lintcode 中等题：Segmemt Tree Build II

题目

Segmemt Tree Build II

The structure of Segment Tree is a binary tree which each node has two attributes

start

and

end

denote an segment / interval.

start and end are both integers, they should be assigned in following rules:

The root's start and end is given by

build

method.

The left child of node A has

start=A.left, end=(A.left + A.right) / 2

.

The right child of node A has

start=(A.left + A.right) / 2 + 1, end=A.right

.

if start equals to end, there will be no children for this node.

Implement a

build

method with a given array, so that we can create a corresponding segment tree with every node value represent the corresponding interval max value in the array, return the root of this segment tree.

样例

Given

[3,2,1,4]

. The segment tree will be:

[0,  3] (max = 4)
/            \
[0,  1] (max = 3)     [2, 3]  (max = 4)
/        \               /             \
[0, 0](max = 3)  [1, 1](max = 2)[2, 2](max = 1) [3, 3] (max = 4)

说明

Segment Tree (a.k.a Interval Tree) is an advanced data structure which can support queries like:

which of these intervals contain a given point

which of these points are in a given interval

See wiki: Segment Tree Interval Tree

解题

理解题意：根据给的数组构建段树，该节点有区间及其该区间的最大值组成。区间的左右节点利用上面的规则计算。

/**
* Definition of SegmentTreeNode:
* public class SegmentTreeNode {
*     public int start, end, max;
*     public SegmentTreeNode left, right;
*     public SegmentTreeNode(int start, int end, int max) {
*         this.start = start;
*         this.end = end;
*         this.max = max
*         this.left = this.right = null;
*     }
* }
*/

这个节点定义要好好理解。

"""
Definition of SegmentTreeNode:
class SegmentTreeNode:
def __init__(self, start, end, max):
self.start, self.end, self.max = start, end, max
self.left, self.right = None, None
"""

class Solution:
# @oaram A: a list of integer
# @return: The root of Segment Tree
def build(self, A):
# write your code here
return self.buildX(0,len(A) - 1,A)
def buildX(self,start,end,A):
if start > end:
return None
maxX = 0
root = SegmentTreeNode(start,end)
if start != end:
mid = int((start + end)/2)
root.left = self.buildX(start,mid,A)
root.right = self.buildX(mid+1,end,A)
root.max = max(root.left.max,root.right.max)
else:
root.max = A[start]
return root

Python Code
总耗时: 750 ms