2-04-2005
... If it is odd, multiply it by 3 and add 1 Do this recursively: Stop if you get to 1. e.g. 5 -> 16 -> 8 -> 4 -> 2 -> 1 ...
... If it is odd, multiply it by 3 and add 1 Do this recursively: Stop if you get to 1. e.g. 5 -> 16 -> 8 -> 4 -> 2 -> 1 ...
Big-O examples
... Consider sorting. When the collection of data that we are sorting is large, it is very important that an efficient algorithm is used, since we would otherwise spend more time than necessary sorting. The algorithms discussed can be applied to any type of objects, including integers, floating point ...
... Consider sorting. When the collection of data that we are sorting is large, it is very important that an efficient algorithm is used, since we would otherwise spend more time than necessary sorting. The algorithms discussed can be applied to any type of objects, including integers, floating point ...
fundamentals of algorithms
... • Build solution to recurrence from bottom up. Write an algorithm that starts with base cases and works its way up to the final solution. Dynamic programming algorithms need to store the results of intermediate sub-problems. This is often but not always done with some kind of table. We will now cove ...
... • Build solution to recurrence from bottom up. Write an algorithm that starts with base cases and works its way up to the final solution. Dynamic programming algorithms need to store the results of intermediate sub-problems. This is often but not always done with some kind of table. We will now cove ...
Recursive Splitting Problem Consider the problem where an
... balancing. In our context, “balanced data structures” are recursive data structures where the recursive sub-units are of almost equal sizes or the tasks operating on them have almost equal computational requirements. Using “balanced” data structures is very important for load balancing purposes. Thi ...
... balancing. In our context, “balanced data structures” are recursive data structures where the recursive sub-units are of almost equal sizes or the tasks operating on them have almost equal computational requirements. Using “balanced” data structures is very important for load balancing purposes. Thi ...
Program revision 2
... • An array is an ordered collection, or numbered list, of values. All of the values in an array must be of the same type. The type of the array is the type of the values it holds, followed by the characters []. An index is used to refer to individual values in the array. If we have N values, we thin ...
... • An array is an ordered collection, or numbered list, of values. All of the values in an array must be of the same type. The type of the array is the type of the values it holds, followed by the characters []. An index is used to refer to individual values in the array. If we have N values, we thin ...
L10: k-Means Clustering
... • Random set of k points. By coupon collectors, we know that we need about k log k to get one in each cluster. • Randomly partition X = {X1 , X2 , . . . , Xk } and take ci = average(Xi ). This biases towards “center” of X (by Chernoff-Hoeffding). • Gonzalez algorithm (for k-center). This biases too ...
... • Random set of k points. By coupon collectors, we know that we need about k log k to get one in each cluster. • Randomly partition X = {X1 , X2 , . . . , Xk } and take ci = average(Xi ). This biases towards “center” of X (by Chernoff-Hoeffding). • Gonzalez algorithm (for k-center). This biases too ...
Performance analysis and optimization of parallel Best
... contributions. Chapter 2 describes the steps to follow in order to transform a real problem into a search problem. Also, it explores the most used sequential search algorithms and compares them so as to select the most suitable to solve the study case. Chapter 3 provides a characterization of the 15 ...
... contributions. Chapter 2 describes the steps to follow in order to transform a real problem into a search problem. Also, it explores the most used sequential search algorithms and compares them so as to select the most suitable to solve the study case. Chapter 3 provides a characterization of the 15 ...
Divide and Conquer
... function DC (x) : answer if length(x) < threshold then return adhoc(x) decompose x into a sub-instances x1, x2 … xa of size n/b for i 1 to a do yi DC(xi) recombine the yi’s to get a solution y for x return y Where : adhoc(x) = is the basic algorithm for small instances a = the number of division ...
... function DC (x) : answer if length(x) < threshold then return adhoc(x) decompose x into a sub-instances x1, x2 … xa of size n/b for i 1 to a do yi DC(xi) recombine the yi’s to get a solution y for x return y Where : adhoc(x) = is the basic algorithm for small instances a = the number of division ...
mining on car database employing learning and clustering algorithms
... (which contains the properties of many different CARS), and thus the following two results are then compared. It was found that K-Means algorithm formed better clusters on the same data set. Keyword-Data Mining, Naïve Bayesian, SMO, K-Mean, SOM, Car review database I. INTRODUCTION Data mining [8][15 ...
... (which contains the properties of many different CARS), and thus the following two results are then compared. It was found that K-Means algorithm formed better clusters on the same data set. Keyword-Data Mining, Naïve Bayesian, SMO, K-Mean, SOM, Car review database I. INTRODUCTION Data mining [8][15 ...
Design and implementation of parallel algorithms for highly
... – Same code used for local computations on all processors, and – Computational task assigned to each processor is small enough to fit into main memory and big enough not to fully fit into cache. ...
... – Same code used for local computations on all processors, and – Computational task assigned to each processor is small enough to fit into main memory and big enough not to fully fit into cache. ...
Analysis of Insertion Sort
... The main idea is to insert A[i] in A[1 . . i − 1] so as to maintain a sorted subsequence A[1 . . i] Invariant: (outer loop) the subarray A[1 . . i − 1] consists of the elements originally in A[1 . . i − 1] in sorted order ...
... The main idea is to insert A[i] in A[1 . . i − 1] so as to maintain a sorted subsequence A[1 . . i] Invariant: (outer loop) the subarray A[1 . . i − 1] consists of the elements originally in A[1 . . i − 1] in sorted order ...
Document
... We solved the Matrix Multiplication problem using n 3 processors in O(logn) steps These two numbers constitute the complexity measure for parallel algorithms: • number of processors • time complexity ...
... We solved the Matrix Multiplication problem using n 3 processors in O(logn) steps These two numbers constitute the complexity measure for parallel algorithms: • number of processors • time complexity ...
Update on Angelic Programming synthesizing GPU friendly parallel scans
... lexically compare string of characters; lexical analysis evaluate polynomials radix sort, quicksort solving tridiagonal linear systems delete marked elements from an array search for regular expressions tree operations label components in two dimensional images dynamic programming (see Evan Pu’s pos ...
... lexically compare string of characters; lexical analysis evaluate polynomials radix sort, quicksort solving tridiagonal linear systems delete marked elements from an array search for regular expressions tree operations label components in two dimensional images dynamic programming (see Evan Pu’s pos ...
Lecture Notes (6up)
... ¤ If we were going to talk about O() complexity for a list, which of these makes more sense: worst, average or best-case complexity? Why? ...
... ¤ If we were going to talk about O() complexity for a list, which of these makes more sense: worst, average or best-case complexity? Why? ...
CS211
... If we were going to talk about O() complexity for a list, which of these makes more sense: worst, average or best-case complexity? Why? ...
... If we were going to talk about O() complexity for a list, which of these makes more sense: worst, average or best-case complexity? Why? ...
Deployment of Sensing Devices on Critical Infrastructure
... Recursion should not be used if the answer to any of the following questions is no: Is the algorithm or data structure naturally suited to recursion (tree is the first choice) ? Is the recursive solution shorter and more understandable? Does the recursive solution run within acceptable time and spac ...
... Recursion should not be used if the answer to any of the following questions is no: Is the algorithm or data structure naturally suited to recursion (tree is the first choice) ? Is the recursive solution shorter and more understandable? Does the recursive solution run within acceptable time and spac ...
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 ...
Self-Improving Algorithms Nir Ailon Bernard Chazelle Seshadhri Comandur
... distribution, the algorithm should be able to spot that and learn to be more efficient. The obvious analogy is data compression, which seeks to exploit low entropy to minimize encoding size. The analogue of Shannon’s noiseless coding theorem would be here: Given an unknown distribution D, design a s ...
... distribution, the algorithm should be able to spot that and learn to be more efficient. The obvious analogy is data compression, which seeks to exploit low entropy to minimize encoding size. The analogue of Shannon’s noiseless coding theorem would be here: Given an unknown distribution D, design a s ...
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 ...
Parallel Computation
... We solved the Matrix Multiplication problem using n 3 processors in O(logn) steps These two numbers constitute the complexity measure for parallel algorithms: • number of processors • time complexity ...
... We solved the Matrix Multiplication problem using n 3 processors in O(logn) steps These two numbers constitute the complexity measure for parallel algorithms: • number of processors • time complexity ...
Algorithms and Data Structures Algorithms and Data Structures
... Model of Computation: An abstract sequential computer, called a Random Access Machine or RAM. Uniform cost model. Computational Problem: A specification in general terms of inputs and outputs and the desired input/output relationship. Problem Instance: A particular collection of inputs for a given p ...
... Model of Computation: An abstract sequential computer, called a Random Access Machine or RAM. Uniform cost model. Computational Problem: A specification in general terms of inputs and outputs and the desired input/output relationship. Problem Instance: A particular collection of inputs for a given p ...
ppt - Multimedia at UCC
... The searching problem The searching problem: If a=[a[i], i=0,1,…,n-1] is an array / list with n elements find whether the element X is in the array and find its position. Inputs: a=[a[i], i=0,1,…,n-1] – the list with n elements Output: pos – int How to do it: Step 1. (initialization) pos=-1; Step 2 ...
... The searching problem The searching problem: If a=[a[i], i=0,1,…,n-1] is an array / list with n elements find whether the element X is in the array and find its position. Inputs: a=[a[i], i=0,1,…,n-1] – the list with n elements Output: pos – int How to do it: Step 1. (initialization) pos=-1; Step 2 ...
Sorting algorithm
A sorting algorithm is an algorithm that puts elements of a list in a certain order. The most-used orders are numerical order and lexicographical order. Efficient sorting is important for optimizing the use of other algorithms (such as search and merge algorithms) which require input data to be in sorted lists; it is also often useful for canonicalizing data and for producing human-readable output. More formally, the output must satisfy two conditions: The output is in nondecreasing order (each element is no smaller than the previous element according to the desired total order); The output is a permutation (reordering) of the input.Further, the data is often taken to be in an array, which allows random access, rather than a list, which only allows sequential access, though often algorithms can be applied with suitable modification to either type of data.Since the dawn of computing, the sorting problem has attracted a great deal of research, perhaps due to the complexity of solving it efficiently despite its simple, familiar statement. For example, bubble sort was analyzed as early as 1956. A fundamental limit of comparison sorting algorithms is that they require linearithmic time – O(n log n) – in the worst case, though better performance is possible on real-world data (such as almost-sorted data), and algorithms not based on comparison, such as counting sort, can have better performance. Although many consider sorting a solved problem – asymptotically optimal algorithms have been known since the mid-20th century – useful new algorithms are still being invented, with the now widely used Timsort dating to 2002, and the library sort being first published in 2006.Sorting algorithms are prevalent in introductory computer science classes, where the abundance of algorithms for the problem provides a gentle introduction to a variety of core algorithm concepts, such as big O notation, divide and conquer algorithms, data structures such as heaps and binary trees, randomized algorithms, best, worst and average case analysis, time-space tradeoffs, and upper and lower bounds.