#201 Segment Tree Build

题目描述：

The structure of Segment Tree is a binary tree which each node has two attributesstart 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 two parameters start and end, so that we can create a corresponding segment tree with every node has the correct start and end value, return the root of this segment tree.

Have you met this question in a real interview? 

Yes

Clarification

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

Example

Given start=0, end=3. The segment tree will be:

               [0,  3]             /        \      [0,  1]           [2, 3]      /     \           /     \   [0, 0]  [1, 1]     [2, 2]  [3, 3]

Given start=1, end=6. The segment tree will be:

               [1,  6]             /        \      [1,  3]           [4,  6]      /     \           /     \   [1, 2]  [3,3]     [4, 5]   [6,6]   /    \           /     \[1,1]   [2,2]     [4,4]   [5,5]

题目思路：

这题就是简单的recursion。

Mycode（AC = 276ms）：

/** * Definition of SegmentTreeNode: * class SegmentTreeNode { * public: *     int start, end; *     SegmentTreeNode *left, *right; *     SegmentTreeNode(int start, int end) { *         this->start = start, this->end = end; *         this->left = this->right = NULL; *     } * } */class Solution {public:    /**     *@param start, end: Denote an segment / interval     *@return: The root of Segment Tree     */    SegmentTreeNode * build(int start, int end) {        // write your code here        if (start > end) {            return NULL;        }        else if (start == end) {            return new SegmentTreeNode(start, end);        }        else {            SegmentTreeNode *root = new SegmentTreeNode(start, end);            root->left = build(start, (start + end) / 2);            root->right = build((start + end) / 2 + 1, end);            return root;        }    }};