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题目

• 原题连接：124. 二叉树中的最大路径和

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1- 思路

模式识别：最大路径和 ——> 递归

递归 dfs 思路

递归公式

• sum = 自己 + 左 + 右

递归中的返回结果

• output = 自己 + max(左,右)

找结果——更新结果

• maxSum = Math.max(maxSum, sum);

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2- 实现

⭐124. 二叉树中的最大路径和——题解思路

class Solution {
    int maxSum = Integer.MIN_VALUE;
    public int maxPathSum(TreeNode root) {
        // 递归
        dfs(root);
        return maxSum;
    }


    public int dfs(TreeNode root){
        // 1. 终止条件
        if(root==null){
            return 0;
        }

        // 2. 递归公式，递归逻辑
        int left = dfs(root.left);
        int right = dfs(root.right);
        int sum = root.val + left + right;

        maxSum = Math.max(sum,maxSum);

        // 3. 每次返回值
        int output = root.val + Math.max(left,right);
        if(output>0) return output;
        return 0;
    }
}

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3- ACM 实现

public class treeMaxPath {

    static class TreeNode{
        int val;
        TreeNode left;
        TreeNode right;
        TreeNode(){}
        TreeNode(int x){
            val = x;
        }
    }

    public static TreeNode build(Integer[] nums){
        // 借助队列来构造树
        Queue<TreeNode> queue = new LinkedList<>();
        TreeNode root = new TreeNode(nums[0]);
        queue.offer(root);
        int index = 1;
        while(!queue.isEmpty()){
            TreeNode node = queue.poll();
            if(index<nums.length && nums[index]!=null){
                node.left = new TreeNode(nums[index]);
                queue.offer(node.left);
            }
            index++;
            if(index<nums.length && nums[index]!=null){
                node.right = new TreeNode(nums[index]);
                queue.offer(node.right);
            }
            index++;
        }
        return root;
    }

    public static int dfs(TreeNode root){
        // 1.终止条件
        if(root==null){
            return 0;
        }

        // 2. 递归
        int left = dfs(root.left);
        int right = dfs(root.right);
        int sum = root.val + left + right;
        maxSum = Math.max(sum,maxSum);

        int output = root.val + Math.max(left,right);
        if(output>0) return output;
        return 0;
    }

    static int maxSum = Integer.MIN_VALUE;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        System.out.println("输入二叉树构造数组");
        String input = sc.nextLine();
        input = input.replace("[","");
        input = input.replace("]","");
        String[] parts = input.split(",");
        Integer[] nums = new Integer[parts.length];
        for(int i = 0 ; i < parts.length;i++){
            if(!parts[i].equals("null")){
                nums[i] = Integer.parseInt(parts[i]);
            }else{
                nums[i] = null;
            }
        }
        TreeNode root = build(nums);
        dfs(root);
        System.out.println("结果是"+maxSum);
    }
}

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