Notes
... Apart from the fact that it fails when there are exceptions other than inexact, the “1 + δ” model of floating point does not reflect the fact that some computations involve no rounding error. For example: • If x and y are floating point numbers within a factor of two of each other, fl(x − y) is comp ...
... Apart from the fact that it fails when there are exceptions other than inexact, the “1 + δ” model of floating point does not reflect the fact that some computations involve no rounding error. For example: • If x and y are floating point numbers within a factor of two of each other, fl(x − y) is comp ...
A short survey of automated reasoning
... Some researchers have attacked the problem of automated theorem proving by attempting to emulate the way humans reason. Crudely we can categorize this as the ‘Artificial Intelligence’ (AI) approach. For example in the 1950s Newell and Simon [81] designed a program that could prove many of the simple ...
... Some researchers have attacked the problem of automated theorem proving by attempting to emulate the way humans reason. Crudely we can categorize this as the ‘Artificial Intelligence’ (AI) approach. For example in the 1950s Newell and Simon [81] designed a program that could prove many of the simple ...
124370-hw2-1-
... 6. [7 pts] Design a 3-way merge sort algorithm, which divides the given array into three equal parts, recursively sorts each part, then merges the results. In the main MergeSort3(A,p,r) algorithm, you may assume the existence of an appropriate Merge3(A,p,q1,q2,r) linear-time ((n)) algorithm. Provid ...
... 6. [7 pts] Design a 3-way merge sort algorithm, which divides the given array into three equal parts, recursively sorts each part, then merges the results. In the main MergeSort3(A,p,r) algorithm, you may assume the existence of an appropriate Merge3(A,p,q1,q2,r) linear-time ((n)) algorithm. Provid ...
Spectral optimizers and equation solvers
... For the past three weeks, we have discussed rather general-purpose optimization methods for nonlinear equation solving and optimization. In practice, of course, we should look at our problems to see if they have structure we can use in specialized algorithms that are faster or more robust than the g ...
... For the past three weeks, we have discussed rather general-purpose optimization methods for nonlinear equation solving and optimization. In practice, of course, we should look at our problems to see if they have structure we can use in specialized algorithms that are faster or more robust than the g ...
Efficient Algorithms and Problem Complexity
... The performance ratio is indeed 2, i.e., for some instances, nextFit uses (almost) twice as many bins as is optimal. [Can you find one?] It is an online algorithm: items are processed as they arrive. It is a 1-bounded-space algorithm: at most one bin is open at a time. These are very useful properti ...
... The performance ratio is indeed 2, i.e., for some instances, nextFit uses (almost) twice as many bins as is optimal. [Can you find one?] It is an online algorithm: items are processed as they arrive. It is a 1-bounded-space algorithm: at most one bin is open at a time. These are very useful properti ...
Lecture Notes
... our discussion of linked lists from two weeks ago. What is the worst case complexity for appending N items on a linked list? For testing to see if the list contains X? What would be the best case complexity for these operations? If we were going to talk about O() complexity for a list, which of ...
... our discussion of linked lists from two weeks ago. What is the worst case complexity for appending N items on a linked list? For testing to see if the list contains X? What would be the best case complexity for these operations? If we were going to talk about O() complexity for a list, which of ...
problem solving and open problem in teachers` training in
... In different countries, mathematics teachers’ education and research programs in math education exhibit differences both in principles and ways to implement them. There are also different research traditions or paradigms to frame mathematics education projects, but all of them recognize that mathema ...
... In different countries, mathematics teachers’ education and research programs in math education exhibit differences both in principles and ways to implement them. There are also different research traditions or paradigms to frame mathematics education projects, but all of them recognize that mathema ...
Chapter 3
... • Intractable: The situation is much worse for problems that cannot be solved using an algorithm with worst-case polynomial time complexity. The problems are called intractable. • NP problem. • NP-complete problem. • Unsolvable problem: no algorithm to solve them. ...
... • Intractable: The situation is much worse for problems that cannot be solved using an algorithm with worst-case polynomial time complexity. The problems are called intractable. • NP problem. • NP-complete problem. • Unsolvable problem: no algorithm to solve them. ...
Lecture Notes (pptx)
... Use the size of the input rather than the input itself – n Count the number of “basic steps” rather than computing exact time Ignore multiplicative constants and small inputs (order-of, big-O) Determine number of steps for either worst-case expected-case These assumptions allow us to analyze algor ...
... Use the size of the input rather than the input itself – n Count the number of “basic steps” rather than computing exact time Ignore multiplicative constants and small inputs (order-of, big-O) Determine number of steps for either worst-case expected-case These assumptions allow us to analyze algor ...
Lecture
... Analysis • Is the algorithm or data structure naturally suited to recursion? A list, such as data read from the keyboard, is not naturally recursive structure. Moreover, the algorithm is not a logarithmic algorithm. • Is the recursive solution shorter and more understandable? Yes • Does the recursi ...
... Analysis • Is the algorithm or data structure naturally suited to recursion? A list, such as data read from the keyboard, is not naturally recursive structure. Moreover, the algorithm is not a logarithmic algorithm. • Is the recursive solution shorter and more understandable? Yes • Does the recursi ...
Logarithms in running time
... Binary Search Solution 2: O(logN) Find the middle element Amid in the list and compare it with X If they are equal, stop If X < Amid consider the left part If X > Amid consider the right part Do until the list is reduced to one element ...
... Binary Search Solution 2: O(logN) Find the middle element Amid in the list and compare it with X If they are equal, stop If X < Amid consider the left part If X > Amid consider the right part Do until the list is reduced to one element ...
Week 1 - Midway ISD
... strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; (Assessed once with 5.3A in 2012) (5.14D) use tools such as real objects, manipulatives, and technology t ...
... strategy, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem; (Assessed once with 5.3A in 2012) (5.14D) use tools such as real objects, manipulatives, and technology t ...
Problem 1.1 - People @ EECS at UC Berkeley
... Collecting like terms, we deduce that x = 1. Thus a = 1. Now f (a) = 2 − a = 1. The slope of the curve at that point is simply the slope of the tangent line, which is the line y = 2 − x. Since this line has slope −1, we know that the slope of the curve at (a, f (a)) is -1 as well. ...
... Collecting like terms, we deduce that x = 1. Thus a = 1. Now f (a) = 2 − a = 1. The slope of the curve at that point is simply the slope of the tangent line, which is the line y = 2 − x. Since this line has slope −1, we know that the slope of the curve at (a, f (a)) is -1 as well. ...
Lesson 2-2
... 4.65 + (-4.65) = 0 and -3.82 + (-4.65) = -8.47 The solution is -8.47. Example 4 Write and Solve an Equation Write an equation for the problem. Then solve the equation. The difference of a number and one fourth is negative two thirds. a number ...
... 4.65 + (-4.65) = 0 and -3.82 + (-4.65) = -8.47 The solution is -8.47. Example 4 Write and Solve an Equation Write an equation for the problem. Then solve the equation. The difference of a number and one fourth is negative two thirds. a number ...
Problem 1212. A Rare, if Obtuse, Ratio Find an obtuse triangle with
... Problem 1212 was first posed by Dick Hess in the Pi Mu Epsilon Journal and the notes below follow the solution of William Pierce (Pi Mu Epsilon Journal, Problem 971, 11:3 Fall 2000, 159-160). These notes start with an elementary solution to the problem, and then discuss a more sophisticated approach ...
... Problem 1212 was first posed by Dick Hess in the Pi Mu Epsilon Journal and the notes below follow the solution of William Pierce (Pi Mu Epsilon Journal, Problem 971, 11:3 Fall 2000, 159-160). These notes start with an elementary solution to the problem, and then discuss a more sophisticated approach ...