654. Maximum Binary Tree**

654. Maximum Binary Tree**

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

题目描述

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

C++ 实现 1

找到数组中的最大元素来构建根节点, 然后再构建左右子树. 下面是采用 std::max_element 来求最大值的递归方法.

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
private:
    TreeNode* constructMaximumBinaryTree(vector<int> &nums, int l, int r) {
        if (nums.empty() || l >= r)
            return nullptr;

        auto idx = std::max_element(nums.begin() + l, nums.begin() + r) - nums.begin();
        TreeNode *root = new TreeNode(nums[idx]);
        root->left = constructMaximumBinaryTree(nums, l, idx);
        root->right = constructMaximumBinaryTree(nums, idx + 1, r);
        return root;
    }
public:
    TreeNode* constructMaximumBinaryTree(vector<int>& nums) {
        return constructMaximumBinaryTree(nums, 0, nums.size());
    }
};

C++ 实现 2

如果自己写求最大值的方法:

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
private:
    pair<int, int> find_max(const vector<int> &nums, int i, int j) {
        pair<int, int> res;
        int max_value = INT32_MIN;
        for (int k = i; k <= j; ++ k) {
            if (nums[k] > max_value) {
                max_value = nums[k];
                res = {k, nums[k]};
            }
        }
        return res;
    }
    TreeNode* construct(const vector<int> &nums, int i, int j) {
        if (i > j) return nullptr;
        auto p = find_max(nums, i, j);
        auto idx = p.first;
        TreeNode *root = new TreeNode(p.second);
        root->left = construct(nums, i, idx - 1);
        root->right = construct(nums, idx + 1, j);
        return root;
    }
public:
    TreeNode* constructMaximumBinaryTree(vector<int>& nums) {
        return construct(nums, 0, nums.size() - 1);
    }
};