Slide 1
... Characteristics of algorithms in C++ standard library: Functional style, generally don’t use explicit recursion or loops Implicit loop structure (for loop) Do something to each element of the vector Implicit data structure is a vector (array) In C++ standard library, there is a set of ve ...
... Characteristics of algorithms in C++ standard library: Functional style, generally don’t use explicit recursion or loops Implicit loop structure (for loop) Do something to each element of the vector Implicit data structure is a vector (array) In C++ standard library, there is a set of ve ...
Georgia Department of Education Accelerated Mathematics III Unit 8
... numbers. In high school mathematics courses we learned to use these same operations for complex numbers thus expanding our number system. However, these operations are not limited to just numerical representations. Since variables and functions represent numbers and their relationships, we can expan ...
... numbers. In high school mathematics courses we learned to use these same operations for complex numbers thus expanding our number system. However, these operations are not limited to just numerical representations. Since variables and functions represent numbers and their relationships, we can expan ...
Stacks - Courses
... http://www.cs.dartmouth.edu/~farid/teaching/cs15/cs5/lectures/0519/0519.html ...
... http://www.cs.dartmouth.edu/~farid/teaching/cs15/cs5/lectures/0519/0519.html ...
model solution ()
... At each instance there are 3 recursive calls with the problem halved at each instance. The work done at each instance is addition linear with the size of the polynomials . So the recureence relation is : T(n) = 3 T(n/2) + (n) By case 1 of Master theorm, this gives an efficiency of (nlg3) ...
... At each instance there are 3 recursive calls with the problem halved at each instance. The work done at each instance is addition linear with the size of the polynomials . So the recureence relation is : T(n) = 3 T(n/2) + (n) By case 1 of Master theorm, this gives an efficiency of (nlg3) ...
14 - Villanova Computer Science
... classes) that interact by passing messages that transform the state. • Need to know: – Ways of sending messages – Inheritance – Polymorphism ...
... classes) that interact by passing messages that transform the state. • Need to know: – Ways of sending messages – Inheritance – Polymorphism ...
07 Data Abstraction
... • a constructor function which builds compound structures from simple units • an accessor function which gets parts of a compound structure • a collection of invariants, or equations, which define the structure's behavior • possibly, a collection of functions which compute properties of specific str ...
... • a constructor function which builds compound structures from simple units • an accessor function which gets parts of a compound structure • a collection of invariants, or equations, which define the structure's behavior • possibly, a collection of functions which compute properties of specific str ...
REVERSE MATHEMATICS AND RECURSIVE GRAPH THEORY
... predecessor and its other vertex with its successor. Theorems 11, 12, and 14 can be modified to address the existence of two-way Euler paths. 4. Hamilton paths. Now we will consider theorems on the existence of Hamilton paths. A path through a graph G is called a (one way) Hamilton path if it uses e ...
... predecessor and its other vertex with its successor. Theorems 11, 12, and 14 can be modified to address the existence of two-way Euler paths. 4. Hamilton paths. Now we will consider theorems on the existence of Hamilton paths. A path through a graph G is called a (one way) Hamilton path if it uses e ...
CONTINUITY IN METRIC SPACES
... Continuity and open sets. Definition. Suppose A ⊆ X, B ⊆ Y , and f : X → Y . The set f (A) = {y ∈ Y : y = f (x) for some x ∈ X} = { f (x) : x ∈ A} is called the image of A and the set f −1 (B) = {x ∈ X : f (x) ∈ B} is called the pre-image of B. (Thus x ∈ f −1 (B) iff f (x) ∈ B.) Theorem. Let (X, d) ...
... Continuity and open sets. Definition. Suppose A ⊆ X, B ⊆ Y , and f : X → Y . The set f (A) = {y ∈ Y : y = f (x) for some x ∈ X} = { f (x) : x ∈ A} is called the image of A and the set f −1 (B) = {x ∈ X : f (x) ∈ B} is called the pre-image of B. (Thus x ∈ f −1 (B) iff f (x) ∈ B.) Theorem. Let (X, d) ...
Chapter5
... • If at least one 4-cent stamp has been used, then a 4-cent stamp can be replaced with a 5-cent stamp to yield a total of k + 1 cents. • Otherwise, no 4-cent stamp have been used and at least three 5-cent stamps were used. Three 5-cent stamps can be replaced by four 4-cent stamps to yield a total of ...
... • If at least one 4-cent stamp has been used, then a 4-cent stamp can be replaced with a 5-cent stamp to yield a total of k + 1 cents. • Otherwise, no 4-cent stamp have been used and at least three 5-cent stamps were used. Three 5-cent stamps can be replaced by four 4-cent stamps to yield a total of ...
Exact solutions of discrete master equations in terms of continued
... fractions of discrete one-variable master equations which in general do not satisfy a detailed balance relation. The explicit expressions are given in mathematical appealing forms which simplify considerably the study of the stationary and time-dependent fluctuation dynamics in nonlinear stochastic ...
... fractions of discrete one-variable master equations which in general do not satisfy a detailed balance relation. The explicit expressions are given in mathematical appealing forms which simplify considerably the study of the stationary and time-dependent fluctuation dynamics in nonlinear stochastic ...
Annals of Pure and Applied Logic Ordinal machines and admissible
... second author recast the proof of the Sacks–Simpson theorem using the computational paradigm instead of constructibility theory. The crucial point involved was how the informally presented recursions in the argument of Sacks and Simpson [11, 12] (and a recursion method presented by Shore [13]) can b ...
... second author recast the proof of the Sacks–Simpson theorem using the computational paradigm instead of constructibility theory. The crucial point involved was how the informally presented recursions in the argument of Sacks and Simpson [11, 12] (and a recursion method presented by Shore [13]) can b ...
Learn to Program with Minecraft Plugins Extracted from:
... together at code/Simple2/src/simple2/Simple2.java. Note that there are a couple of different ways to accomplish even this simple function. There usually isn’t just one “correct” way to write code. That’s a good start, but there’s more to Java than just variables and functions. The Java language has ...
... together at code/Simple2/src/simple2/Simple2.java. Note that there are a couple of different ways to accomplish even this simple function. There usually isn’t just one “correct” way to write code. That’s a good start, but there’s more to Java than just variables and functions. The Java language has ...
CS 345 - Programming Languages
... Take a look at Dybvig’s book (linked from the course website) ...
... Take a look at Dybvig’s book (linked from the course website) ...
Functional programming in Scheme.
... Take a look at Dybvig’s book (linked from the course website) ...
... Take a look at Dybvig’s book (linked from the course website) ...
Multiple Perspectives on the Important Concepts for Understanding
... between them, there is an important difference as well. A recursive process stops when it arrives back at stage S1, whereas an inductive process (in principle) can be continued forever. Inductive and recursive processes include, but are not confined to, dealing with mathematical objects, phenomena, ...
... between them, there is an important difference as well. A recursive process stops when it arrives back at stage S1, whereas an inductive process (in principle) can be continued forever. Inductive and recursive processes include, but are not confined to, dealing with mathematical objects, phenomena, ...
The Scala Experience Safe Programming Can be Fun!
... • Each step is very fast (a small constant number of operations) • There are log2(n) such steps • So it takes ~ log2(n) steps per search • Much faster then ~ n ...
... • Each step is very fast (a small constant number of operations) • There are log2(n) such steps • So it takes ~ log2(n) steps per search • Much faster then ~ n ...
Functional Programming, Parametricity, Types
... Types are documentation reliable and dense documentation ...
... Types are documentation reliable and dense documentation ...
Higher Order Functions
... • If initializer is provided, initializer will stand as the first argument in the sum • Unfortunately in python 3 reduce() requires an import ...
... • If initializer is provided, initializer will stand as the first argument in the sum • Unfortunately in python 3 reduce() requires an import ...
Data Structures Name:___________________________ iterator our
... 1. The Python for loop allows traversal of built-in data structures (strings, lists, tuple, etc) by an iterator. To accomplish this with our data structures we need to include an __iter__(self) method that gets used by the built-in iter function to create a special type of object called a generator ...
... 1. The Python for loop allows traversal of built-in data structures (strings, lists, tuple, etc) by an iterator. To accomplish this with our data structures we need to include an __iter__(self) method that gets used by the built-in iter function to create a special type of object called a generator ...
Sense and denotation as algorithm and value
... The circular nature of these instructions corresponds to the self reference of the sentences, but there is nothing unusual about circular clauses like these in programs. The algorithms defined by them are recursive algorithms and (in this case, as one might expect), they do not compute any value at ...
... The circular nature of these instructions corresponds to the self reference of the sentences, but there is nothing unusual about circular clauses like these in programs. The algorithms defined by them are recursive algorithms and (in this case, as one might expect), they do not compute any value at ...
File
... to work with an arbitrary number of inputs, so the efficiency or complexity of an algorithm is stated in terms of time complexity and space complexity. The time Complexity of an algorithm is basically the running time of the program as a function of the input size. On similar grounds, space complexi ...
... to work with an arbitrary number of inputs, so the efficiency or complexity of an algorithm is stated in terms of time complexity and space complexity. The time Complexity of an algorithm is basically the running time of the program as a function of the input size. On similar grounds, space complexi ...
PPTX
... be integers • But what if E1 and E2 aren’t integers? – E.g., what if we write + false true ? – It can be parsed, but we can’t execute it ...
... be integers • But what if E1 and E2 aren’t integers? – E.g., what if we write + false true ? – It can be parsed, but we can’t execute it ...
Slides09_24 (Data Types)
... • Discuss purpose, scope, and expectations of the course • Discuss personal expectations & strategy for doing well • Review Web Page (http://faculty.washington.edu/lcrum) • Review Syllabus, Textbook, and Simulator book • Discuss Laboratory (CP 206D), Access, Etiquette, Equipment/supplies Usage • Dis ...
... • Discuss purpose, scope, and expectations of the course • Discuss personal expectations & strategy for doing well • Review Web Page (http://faculty.washington.edu/lcrum) • Review Syllabus, Textbook, and Simulator book • Discuss Laboratory (CP 206D), Access, Etiquette, Equipment/supplies Usage • Dis ...
x - mor media international
... We say f(x) is continuous at x = c, if all the following properties are satisfied: 1. f(c) is defined, i.e., f(c) must be some real number. 2. limxc– f(x) = f(c), i.e., the left-sided limit must be same as f(c). 3. limxc+ f(x) = f(c), i.e., the right-sided limit must be same as f(c). In other word ...
... We say f(x) is continuous at x = c, if all the following properties are satisfied: 1. f(c) is defined, i.e., f(c) must be some real number. 2. limxc– f(x) = f(c), i.e., the left-sided limit must be same as f(c). 3. limxc+ f(x) = f(c), i.e., the right-sided limit must be same as f(c). In other word ...
Recursion (computer science)
Recursion in computer science is a method where the solution to a problem depends on solutions to smaller instances of the same problem (as opposed to iteration). The approach can be applied to many types of problems, and recursion is one of the central ideas of computer science.""The power of recursion evidently lies in the possibility of defining an infinite set of objects by a finite statement. In the same manner, an infinite number of computations can be described by a finite recursive program, even if this program contains no explicit repetitions.""Most computer programming languages support recursion by allowing a function to call itself within the program text. Some functional programming languages do not define any looping constructs but rely solely on recursion to repeatedly call code. Computability theory proves that these recursive-only languages are Turing complete; they are as computationally powerful as Turing complete imperative languages, meaning they can solve the same kinds of problems as imperative languages even without iterative control structures such as “while” and “for”.