654. Maximum Binary Tree

Problem Statement

You are given an integer array nums with no duplicates. A maximum binary tree can be built recursively from nums using the following algorithm:

Create a root node whose value is the maximum value in nums.
Recursively build the left subtree on the subarray prefix to the left of the maximum value.
Recursively build the right subtree on the subarray suffix to the right of the maximum value.

Return the maximum binary tree built from nums.

Example 1:

Input: nums = [3,2,1,6,0,5]
Output: [6,3,5,null,2,0,null,null,1]
Explanation: The recursive calls are as follow:
- The largest value in [3,2,1,6,0,5] is 6. Left prefix is [3,2,1] and right suffix is [0,5].
    - The largest value in [3,2,1] is 3. Left prefix is [] and right suffix is [2,1].
        - Empty array, so no child.
        - The largest value in [2,1] is 2. Left prefix is [] and right suffix is [1].
            - Empty array, so no child.
            - Only one element, so child is a node with value 1.
    - The largest value in [0,5] is 5. Left prefix is [0] and right suffix is [].
        - Only one element, so child is a node with value 0.
        - Empty array, so no child.

Example 2:

Input: nums = [3,2,1]
Output: [3,null,2,null,1]

Constraints:

1 <= nums.length <= 1000
0 <= nums[i] <= 1000
All integers in nums are unique.

Intuition

Here, we recursively build the tree, Divide into left
and right sub-tree

Find the maximum and build

Links

https://leetcode.com/problems/maximum-binary-tree/description/

Video Links

Approach 1:

Recursion

C++

class Solution {
public:
    TreeNode* find_ans(vector<int>& nums, int i, int j){
        if(i>j)
            return nullptr;

        int index = helper(nums, i, j);
        TreeNode *root = new TreeNode(nums[index]);

        root->left = find_ans(nums, i, index-1);
        root->right = find_ans(nums, index+1, j);

        return root;
    }

    int helper(vector<int>& nums, int i, int j){
        int idx = 0;
        int maxi = 0;

        for(int index=i; index<=j; index++){
            if(maxi <= nums[index]){
                maxi = nums[index];
                idx = index;
            }
        }

        return idx;
    }

    TreeNode* constructMaximumBinaryTree(vector<int>& nums) {
        int i=0;
        int j=nums.size()-1;

        return find_ans(nums, i, j);
    }
};

Approach 2:

C++

Approach 3:

C++

Approach 4:

C++