二进制搜索树-搜索范围

Question

If I have a binary search tree S with the number pair (a,b) where (a<=b); is there an algorithm that would help me find the elements in S with the key values that are within the range of a,b inclusive ([a,b]).

The runtime restriction is O(h+k), h is the tree height of S, and k is the number of elements within the range.

Answer 1

The classic answer is from "Introduction to Algorithms": http://staff.ustc.edu.cn/~csli/graduate/algorithms/book6/chap14.htm

Step 1: find a, using the normal binary tree lookup.

Step 2: call tree successor iteratively until you find b. Tree successor gives you the next item in the tree:

TREE-SUCCESSOR(x)
  if right[x] ≠ NIL
      then return TREE-MINIMUM (right[x])
  y ← p[x]
  while y ≠ NIL and x = right[y]
      do x ← y
         y ← p[y]
  return y

TREE-MINIMUM (x)
  while left[x] ≠ NIL
      do x ← left[x]
  return x