654. Maximum Binary Tree

Given an integer array with no duplicates. A maximum tree building on this array is defined as follow:

1. The root is the maximum number in the array. 
2. The left subtree is the maximum tree constructed from left part subarray divided by the maximum number.
3. The right subtree is the maximum tree constructed from right part subarray divided by the maximum number.

Construct the maximum tree by the given array and output the root node of this tree.

Example 1:

Input: [3,2,1,6,0,5]
Output: return the tree root node representing the following tree:

      6
    /   \
   3     5
    \    / 
     2  0   
       \
        1

Note:

1. The size of the given array will be in the range [1,1000].

Solution:

Given an index, we can find the maximum value of its left and the maximum value of its right.

We recursively build the left max as left child and right max as right child.

For each node, we need O(n) to go through the array and find the max value. And we have n nodes in total.

Therefore, the time complexity is O(n²), and the space complexity is O(n).


Code:

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public TreeNode constructMaximumBinaryTree(int[] nums) {
        return buildTree(nums, 0, nums.length);
    }
    
    public TreeNode buildTree(int[] nums, int left, int right) {
        if (left == right) {
            return null;
        }
        int maxIndex = findMax(nums, left, right);
        TreeNode root = new TreeNode(nums[maxIndex]);
        root.left = buildTree(nums, left, maxIndex);
        root.right = buildTree(nums, maxIndex + 1, right);
        return root;
    }

    public int findMax(int[] nums, int left, int right) {
        int maxIndex = left;
        for (int i = left; i < right; i++) {
            if (nums[i] > nums[maxIndex]) {
                maxIndex = i;
            }
        }
        return maxIndex;
    }
}