2-04-2005
... to prove it. Some have said this problem is to hard for modern day mathematics and computer science. ...
... to prove it. Some have said this problem is to hard for modern day mathematics and computer science. ...
expositions
... Analyze these in detail, presenting or writing them up so that others can really understand in depth. Go beyond what is provided in the text. 3.1 Selection Sort and Bubble Sort: Consider when one would want to use these 3.3 Closest Pair and Convex Hull Problems by brute force 3.4 (Exhaustive Search) ...
... Analyze these in detail, presenting or writing them up so that others can really understand in depth. Go beyond what is provided in the text. 3.1 Selection Sort and Bubble Sort: Consider when one would want to use these 3.3 Closest Pair and Convex Hull Problems by brute force 3.4 (Exhaustive Search) ...
Chapter 2: Fundamentals of the Analysis of Algorithm
... A way of comparing functions that ignores constant factors and small input sizes • O(g(n)): class of functions f(n) that grow no ...
... A way of comparing functions that ignores constant factors and small input sizes • O(g(n)): class of functions f(n) that grow no ...
Algorithm - SSUET - Computer Science Department
... 1. An algorithm is a precise prescription of how to accomplish a task. 2. Two important issues determine the character of an algorithm: 3. Which operations are available to us? 4. In which order can the operations be performed? 5. One at a time (sequentially). 6. Several at once (in parallel). A Sim ...
... 1. An algorithm is a precise prescription of how to accomplish a task. 2. Two important issues determine the character of an algorithm: 3. Which operations are available to us? 4. In which order can the operations be performed? 5. One at a time (sequentially). 6. Several at once (in parallel). A Sim ...
review1
... 3. What does it mean for the return type of a method to be void? 4. What Java keyword is used when invoking a constructor? 5. Suppose a is a one-dimensional array of double. Fill in the blanks in the following code so that it finds the largest element of the array and stores this value in max. doubl ...
... 3. What does it mean for the return type of a method to be void? 4. What Java keyword is used when invoking a constructor? 5. Suppose a is a one-dimensional array of double. Fill in the blanks in the following code so that it finds the largest element of the array and stores this value in max. doubl ...
CS173: Discrete Math
... Time complexity of binary search • For simplicity, assume n=2k,k=log2n • At each iteration, 2 comparisons are used • For example, 2 comparisons are used when the list has 2k-1 elements, 2 comparisons are used when the list has 2k-2, …, 2 comparisons are used when the list has 21 elements • 1 compar ...
... Time complexity of binary search • For simplicity, assume n=2k,k=log2n • At each iteration, 2 comparisons are used • For example, 2 comparisons are used when the list has 2k-1 elements, 2 comparisons are used when the list has 2k-2, …, 2 comparisons are used when the list has 21 elements • 1 compar ...
doc
... believe that a different method is necessary. Existing random and efficient algorithms use scatter/gather I/O to analyze ubiquitous communication. Although similar systems measure vacuum tubes, we realize this purpose without deploying A* search. Our contributions are twofold. We demonstrate that th ...
... believe that a different method is necessary. Existing random and efficient algorithms use scatter/gather I/O to analyze ubiquitous communication. Although similar systems measure vacuum tubes, we realize this purpose without deploying A* search. Our contributions are twofold. We demonstrate that th ...
Problem Set 2 Solutions - Massachusetts Institute of Technology
... only asked you to devise an algorithm.) Notice that each E XTRACT-M IN and I NSERT operation requires O(lg k) time, since there are never more than 2k elements in the heap. The loop requires only a constant amount of other work, and is repeated n times, resulting in O(n lg k) running time. In order ...
... only asked you to devise an algorithm.) Notice that each E XTRACT-M IN and I NSERT operation requires O(lg k) time, since there are never more than 2k elements in the heap. The loop requires only a constant amount of other work, and is repeated n times, resulting in O(n lg k) running time. In order ...
CS 332: Algorithms
... less than twice the cost? ● Yes: ■ Walk through elements by pairs ○ Compare each element in pair to the other ○ Compare the largest to maximum, smallest to minimum ■ Total cost: 3 comparisons per 2 elements = O(3n/2) David Luebke ...
... less than twice the cost? ● Yes: ■ Walk through elements by pairs ○ Compare each element in pair to the other ○ Compare the largest to maximum, smallest to minimum ■ Total cost: 3 comparisons per 2 elements = O(3n/2) David Luebke ...
Mouse in a Maze - Bowdoin College
... 2. What variables are needed? 3. What computations are required to achieve the output? 4. Usually, the first steps in your algorithm bring input values to the variables. 5. Usually, the last steps display the output 6. So, the middle steps will do the computation. 7. If the process is to be repeated ...
... 2. What variables are needed? 3. What computations are required to achieve the output? 4. Usually, the first steps in your algorithm bring input values to the variables. 5. Usually, the last steps display the output 6. So, the middle steps will do the computation. 7. If the process is to be repeated ...
lec12c-Simon
... Proposition 1: There exists a classical deterministic algorithm that, given a subset X G Z 2n , returns a linearly independent subset of G that generates the subgroup X . The algorithm runs in time polynomial in n and linear in the cardinality of X ...
... Proposition 1: There exists a classical deterministic algorithm that, given a subset X G Z 2n , returns a linearly independent subset of G that generates the subgroup X . The algorithm runs in time polynomial in n and linear in the cardinality of X ...
Algorithms examples Correctness and testing
... • Design a Θ(n lg n) algorithm which, given a sequence s of n real numbers and a real number x, checks if s contains two elements with sum x. Let n be the length of s. We can assume the elements of s are sorted (i.e. s[1] < s[2] < ... < s[n]) because sorting takes Θ(n lg n). With this hypothesis, al ...
... • Design a Θ(n lg n) algorithm which, given a sequence s of n real numbers and a real number x, checks if s contains two elements with sum x. Let n be the length of s. We can assume the elements of s are sorted (i.e. s[1] < s[2] < ... < s[n]) because sorting takes Θ(n lg n). With this hypothesis, al ...
Chapter 2: Fundamentals of the Analysis of Algorithm Efficiency
... A way of comparing functions that ignores constant factors and small input sizes ...
... A way of comparing functions that ignores constant factors and small input sizes ...
Lecture 2 - Rabie A. Ramadan
... incoming edges and delete it along with all edges outgoing from it. • There must be at least one source to have the problem solved. • Repeat this process in a remaining diagraph. • The order in which the vertices are deleted yields the desired solution. ...
... incoming edges and delete it along with all edges outgoing from it. • There must be at least one source to have the problem solved. • Repeat this process in a remaining diagraph. • The order in which the vertices are deleted yields the desired solution. ...
CUSTOMER_CODE SMUDE DIVISION_CODE SMUDE
... required to perform a step should always bound above by a constant. In some instances, count of addition of two numbers might be as one step. In such cases approximation of time efficient becomes critical. This consideration might not justify certain situations. If the numbers involved in a computat ...
... required to perform a step should always bound above by a constant. In some instances, count of addition of two numbers might be as one step. In such cases approximation of time efficient becomes critical. This consideration might not justify certain situations. If the numbers involved in a computat ...
Algorithm 1.1 Sequential Search Problem Inputs Outputs
... c) For both of the above algorithms, we want to derive a function for the number of times that the basic operation is performed relative to the problem size. ...
... c) For both of the above algorithms, we want to derive a function for the number of times that the basic operation is performed relative to the problem size. ...
CS214 * Data Structures Lecture 01: A Course Overview
... • Algorithms must satisfy the following criteria: 1) Input – Zero or more quantities are externally supplied. 2) Output – At least one quantity is produced. 3) Definiteness – Each instruction is clear and unambiguous. 4) Finiteness – If we trace out the instructions of an algorithm, then for all cas ...
... • Algorithms must satisfy the following criteria: 1) Input – Zero or more quantities are externally supplied. 2) Output – At least one quantity is produced. 3) Definiteness – Each instruction is clear and unambiguous. 4) Finiteness – If we trace out the instructions of an algorithm, then for all cas ...
PPT
... Sorting to rescue in 2-D? Pick pairs of points closest in x co-ordinate Pick pairs of points closest in y co-ordinate Choose the better of the two ...
... Sorting to rescue in 2-D? Pick pairs of points closest in x co-ordinate Pick pairs of points closest in y co-ordinate Choose the better of the two ...
Rotational Motion
... inertia for the washer about its axis if the inner radius is 1.0 cm and the outer radius is 3.0 cm and the mass is 20 g? ...
... inertia for the washer about its axis if the inner radius is 1.0 cm and the outer radius is 3.0 cm and the mass is 20 g? ...
Rotational Motion
... inertia for the washer about its axis if the inner radius is 1.0 cm and the outer radius is 3.0 cm and the mass is 20 g? ...
... inertia for the washer about its axis if the inner radius is 1.0 cm and the outer radius is 3.0 cm and the mass is 20 g? ...
Quicksort
Quicksort (sometimes called partition-exchange sort) is an efficient sorting algorithm, serving as a systematic method for placing the elements of an array in order. Developed by Tony Hoare in 1959, with his work published in 1961, it is still a commonly used algorithm for sorting. When implemented well, it can be about two or three times faster than its main competitors, merge sort and heapsort.Quicksort is a comparison sort, meaning that it can sort items of any type for which a ""less-than"" relation (formally, a total order) is defined. In efficient implementations it is not a stable sort, meaning that the relative order of equal sort items is not preserved. Quicksort can operate in-place on an array, requiring small additional amounts of memory to perform the sorting.Mathematical analysis of quicksort shows that, on average, the algorithm takes O(n log n) comparisons to sort n items. In the worst case, it makes O(n2) comparisons, though this behavior is rare.