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Powerpoint Algorithm Template

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Transcript: 3) The number of other Web pages that link to the page in question Google search engine example.. Google's algorithm does the work for you by searching out Web pages that contain the keywords you used to search, then assigning a rank to each page based several factors, including how many times the keywords appear on the page. Higher ranked pages appear further up iى Google's search engine results page (SERP), meaning that the best links relating to your search query are theoretically the first ones Google lists. Google uses automated programs called spiders or crawlers, just like most search engines.Also like other search engines, Google has a large index of keywords and where those words can be found.Google uses a trademarked algorithm called PageRank... third factor second factor Google's search engine is a powerful tool. Without search engines like Google, it would be practically impossible to find the information you need when you browse the Web. Like all search engines, Google uses a special algorithm to generate search results. While Google shares general facts about its algorithm, the specifics are a company secret. This helps Google remain competitive with other search engines on the Web and reduces the chance of someone finding out how to abuse the system. Algorithm.. Finding useful information on the World Wide Web is something many of us take for granted. The main purpose of Google Search is to hunt for text in publicly accessible documents offered by web servers, as opposed to other data, such as images or data contained in databases. google search's goal is to get you to the answer you're looking for faster, creating a nearly seamless connection between you and the knowledge you seek. to find the most relevant information for the user they need in the fastest time possible...if they need a picture book an so on.. first factor 1) the frequency and location of keywords within the Web page A Web page's PageRank depends on a few factors:- Introduction 2) How long the Web page has existed Why is the Google algorithm so important?


Transcript: _ Σ0={ε} the empty string Σ = Σ1 = {a,b} all strings (|x|=1) of length 1 _ Automata ex. Σ = {a,b} A = {aa, ab, ba} A={w|w contains a and |w|=2} A = {ε, a, b, bb, aaa...} A={w|w !(contains a) or |w|!=2} (Languages containing only 1 element are called Singleton languages) ex. Σ = {a,b} A = {aa, ab, ba} A={w|w contains a, |w|=2} B = {ab, ba, bb} A={w|w contains b, |w|=2} AUB = {aa, ab, ba, bb} AUB={w|w contains a or b, |w|=2} Context free languages (2 elements, in the case of this alphabet) Muhammed AL CHWARIZMI - 8th - 9th century A U B = {x < Σ* | x < A v x < B} REG = {L(M) | M is a DFA} The length of the input string determines the number of calculation steps So each symbol of the input string represents a calculation step The output is given after the last symbol has been processed A PDA Some languages can be recognized by a particular algorithm. Automata can be constructed to 'embody' such an algorithm. An input problem is encoded using an input alphabet, which creates an input string. If the string is contained within the language recognized by a given automaton, the output is true. Otherwise it is false. (0 elements) ={} the empty set DFA ( <{ε}<Σ*) ex. Σ = {a,b} A = {aa, ab, ba} A={w|w contains a, |w|=2} B = {ab, ba, bb} A={w|w contains b, |w|=2} A o B = {aaab, aaba, aabb, abab, abba, abbb, baab, baba, babb} A o B={w1w2|w1 contains a, |w1|=2, w1 contains b, |w2|=2} |A o B| = |A| x |B| A o B = AB (=aB when A={a}=singleton language) AAA=A3=An, n=3 A* = An(n>=0) A+= An(n>0) = AA* Push down automata A U B DPDA NFA A = {x < Σ* | x !< A} A ∩ B = {x < Σ* | x < A, x < B} Z = {q0, q1, q2,..., qn} a set of states Σ = {a, b} an input alphabet δ : Z x Σ --> S a transition function q0 = the start state E = {q1, q2} a set of final states < Turing machine An alphabet Σ = {a1, . . . , am} is an ordered set consisting of a limited number of symbols (represented here by "a") A sequence x = x1 . . . xn where each "x" represents a symbol from the input alphabet, is an input string Σn = all strings of length n Σ* = all strings of every length, including Σ0 = the only word of length 0: ε = the empty string Every subset L < Σ* is a language derived from Σ _ A ∩ B Algorithm The langue recognized by M is L(M), where M finds itself in a final state after processing the last symbol of the input string Regular languages A o B < Finds a solution for any input problem after a finite number of calculation steps, ultimately producing the output true or false Input problems are encoded using an input Alphabet Σ _ A Deterministic Finite Automaton (M) is composed of 5 parts: Transition from algorithm to automaton Context sensitive languages Language operations Σ*={ε,a,b,aa,ab,ba,bb,aaa...} Finite automata ex. Σ = {a,b} A = {aa, ab, ba} A={w|w contains a, |w|=2} B = {ab, ba, bb} A={w|w containts b, |w|=2} A∩B = {ab, ba} A∩B={w|w contains a and b, |w|=2} A o B = {xy | x < A, y < B} Σ ={a,b}


Transcript: Put the numbers one under the other Then we add column by column First the ONES, then the TENS, then the HUNDREDS and so on Regrouping (carrying, trading) as needed Base Ten Drawings Addition Liam and Skylar together have collected 225 comic books. Skylar lost 116 of them. How many comic books do Liam and Skylar have left? (use base ten drawings to solve) STEM Project Algorithm Ms. Smith's & Ms. Abrego's Class A step-by-step procedure to solve a problem Example: Cake recipe Subtraction Algorithms for Whole Numbers Objectives Given step-by-step instructions on how to build a catapult Be creative on what material to use!! Launch snowballs and determine the difference of the farthest distance and shortest distance traveled (in inches) What factors might determine the distance obtained??! Genesis has 151 bracelets and Haley has 29 more bracelets than Genesis. How many bracelets does Haley have in all? (use base ten drawings to solve) Section 3.3 Algorithms Grades 2nd, 3rd, 4th, & 5th Addition & Subtraction Algorithms for Decimals Base Ten Drawing Subtraction Put numbers one under the other, lining up like places Subtract column by column Regrouping (trading, or borrowing) as needed Genesis, 18 months!! Same ideas as for whole numbers Line up like places, by lining up the decimal points Then add or subtract Addition Algorithm for Whole Numbers Addition Algorithm for Decimals Subtraction Algorithm for Whole Numbers Subtraction Algorithm for Decimals Addition Algorithms for Whole Numbers Section 3.3: Algorithms


Transcript: Recursive function - example: factorial n Problem is defined by itself: n! = n * (n-1)! if n = 1 then n!=1 and 0!=1 4!=4 * (4-1)! = 4 * 3! 3!= 3 * 2! 2!= 2 * 1!= 2 * 1 The principle of the development of algorithm In mathematics and computer science, an algorithm is a self-contained step-by-step set of operations to be performed. Specifies a block of one or more statements that are repeatedly executed until a condition is satisfied. The keyword used is while. Format: while (condition) loop-body end_while Flowchart Symbols Pseudocodes A pseudocode is a semiformal, English-like language with limited vocabulary that can be used to design and describe algorithms. Criteria of a good pseudocode: Easy to understand, precise and clear Gives the correct solution in all cases Eventually ends Problem: calculate a person's age Ways of describing algorithms: You may have more than one control structure in one program in order to solve a problem. Recursive - mathematical function Natural language Flow chart – block diagram Formal languages Note that in this example, we are using all the three control structures: sequence, selection and repetition Features of a good algorithm Thank you for attention Natural language – example: y = Max{ xi }, where 1 ≤ i ≤ n sequence x: 3 4 2 5 quantity of x elements: n = 4 index of processing element: i=? present maximum: y=? 1. i ← 1, go to 2 2. y ← xi, go to 3 3. whether i = n ? If yes – the end, if no – go to 4 4. i ← i + 1, go to 5 5. whether xi > y ? If yes – go to 2, if no– go to 3 Begin read age if (age is greater than 55) print “Pencen” else print “Kerja lagi” end_if End Flowchart Symbols Begin read birth year age = current year – birth year display age End The Selection control structure Defines two courses of action depending on the outcome of a condition. A condition is an expression that is, when computed, evaluated to either true or false. The keyword used are if and else. Format: if (condition) then-part else else-part end_if Flowcharts Flowcharts is a graph used to depict or show a step by step solution using symbols which represent a task. The symbols used consist of geometrical shapes that are connected by flow lines. It is an alternative to pseudocoding; whereas a pseudocode description is verbal, a flowchart is graphical in nature. Begin read age if (age > 55) print “Pencen” else print “Kerja lagi” end_if End Ways of describing algorithms: Natural language advantage: easy to understand, simplicity, no need to use special conventions, wide vocabulary disadvantage: lack of precision, possibility of misunderstanding The Repetition control structure The Sequence control structure A series of steps or statements that are executed in the order they are written in an algorithm. The beginning and end of a block of statements can be optionally marked with the keywords begin and end. begin statement 1. statement 2. … … statement n. end Algorithms perform calculation, data processing, and/or automated reasoning tasks. Basic way in creating algorithms: problem definition problem analysis preparation of rules create concise procedure for solving problem Algorithm Control Structure In 1966, two researchers, C. Bohn and G. Jacopini, demonstrated that any algorithm can be described using only 3 control structures: sequence, selection and repetition. The Selection control structure Natural language - example Give an algorithm of finding the value: y = Max{ xi }, where 1 ≤ i ≤ n 1. i ← 1, go to 2 2. y ← xi, go to 3 3. whether i = n ? If yes – the end, if no – go to 4 4. i ← i + 1, go to 5 5. whether xi > y ? If yes – go to 2, if no– go to 3 The Sequence control structure Begin users = 1 while (users <= 10) begin Read birth year age = current year – birth year print age if age > 55 print “Pencen” else print “Kerja lagi” end_if users = users + 1 end end_while End Ways of describing algorithms: Recursive - mathematical function n! = n * (n-1)! advantage: high precision disadvantage: can describe only few kinds of problems finiteness - executed algorithm must have the end specificness - all operations and their order should be precisely defined efficiency - algorithm must give a result in a shortest way generality - algorithm must give solution to any problem from a specific class of problems correctness - must give a correct solution Now let us put together everything that you have learnt so far. Problem: Write a program that will calculate and print the age of 10 persons, given their birth year. If the age of the person is above 55, then the program will print “Pencen”, otherwise, the program will print “Kerja lagi”. Ways of describing algorithms: Recursive - mathematical function n! = n * (n-1)! advantage: high precision disadvantage: can describe only few kinds of problems

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