We develop an algorithm for the Dutch National Flag problem that has an adjustable integer parameter $\operatorname{smax} \geqq 0$ allowing a time/space tradeoff. (Let n be the length of the input to be ordered.) The space required is proportional to smax (but independent of n), and the average number of swaps required is 关键词： Dutch National Flag problem   eulerian digraphs   algorithm design   loop invariant   stepwise refinement   probabilistic analysis of algorithms  

We consider the problem of choosing K “medians” among n points on the Euclidean plane such that the sum of the distances from each of the n points to its closest median is minimized. We show that this problem is NP-complete. We also present two heuristics that produce arbitrarily good solutions with probability going to 1. One is a partition heuristic, and works when K grows linearly—or almost so—with n. The other is the “honeycomb” heuristic, and is applicable to rates of growth of K of the form K∼n location problem   K-median problem   NP-complete problem   probabilistic analysis of algorithms