Lintcode: Segment Tree Build
3951 ワード
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 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
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]
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
1 /**
2 * Definition of SegmentTreeNode:
3 * public class SegmentTreeNode {
4 * public int start, end;
5 * public SegmentTreeNode left, right;
6 * public SegmentTreeNode(int start, int end) {
7 * this.start = start, this.end = end;
8 * this.left = this.right = null;
9 * }
10 * }
11 */
12 public class Solution {
13 /**
14 *@param start, end: Denote an segment / interval
15 *@return: The root of Segment Tree
16 */
17 public SegmentTreeNode build(int start, int end) {
18 // write your code here
19 if (start > end) return null;
20 if (start == end) return new SegmentTreeNode(start, start);
21 SegmentTreeNode cur = new SegmentTreeNode(start, end);
22 cur.left = build(cur.start, (cur.start+cur.end)/2);
23 cur.right = build((cur.start+cur.end)/2+1, cur.end);
24 return cur;
25 }
26 }