NADAR SARASWATHI COLLEGE OF ARTS AND SCIENCE Analysis of Algorithm & Analysis Framework
Analysis of Algorithm Analysis of algorithms is usually used in a narrower technical sense to mean an investigation of an algorithms efficiency with respect to two resources. Running time Memory space
Runtime Analysis Run-time analysis is a theoretical classification that estimates and anticipates the increase in running time (or run-time) of an algorithm as its input size (usually denoted as n) increases.  Orders of growth  Empirical orders of growth  Evaluating run-time complexity Shortcomings of empirical metrics
Analysis Framework Issuses  Correctness  Time efficiency  Space efficiency  Optimality
An algorithm is said to be asymptotically optimal if, roughly speaking, for large input it performs at worst a constant factors were than the best possible algorithm. A Sequence of an algorithm being asymptotically optimal is that, for large enough input, no algorithm can outperform it by more than a fixed constants factors. Approches 1. Theoretical analysis 2. Empirical analysis
Measuring an input size  Time efficiency is analyzed by determining the number of repetitions of the basic operation as a function of input size Influenced by the data representation, e.g. matrix Influenced by the operations of the algorithm, e.g. spell-checker Influenced by the properties of the objects in the problem, e.g. checking if a given integer is a prime number.
Unit for measuring running time  Using Standard unit of time measurement a second, a millisecond and the running time of a program implementing the algorithm.  Basic operation:  Applied to all input items in order to carry out the algorithm.  Contributes most towards the running time of the algorithm.
An important applications. Let c op be the time of execution algorithms basic operation on particular computer and let C(n) be the number times this operation needs to be executed for this algorithm. T(n): running time c op : execution time for basic operation C(n) : number of times basic operation is executed Then we have: T(n) ≈ c op C(n)
Types of formulas count for basic operations  Exact formula e.g., C(n) = n(n-1)/2  Formula indicating order of growth with specific multiplicative constant e.g. C(n) ≈ 0.5 n2  Formula indicating order of growth with unknown multiplicative constant e.g., C(n) ≈ cn2  Example: Let C(n) = 3n(n-1) 3n2
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Analysis algorithm

  • 1.
    NADAR SARASWATHI COLLEGEOF ARTS AND SCIENCE Analysis of Algorithm & Analysis Framework
  • 2.
    Analysis of Algorithm Analysisof algorithms is usually used in a narrower technical sense to mean an investigation of an algorithms efficiency with respect to two resources. Running time Memory space
  • 3.
    Runtime Analysis Run-time analysisis a theoretical classification that estimates and anticipates the increase in running time (or run-time) of an algorithm as its input size (usually denoted as n) increases.  Orders of growth  Empirical orders of growth  Evaluating run-time complexity Shortcomings of empirical metrics
  • 4.
    Analysis Framework Issuses  Correctness Time efficiency  Space efficiency  Optimality
  • 5.
    An algorithm issaid to be asymptotically optimal if, roughly speaking, for large input it performs at worst a constant factors were than the best possible algorithm. A Sequence of an algorithm being asymptotically optimal is that, for large enough input, no algorithm can outperform it by more than a fixed constants factors. Approches 1. Theoretical analysis 2. Empirical analysis
  • 6.
    Measuring an inputsize  Time efficiency is analyzed by determining the number of repetitions of the basic operation as a function of input size Influenced by the data representation, e.g. matrix Influenced by the operations of the algorithm, e.g. spell-checker Influenced by the properties of the objects in the problem, e.g. checking if a given integer is a prime number.
  • 7.
    Unit for measuringrunning time  Using Standard unit of time measurement a second, a millisecond and the running time of a program implementing the algorithm.  Basic operation:  Applied to all input items in order to carry out the algorithm.  Contributes most towards the running time of the algorithm.
  • 8.
    An important applications.Let c op be the time of execution algorithms basic operation on particular computer and let C(n) be the number times this operation needs to be executed for this algorithm. T(n): running time c op : execution time for basic operation C(n) : number of times basic operation is executed Then we have: T(n) ≈ c op C(n)
  • 9.
    Types of formulascount for basic operations  Exact formula e.g., C(n) = n(n-1)/2  Formula indicating order of growth with specific multiplicative constant e.g. C(n) ≈ 0.5 n2  Formula indicating order of growth with unknown multiplicative constant e.g., C(n) ≈ cn2  Example: Let C(n) = 3n(n-1) 3n2
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