算法导论习题[Exercises 9.3-7 ]

原创于 2006-09-05 22:36:00 发布 · 2.7k 阅读

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#算法 #numbers #output #integer #algorithm

本文介绍了一种线性时间复杂度O(n)的算法，该算法能在给定的一组n个不同数值中找到距离中位数最近的k个数。通过一次遍历确定中位数，并计算每个数与中位数的距离，再次使用线性选择算法找出距离中位数最近的k个数。

Describe an O(n)-time algorithm that, given a set S of n distinct numbers and a positive integer k ≤ n, determines the k numbers in S that are closest to the median of S.

solution:

1: procedure k_Closest(S, k) //S: a set of n numbers and k: an integer
2: Output = nothing;
3: m = Select(S, n,n/2)                       //O(n)
4: for all s in S and s != m               //O(n)
5: s.distance = |m − s|
6: end for
7: md = Select(S.distance, k)        //O(n)
8: for all s in S
9: if s.distance <= md.distance then   //O(n)
10: Output = Output + s
11: end if
12: end for
13: return Output
14: end procedure

可见可以在线形时间能得到集合S的K个最邻近点