LintCode: Segment 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.

Have you met this question in a real interview? 

Yes

Example

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)

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

Code (Java):

/**
 * 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;
 *     }
 * }
 */
public class Solution {
    /**
     *@param A: a list of integer
     *@return: The root of Segment Tree
     */
    public SegmentTreeNode build(int[] A) {
        // write your code here
        if (A == null || A.length == 0) {
            return null;
        }
        
        return buildHelper(A, 0, A.length - 1);
    }
    
    private SegmentTreeNode buildHelper(int[] A, int lo, int hi) {
        if (lo > hi) {
            return null;
        }
        
        if (lo == hi) {
            SegmentTreeNode node = new SegmentTreeNode(lo, hi, A[lo]);
            return node;
        }
        
        int mid = lo + (hi - lo) / 2;
        SegmentTreeNode root = new SegmentTreeNode(lo, hi);
        
        root.left = buildHelper(A, lo, mid);
        root.right = buildHelper(A, mid + 1, hi);
        
        root.max = Math.max(root.left.max, root.right.max);
        
        return root;
    }
}