从 Preorder 计算完整二叉树的深度

给定二叉树的前序，计算其深度（或高度）[从深度 0 开始]。预购以具有两个可能字符的字符串形式给出。

1. 'l' 表示叶子
2. 'n' 表示内部节点

给定的树可以看作是一个完整的二叉树，其中每个节点都有 0 个或两个子节点。一个节点的两个子节点可以是“n”或“l”或两者的混合。
例子 ：

Input  : nlnll
Output : 2
Explanation :

Input  : nlnnlll
Output : 3

给定二叉树的前序所以遍历
此外，我们会得到一个 char字符串（由 'n' 和 'l' 组成），因此也不需要实现树。
递归函数将是：
1）基本情况：返回0；当 tree[i] = 'l' 或 i >= strlen(tree)
2) find_depth( tree[i++] ) //左子树
3) find_depth( tree[i++] ) //右子树
其中 i 是字符串树的索引。

C++

// C++ program to find height of full binary tree
// using preorder
#include 
using namespace std;
 
// function to return max of left subtree height
// or right subtree height
int findDepthRec(char tree[], int n, int& index)
{
    if (index >= n || tree[index] == 'l')
        return 0;
 
    // calc height of left subtree (In preorder
    // left subtree is processed before right)
    index++;
    int left = findDepthRec(tree, n, index);
 
    // calc height of right subtree
    index++;
    int right = findDepthRec(tree, n, index);
 
    return max(left, right) + 1;
}
 
// Wrapper over findDepthRec()
int findDepth(char tree[], int n)
{
    int index = 0;
    findDepthRec(tree, n, index);
}
 
// Driver program
int main()
{
    // Your C++ Code
    char tree[] = "nlnnlll";
    int n = strlen(tree);
 
    cout << findDepth(tree, n) << endl;
 
    return 0;
}

Java

// Java program to find height
// of full binary tree using
// preorder
import java .io.*;
 
class GFG
{
    // function to return max
    // of left subtree height
    // or right subtree height
    static int findDepthRec(String tree,
                            int n, int index)
    {
        if (index >= n ||
            tree.charAt(index) == 'l')
            return 0;
 
        // calc height of left subtree
        // (In preorder left subtree
        // is processed before right)
        index++;
        int left = findDepthRec(tree,
                                n, index);
 
        // calc height of
        // right subtree
        index++;
        int right = findDepthRec(tree, n, index);
 
        return Math.max(left, right) + 1;
    }
 
    // Wrapper over findDepthRec()
    static int findDepth(String tree,
                         int n)
    {
        int index = 0;
        return (findDepthRec(tree,
                             n, index));
    }
 
    // Driver Code
    static public void main(String[] args)
    {
        String tree = "nlnnlll";
        int n = tree.length();
        System.out.println(findDepth(tree, n));
    }
}
 
// This code is contributed
// by anuj_67.

Python3

#Python program to find height of full binary tree
# using preorder
     
# function to return max of left subtree height
# or right subtree height
def findDepthRec(tree, n, index) :
 
    if (index[0] >= n or tree[index[0]] == 'l'):
        return 0
 
    # calc height of left subtree (In preorder
    # left subtree is processed before right)
    index[0] += 1
    left = findDepthRec(tree, n, index)
 
    # calc height of right subtree
    index[0] += 1
    right = findDepthRec(tree, n, index)
    return (max(left, right) + 1)
 
# Wrapper over findDepthRec()
def findDepth(tree, n) :
 
    index = [0]
    return findDepthRec(tree, n, index)
 
         
# Driver program to test above functions
if __name__ == '__main__':
    tree= "nlnnlll"
    n = len(tree)
 
    print(findDepth(tree, n))
 
# This code is contributed by SHUBHAMSINGH10

C#

// C# program to find height of
// full binary tree using preorder
using System;
 
class GFG {
 
    // function to return max of left subtree
    // height or right subtree height
    static int findDepthRec(char[] tree, int n, int index)
    {
        if (index >= n || tree[index] == 'l')
            return 0;
 
        // calc height of left subtree (In preorder
        // left subtree is processed before right)
        index++;
        int left = findDepthRec(tree, n, index);
 
        // calc height of right subtree
        index++;
        int right = findDepthRec(tree, n, index);
 
        return Math.Max(left, right) + 1;
    }
 
    // Wrapper over findDepthRec()
    static int findDepth(char[] tree, int n)
    {
        int index = 0;
        return (findDepthRec(tree, n, index));
    }
 
    // Driver program
    static public void Main()
    {
        char[] tree = "nlnnlll".ToCharArray();
        int n = tree.Length;
        Console.WriteLine(findDepth(tree, n));
    }
}
 
// This code is contributed by vt_m.

Javascript

    // Javascript program to find height of
    // full binary tree using preorder
     
    // function to return max of left subtree
    // height or right subtree height
    function findDepthRec(tree, n, index)
    {
        if (index >= n || tree[index] == 'l')
            return 0;
  
        // calc height of left subtree (In preorder
        // left subtree is processed before right)
        index++;
        let left = findDepthRec(tree, n, index);
  
        // calc height of right subtree
        index++;
        let right = findDepthRec(tree, n, index);
  
        return Math.max(left, right) + 1;
    }
  
    // Wrapper over findDepthRec()
    function findDepth(tree, n)
    {
        let index = 0;
        return (findDepthRec(tree, n, index));
    }
     
    let tree = "nlnnlll".split('');
    let n = tree.length;
    document.write(findDepth(tree, n));
     

输出：

3

时间复杂度： O(N)

辅助空间： O(1)