654-Maximum Binary Tree

Description

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.

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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

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Note:

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

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問題描述

給定一個沒有重複元素的陣列。由此陣列建立的最大樹定義如下:

1. 根節點為陣列中的最大的數
2. 左子樹為根據陣列的最大的數的左半部分建立的最大樹
3. 右子樹為根據陣列的最大的數的右半部分建立的最大樹

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問題分析

遞迴的話， 注意起始位置和結束位置， 找到最大的數建立當前根節點即可

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解法1

class Solution {
    public TreeNode constructMaximumBinaryTree(int[] nums) {
        Deque<TreeNode> stack = new LinkedList();

        for(int i = 0; i < nums.length; i++) {
            TreeNode curr = new TreeNode(nums[i]);
            while(!stack.isEmpty() && stack.peek().val < nums[i]) {
                curr.left = stack.pop();
            }
            if(!stack.isEmpty()) {
                stack.peek().right = curr;
            }
            stack.push(curr);
        }

        return stack.isEmpty() ? null : stack.removeLast();
    }
}

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解法2

class Solution {
    public TreeNode constructMaximumBinaryTree(int[] nums) {
        if(nums == null) return null;

        return constructTree(nums, 0, nums.length);
    }
    public TreeNode constructTree(int[] nums,int start,int end){
        if(start == end) return null;

        int index = findMax(nums, start, end);
        TreeNode root = new TreeNode(nums[index]);

        root.left = constructTree(nums, start, index);
        root.right = constructTree(nums, index + 1, end);

        return root;
    }
    public int findMax(int[] nums, int start, int end){
        int index = start;

        for(int i = start;i < end;i ++){
            if(nums[i] > nums[index]){
                index = i;
            }
        }

        return index;
    }