id: 04145299 dt: j an: 04145299 au: Rem, M. ti: Small programming exercises 24. so: Sci. Comput. Program. 14, No.1, 97-101 (1990). py: 1990 pu: Elsevier Science B.V. (North-Holland), Amsterdam la: EN cc: ut: convex neighbour equality; lexicographically greatest subsequence ci: li: doi:10.1016/0167-6423(90)90060-Q ab: Summary: A function f is called convex if f(i) does not exceed the average of f(i- 1) and \$f(i+1)\$. Examples of convex functions are \$f(x)=0\$ and \$f(x)=x\sp 2\$. Exercise 55 deals with an array that represents a convex function. We have to check whether the array contains equal consecutive elements. This problem may be solved in O(log N) time for an array of size N. I owe this problem to Jan L. A. van de Snepscheut. A subsequence of a sequence is one that can be obtained by deleting zero or more elements from the original sequence. Exercise 56 asks to write a program that determines the lexicographically greatest subsequence of a given sequence. It allows a solution with an execution time that is linear in the length of the given sequence. This problem is due to Anne Kaldewaij. rv: