Midterm Review1.3

Midterm Review1.3 - Time Complexity of an Algorithm The...

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Unformatted text preview: Time Complexity of an Algorithm The time complexity of an algorithm is the largest time required on any input of size n. (Worst case analysis.) O(n2): For any input size n n0, the algorithm takes no more than cn2 time on every input. (n2): For any input size n n0, the algorithm takes at least cn2 time on at least one input. (n2): Do both. CSE 2011 Prof. J. Elder - 11 - Last Updated: 1/7/10 10:14 AM Time Complexity of a Problem The time complexity of a problem is the time complexity of the fastest algorithm that solves the problem. O(n2): Provide an algorithm that solves the problem in no more than this time. Remember: for every input, i.e. worst case analysis! (n2): Prove that no algorithm can solve it faster. Remember: only need one input that takes at least this long! (n2): Do both. CSE 2011 Prof. J. Elder - 12 - Last Updated: 1/7/10 10:14 AM Data Structures So Far Linear Data Structures Arrays Linked Lists Stacks Queues Priority Queues Non-Linear Data Structures Trees Heaps Hash Tables CSE 2011 Prof. J. Elder - 13 - Last Updated: 1/7/10 10:14 AM Arrays CSE 2011 Prof. J. Elder - 14 - Last Updated: 1/7/10 10:14 AM Arrays Array: a sequence of indexed components with the following properties: array size is fixed at the time of array’s construction int numbers = new int [10]; array elements are placed contiguously in memory address of any element can be calculated directly as its offset from the beginning of the array consequently, array components can be efficiently inspected or updated in O(1) time, using their indices randomNumber = numbers[5]; numbers[2] = 100; CSE 2011 Prof. J. Elder - 15 - Last Updated: 1/7/10 10:14 AM ...
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This note was uploaded on 02/14/2012 for the course CSE 2011Z taught by Professor Elder during the Fall '11 term at York University.

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