PPT-big-O notation Big-O Notation is the most widely used method which describes algorithm

the execution time required or the space used in memory or in disk by an algorithm Big O notation is used describe the rough estimate of the number of steps to complete the algorithm Definition. Consider the coordinate system illustrated in Figure 1 Instead of using the typical axis labels and we use and or 1 The corresponding unit basis vectors are then and or 1 The basis vectors and have the following properties 1 1 0 2 Figu Shantanu. . Dutt. ECE Dept.. UIC. Time Complexity. An algorithm time complexity is a function T(n) of problem size n that represents how much time the algorithm will take to complete its task.. Note that there could be more than one problem size parameter n, in which case we can denote the time complexity function as T(S), where S is the set of size parameters. E.g., for the shortest path problem on a graph G, we have 2 size parameters, n the # of vertices and e the # of edges (thus T(S) = T(. Order Properties of Real Numbers. In addition to the properties of numbers that you have been learning, the real numbers also have properties of . order. We can most easily see this on a number line. Multiplying Numbers in Scientific Notation. Multiply the decimal numbers together.. Add the exponents to get the power of 10. . General formula. : . . (N X 10. x. ) (M X 10. y. ) = (N) (M) X 10. Multiplying Numbers in Scientific Notation. Multiply the decimal numbers together.. Add the exponents to get the power of 10. . General formula. : . . (N X 10. x. ) (M X 10. y. ) = (N) (M) X 10. Slide . 2. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. . 3.1. Decimal Notation, Order, and Rounding. 3.2. Addition and Subtraction. 3.3. Multiplication. 3.4. Division. 3.5. Converting from Fraction Notation to Decimal Notation. dave@create.aau.dk. Source. Chapter 3 of. Cormen. , T. H., . Leiserson. , C. E., . Rivest. , R. L. and Stein, C. (2001). . Introduction to Algorithms. (Second Edition). MIT Press, Cambridge, MA.. Introduction. REALLY, REALLY . BIG . OR. . REALLY, REALLY . SMALL. . NUMBERS.. Mathematicians . are Lazy!!!. They decided that by using powers of 10, they can create short versions of long numbers.. Rules for Scientific Notation. algorithm. is a sequence of instructions . that one . must perform in order to solve a . well formulated . problem. .. Algorithm vs. Program. • An algorithm is an “abstract” description of a. process . For example, to which populations do you belong? Do you categorize yourself as a college student?. What about your gender?. What about your academic major or your ethnic background?. Our minds cannot find order and meaning without creating collections. . Power . Exponential Notation. A short hand of writing a number with out changing its Value. It only changes the way it looks.. * . . . . .  . X10. #. x10. - #. Number gets larger . 210,000,000,000,000,000,000,000 miles. (22 zeros). This number is written in decimal notation. When numbers get this large, it is easier to write them in scientific notation.. Scientific Notation. A number is expressed in scientific notation when it is in the form. 4. 3. 2. 1. 0. In addition to 3, student will be able to go above and beyond by applying what they know about working with . integer . exponents..  .  .  .  .  . The student will be able to work with . LO: To use and understand the notation used for functions.. 3, 5, 7, 8 ….. Functions. 11, 15, 19, 21. 3. 11. We sometimes use a function machine to illustrate how functions behave ..