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Algorithm Analysis

Algorithm Analysis. Run time complexity. Analysis Concepts. Input Size Number of input units Sorting – List length Adding 2 numbers – Number digits Running Time Number of basic operations Sorting – Comparison Adding 2 numbers – Computing sum & carry. Orders of Growth.

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Algorithm Analysis

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  1. Algorithm Analysis Run time complexity

  2. Analysis Concepts • Input Size • Number of input units • Sorting – List length • Adding 2 numbers – Number digits • Running Time • Number of basic operations • Sorting – Comparison • Adding 2 numbers – Computing sum & carry

  3. Orders of Growth

  4. Worst Case / Every Case • Every case refers to algorithms whose run time do not depend on input but only size. Examples : Adding sequence of numbers, etc. • Worst case refers to algorithms whose run time does depend on input as well as size. Examples : Insertion Sort

  5. Big Oh Notation • A function f(n) is O(g(n)) iff • There is an integer no and • There is a constant c such that • f(k) < c g(k) when k > no • Show that an2 + bn + c is O(n2)

  6. Analysis of MaxElement • Determines value of largest element in array • Maxval = A(0) • For I = 1 to n-1 • If A(I) > Maxval • Maxval = A(I) • Return Maxval

  7. Unique Element • For I = 0 to n-1 • For J = I+1 to n-2 • If A(J) = A(I) return false • Return True

  8. Efficiency Analysis • Measure input size • Identify basic operation • Determine whether number of times basic operation is every case or worst case • Calculate number of times T(n) basic operation is executed as function of input size n • Determine Order of T

  9. Analysis of MaxElt and UniqueElt • MaxElt • Has to go thru entire array, regardless of values • Every Case • O(n) • UniqueElt • May detect false on 1st comparison or last • Best Case / Worst Case • O(1) / O(n2)

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