'Asymptotically tight' presentation slideshows

Discrete Structures & Algorithms Functions & Asymptotic Complexity

Discrete Structures & Algorithms Functions & Asymptotic Complexity. To understand how to perform computations efficiently, we need to know How to count! How to sum a sequence of steps. Reason about the complexity/efficiency of an algorithm. Prove the correctness of our analysis. Logic

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Analysis of Algorithms CS 477/677

Analysis of Algorithms CS 477/677. Instructor: Monica Nicolescu Lecture 9. Array Representation of Heaps. A heap can be stored as an array A . Root of tree is A[1] Left child of A[i] = A[2i] Right child of A[i] = A[2i + 1] Parent of A[i] = A[ ? i/2 ? ] Heapsize[A] ? length[A]

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Asymptotic Notation, Review of Functions & Summations

Asymptotic Notation, Review of Functions & Summations. Asymptotic Complexity. Running time of an algorithm as a function of input size n for large n . Expressed using only the highest-order term in the expression for the exact running time.

600 views • 39 slides

Asymptotic Notation, Review of Functions & Summations

Asymptotic Notation, Review of Functions & Summations. Asymptotic Complexity. Running time of an algorithm as a function of input size n for large n . Expressed using only the highest-order term in the expression for the exact running time.

638 views • 39 slides

Asymptotic Notation, Review of Functions & Summations

Asymptotic Notation, Review of Functions & Summations. Asymptotic Complexity. Running time of an algorithm as a function of input size n for large n . Expressed using only the highest-order term in the expression for the exact running time. Instead of exact running time, say Q ( n 2 ).

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???? ?? Email: { lvmin05@ustc } Spring 2012 ? USTC

????. ???? ?? Email: { lvmin05@ustc.edu.cn } Spring 2012 ? USTC. ??? ????. ????? ???? ???? ????. n ?? , ???? ?( n lg n ), ?????? ???? ?( n 2 ) ???????????????????????????????? ???????? ??????????? ???????????? ??????????? ?????????. ??? ????. ????? ????

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Complexity Analysis

Complexity Analysis. Asymptotic Complexity Big-O (asymptotic) Notation Big-O Computation Rules Proving Big-O Complexity How to determine complexity of code structures. Asymptotic Complexity. Finding the exact complexity, f(n) = number of basic operations , of an algorithm is difficult.

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Chapter 3. Growth of Functions

Chapter 3. Growth of Functions. Outline. Study the asymptotic efficiency of algorithms Give several standard methods for simplifying the asymptotic analysis of algorithms Present several notational conventions used throughout this book

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Long cycles, short cycles, min-degree subgraphs , and feedback arc sets in Eulerian digraphs

Long cycles, short cycles, min-degree subgraphs , and feedback arc sets in Eulerian digraphs. Raphael Yuster joint work with Asaf Shapira. Eilat 2012. Eulerian Digraph : A digraph in which the in-degree equals the out-degree at each vertex. Some properties of Eulerian digraphs:

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Asymptotic Analysis

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Growth of Functions

Growth of Functions. Asymptotic Notation. When we look at a large enough input n , we are studying the asymptotic efficiency Concerned with the running time as the input increases without bound

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Asymptotic Notation, Review of Functions & Summations

Asymptotic Notation, Review of Functions & Summations. Asymptotic Complexity. Running time of an algorithm as a function of input size n for large n . Expressed using only the highest-order term in the expression for the exact running time. Describes behavior of function in the limit.

376 views • 18 slides

Growth of Functions

Growth of Functions. Asymptotic Notation. When we look at a large enough input n , we are studying the asymptotic efficiency Concerned with the running time as the input increases without bound

224 views • 18 slides