High-Level Programming Languages
... • If the language does not already include a particular behavior, we can define one! • We give a section of code a name and use that name as a statement in another part of the program • When the name is encountered, the processing in the other part of the program halts while the named code is execut ...
... • If the language does not already include a particular behavior, we can define one! • We give a section of code a name and use that name as a statement in another part of the program • When the name is encountered, the processing in the other part of the program halts while the named code is execut ...
Recursion (Ch. 10)
... File "/Users/me/ch10.py", line 3, in countdown countdown(n-1) File "/Users/me/ch10.py", line 2, in countdown print(n) RuntimeError: maximum recursion depth exceeded while calling a Python object ...
... File "/Users/me/ch10.py", line 3, in countdown countdown(n-1) File "/Users/me/ch10.py", line 2, in countdown print(n) RuntimeError: maximum recursion depth exceeded while calling a Python object ...
Chapter 2
... To solve this problem, we are told to assume that each pair produces a new pair of offspring every month, ant that each new pair becomes fertile at the age of one month. Furthermore, the rabbits never die. ...
... To solve this problem, we are told to assume that each pair produces a new pair of offspring every month, ant that each new pair becomes fertile at the age of one month. Furthermore, the rabbits never die. ...
06-Recursion
... General case: The size of the arr is greater then 1 to find the largest element in arr[a]…arr[b] - find the largest element in arr[a+1]…arr[b] and call it max - compare the elements arr[a] and max if (arr[a]>=max ) the largest element in arr[a]…arr[b] is arr[a] otherwise the largest element in arr[a ...
... General case: The size of the arr is greater then 1 to find the largest element in arr[a]…arr[b] - find the largest element in arr[a+1]…arr[b] and call it max - compare the elements arr[a] and max if (arr[a]>=max ) the largest element in arr[a]…arr[b] is arr[a] otherwise the largest element in arr[a ...
(add1 (sum 2 2))
... Example of a bad data definition A Purple number is one of • the number 1 • a number of the form (+ n1 n2) Just knowing the value of a purple number, like 56, doesn't tell you how it was constructed as (+ n1 n2) . There are many choices of n1 and n2 that would build 56. ...
... Example of a bad data definition A Purple number is one of • the number 1 • a number of the form (+ n1 n2) Just knowing the value of a purple number, like 56, doesn't tell you how it was constructed as (+ n1 n2) . There are many choices of n1 and n2 that would build 56. ...
Introduction to Algorithms
... before termination T(n) =1 [first step] + (n) [for loop] + (n-1) [if condition] + (n-1) [the assignment in then] = 3n - 1 ...
... before termination T(n) =1 [first step] + (n) [for loop] + (n-1) [if condition] + (n-1) [the assignment in then] = 3n - 1 ...
Practical 10 - OCaml 2 - Computing Science and Mathematics
... However, OCaml’s type system means that we can match, not only against exact values, but also predicates and other type constructors! For example, # let is_zero x = match x with | 0 -> true | _ -> false (* The "_" pattern means "anything else". *) ...
... However, OCaml’s type system means that we can match, not only against exact values, but also predicates and other type constructors! For example, # let is_zero x = match x with | 0 -> true | _ -> false (* The "_" pattern means "anything else". *) ...
worksheet - domains and ranges of relations
... Part 1 - Identify Domains, Ranges, and Functions. Identify the domain and range of each relation given below. Then determine if the relation represents a function. Record your answers in the appropriate spaces provided for each problem. 1. {(2, 3), (-1,5), (0, -1), (3,5), (5, O)} ...
... Part 1 - Identify Domains, Ranges, and Functions. Identify the domain and range of each relation given below. Then determine if the relation represents a function. Record your answers in the appropriate spaces provided for each problem. 1. {(2, 3), (-1,5), (0, -1), (3,5), (5, O)} ...
lisp_47542238
... The two most important kinds of objects in LISP for you to know about are atoms and lists. Atoms are represented as sequences of characters of reasonable length. Such as :34 or join. Lists are recursively constructed from atoms Such as: (a john 34 c3po). The interpreter treats any list as containing ...
... The two most important kinds of objects in LISP for you to know about are atoms and lists. Atoms are represented as sequences of characters of reasonable length. Such as :34 or join. Lists are recursively constructed from atoms Such as: (a john 34 c3po). The interpreter treats any list as containing ...
Recursion (Ch. 10)
... File "/Users/me/ch10.py", line 3, in countdown countdown(n-1) File "/Users/me/ch10.py", line 2, in countdown print(n) RuntimeError: maximum recursion depth exceeded while calling a Python object ...
... File "/Users/me/ch10.py", line 3, in countdown countdown(n-1) File "/Users/me/ch10.py", line 2, in countdown print(n) RuntimeError: maximum recursion depth exceeded while calling a Python object ...
Other Functions and Reflections
... Functions can be reflected about the x-axis or y-axis by the multiplication of -1. Where the multiplication occurs will determine which axis the graph is reflected about. Let’s use the square root function as an example of reflection. If we multiply the radicand by -1, we would have the function − x ...
... Functions can be reflected about the x-axis or y-axis by the multiplication of -1. Where the multiplication occurs will determine which axis the graph is reflected about. Let’s use the square root function as an example of reflection. If we multiply the radicand by -1, we would have the function − x ...
Paradigms
... • Describe the Outputs (as above) • Describe the Relationships Between I x O – As a possibly infinite table – Equations and other predicates between input and output expressions – For a given input, output may not be unique CS784 ...
... • Describe the Outputs (as above) • Describe the Relationships Between I x O – As a possibly infinite table – Equations and other predicates between input and output expressions – For a given input, output may not be unique CS784 ...
function - City Tech OpenLab
... • Parameters and arguments: – A parameter is the variable which is part of the function’s definition. An argument is the value or expression used when calling the method. ...
... • Parameters and arguments: – A parameter is the variable which is part of the function’s definition. An argument is the value or expression used when calling the method. ...
to x - Read
... can become ineffective if the number of possible function values is too high to save Also, if the values involved are floating point values, then we cannot save the values by indexing into an array This is a fundamental problem and no good solution is known to problems of this type Lecture 15 ...
... can become ineffective if the number of possible function values is too high to save Also, if the values involved are floating point values, then we cannot save the values by indexing into an array This is a fundamental problem and no good solution is known to problems of this type Lecture 15 ...
Group C
... a) expand the node that appears to be closest to the goal b) expand the node that is closest to the goal c) expand the node that is the most expensive d ) expand the leftmost node ix) What is the difference between the cost function and heuristic function portions of the A* evaluation function? a) A ...
... a) expand the node that appears to be closest to the goal b) expand the node that is closest to the goal c) expand the node that is the most expensive d ) expand the leftmost node ix) What is the difference between the cost function and heuristic function portions of the A* evaluation function? a) A ...
Discrete Mathematics (2009 Spring) Induction and Recursion
... The set of rooted trees, where a rooted tree consists of a set of vertices containing a distinguished vertex called the root, and edges connecting these vertices, can be de…ned recursively by these steps: BASIS STEP: A single vertex r is a rooted tree. RECURSIVE STEP: Suppose that T1 , T2 , . . . , ...
... The set of rooted trees, where a rooted tree consists of a set of vertices containing a distinguished vertex called the root, and edges connecting these vertices, can be de…ned recursively by these steps: BASIS STEP: A single vertex r is a rooted tree. RECURSIVE STEP: Suppose that T1 , T2 , . . . , ...
PSet 1 Solutions
... (b) Give a divide-and-conquer algorithm for multiplying two polynomials of degree-bound that runs in time )* *-, . .2 . Solution: Divide the coefficients of each -degree polynomial and ! ...
... (b) Give a divide-and-conquer algorithm for multiplying two polynomials of degree-bound that runs in time )* *-, . .2 . Solution: Divide the coefficients of each -degree polynomial and ! ...
Divide and Conquer
... Where : adhoc(x) = is the basic algorithm for small instances a = the number of divisions at each level n/b = the fraction of the whole for a sub-instance ...
... Where : adhoc(x) = is the basic algorithm for small instances a = the number of divisions at each level n/b = the fraction of the whole for a sub-instance ...
Functional Programming Pure Functional Languages
... Functional Programming • Pure functional PLs • S-expressions ...
... Functional Programming • Pure functional PLs • S-expressions ...
CITS 3242 Programming Paradigms
... a function, and the function is called many times. This is exactly what is done in mathematics. Instead of loops and gotos, recursive functions are emphasized, as well as applying functions to each element in a list or collection. There is also an emphasis on writing simple but general functions. E. ...
... a function, and the function is called many times. This is exactly what is done in mathematics. Instead of loops and gotos, recursive functions are emphasized, as well as applying functions to each element in a list or collection. There is also an emphasis on writing simple but general functions. E. ...
Section 9.1 WS
... Invertible functions: When the inverse of a function, f, is also a function, we say that f is invertible. f and f –1 are inverse functions of each other. In general, linear functions of the form y = mx + b with m 0, are invertible. Futhermore, only functions that are one-to-one are invertible. A f ...
... Invertible functions: When the inverse of a function, f, is also a function, we say that f is invertible. f and f –1 are inverse functions of each other. In general, linear functions of the form y = mx + b with m 0, are invertible. Futhermore, only functions that are one-to-one are invertible. A f ...
CS2007Ch05
... In the recursive solution to the Eight Queens problem, the problem size decreases by ______ at each recursive step. ...
... In the recursive solution to the Eight Queens problem, the problem size decreases by ______ at each recursive step. ...
PDF hosted at the Radboud Repository of the Radboud University
... Every year there is an International Mathematical Olympiad (IMO) for high school students; in 2010 it was held in Kazakhstan, with 517 participants from 97 countries. As every year, they got six problems to solve. Problem 5 of IMO 2010 was proposed by Hans Zantema. He was inspired by some observatio ...
... Every year there is an International Mathematical Olympiad (IMO) for high school students; in 2010 it was held in Kazakhstan, with 517 participants from 97 countries. As every year, they got six problems to solve. Problem 5 of IMO 2010 was proposed by Hans Zantema. He was inspired by some observatio ...
An application of results by Hardy, Ramanujan and Karamata
... Ackermannanian functions grow very rapidly, since for example F3 grows like the superexponential function. Therefore they usually do not show up in mathematical textbooks on analytic number theory. The deeper reason for this can be described briefly as follows. Usual analytic number theory can be fo ...
... Ackermannanian functions grow very rapidly, since for example F3 grows like the superexponential function. Therefore they usually do not show up in mathematical textbooks on analytic number theory. The deeper reason for this can be described briefly as follows. Usual analytic number theory can be fo ...
View
... Every time a function gets called, Python creates a new function frame, which contains the function's local variables and parameters. For a recursive function, there might be more than one frame on the stack at the same time. This figure shows a stack diagram for countdown called with n = 3: ...
... Every time a function gets called, Python creates a new function frame, which contains the function's local variables and parameters. For a recursive function, there might be more than one frame on the stack at the same time. This figure shows a stack diagram for countdown called with n = 3: ...
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”.