Basic Techniques for Design and Analysis of Algorithms EDWARD M. REINGOLD Department of Computer Science, University of Illinois at Urbana-Champaign reingold@cs.uiuc.edu ANALYZING ALGORITHMS It is convenient to classify algorithms based on the relative amount of time they require: how fast does the time required grow as the size of the problem increases? For example, in the case of arrays, the size of the problem is ordinarily the number of elements in the array. If the size of the problem is measured by a variable n, we can express the time required as function of n, T(n). When this function T(n) grows rapidly, the algorithm becomes unusable for large n; conversely, when T(n) grows slowly, the algorithm remains useful even when n becomes large. The time required by an algorithm is often analyzed by finding and solving a recurrence relation that describes the time required by the algorithm. AN EXAMPLE: INSERTION SORT 10. } 11. 12. void insertionSort (int float x[ ]) { 13. // Sort x[1] . . . x[n] 14. if (n 1) { 15. insertionSort (n 1, x); 16. insert (x, n, x[n]); 17. } 18. } n, To determine the time required in the
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Basic techniques for design and analysis of algorithms
Reingold, Edward M.
Follow ACM Computing Surveys (CSUR)
, Volume 28 (1)
Association for Computing Machinery – Mar 1, 1996
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