Segment Tree Build II

Problem

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.

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)

Note

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

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) {
        if (A.length < 1) return null;
        SegmentTreeNode root = build(0, A.length - 1);
        setMax(A, root);
        return root;
    }

    private SegmentTreeNode build(int start, int end) {
        if (start > end) {
            return null;
        }
        SegmentTreeNode node = new SegmentTreeNode(start, end);
        if (start == end) {
            return node;
        }

        node.left = build(start, (start + end) / 2);
        node.right = build((start + end) / 2 + 1, end);

        return node;
    }

    private int setMax(int[] A, SegmentTreeNode node) {
        if (node.start == node.end) {
            node.max = A[node.start];

        } else {
            node.max = Math.max(setMax(A, node.left), setMax(A, node.right));

        }
        return node.max;
    }
}