exambel01234567 1 2 34 56 2 78 0 102/24/201115
- 16. 2-linked listIs adata structure in which the first element is (head) stored on its ownDataList head /Dummy NodeNull2/24/201116
- 17. Linked list propertiesThesize not fixed grow/shrinkThe extra space is needed to store the pointer of each element More timeImplement linked list use array but not efficientComplex to code and manage2/24/201117
- 18. Appending Node add Nodeto the end of the list.Traversing check the linked list.Inserting Node add Node in the middle of a list.Deleting Node from memory Modified linksDestroyOperation on linked list2/24/201118
- 19. Which is fastarray or linked list?Why?2/24/201119
- 20. Is a datastructure consisting of data nodes connected to each other with pointers.Each node connected to 2 or more other nodes.2/24/201120 5-Trees
- 21. The order ofthe tree:- is the max number of nodes to which any single node connected. binary tree:- is the simplest tree is of order 2. each child have two pointers.Root node:- the topmost node in the tree. leaf node:- node with no children.2/24/201121Tree properties
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- 23. Create binary treeInsertingNodeTraversing the tree recursionSearching the treeDeleting the tree2/24/201123Binary search tree op…
- 24. Logical sequence ofsteps describe complete solution to solve problem in finite amount of timeMay involve alternation, iteration or recursionMore than one algorithm possible for the same taskAlgorithms2/24/201124
- 25. Sorting Searching-Insertion sort -linear search-Merge sort -Binary search -Heap sort-Quick sort2/24/201125Algorithmes
- 26. What resources arerequired to accomplish the task How one algorithm compares with other algorithms How much time or space is required Measured in terms of common basic operationsEfficiency of Algorithms2/24/201126
- 27. Worst-case: (usually) T(n) = maximum time of algorithm on any input of size n.Average-case: (sometimes)T(n) = expected time of algorithm over all inputs of size n.Need assumption of statistical distribution of inputs.Best-case: (bogus) Cheat with a slow algorithm that works fast on some input.2/24/201127Kinds of analyses
- 28. Running time: Ona particular input, it is the number ofprimitive operations (steps) executed. One line may take a different amount of time thananother, but each execution of line i takes the sameamount of time c .Running time of the algorithm is Ʃ (cost of statement)*(number of times statement is executed)2/24/201128
- 29. How efficiency varieswith the size of the task E.g. if the size of the task increases linearly, do the efficiency measures increase linearly, quadratically, exponentially,...? Expressed in terms of standard functions of nComplexity2/24/201129
- 30. notationsBig oBig ƟBigΩ F(n)=g(n)C1g(n)<=f(n)<=c2g(n)F(n)<=g(n)F(n)>=g(n)Data shapeEx - insertion sortbest caseData methodEx – insertion sortworst case2/24/201130
- 31. PseudoCodeconventionsIndentation indicates blockstructure. While, for, repeat , if , then, and else.▹indicates comment.indicates assignment.Variables are local by default.Array elements accessed as in A[i].2/24/201131
- 32. Calculate x^n, wheren is an integer greater than 0.Algorithm1. Set r = 12. Set i = 13. Repeat 3.1 If i=n then terminate loop 3.2 Multiply r by x 3.3 Add 1 to i4. Exit with result rExampleSimple Power Algorithm2/24/201132
- 33. O(n) - thealgorithm requires n multiplications.Time complexity2/24/201133
- 34. Formulate a ConciseSpecification of the ProblemDesign a high-level strategy for a solutionRefine steps 1 and 2 if necessaryComplete the details of the designImplement in the chosen languageHow to Approach Recursive Algorithms2/24/201134
- 35. Calculate x^n, wheren is an integer greater than 0. Recursive Algorithm1. If n=0 then 1.1 set r = 1 2. Else 2.1 set p = n/2 (dropping any remainder) 2.2 set r = (xp)2 2.3 if n is odd then 2.3.1 multiply r by x 3. Exit with result rRecursive Power Algorithm2/24/201135
- 36. static int power(int x, int n) { int r; if (n == 0) r = 1; else { r = power(x,n/2); r = r*r; if (n%2 != 0) r *= x; } return r;}2/24/201136implementation
- 37. O(log n) -the algorithm requires approximately log n multiplications.2Time complexity2/24/201137
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- 47. Solution' ≡ shortestpath Recursive Solution:1. Identify biggest discrepancy (=disk N) 2. If moveable to goal peg Then move Else3. Subgoal: set-up (N−1)-disk tower on non-goal peg. 4. Go to 1. ...2/24/201147
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- 49. SDLC (s/w Developmentlife cycle)DesignProblem analysisMaintenance TestingRequirement definitionsImplementation Using program Delivery2/24/201149
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