[The sword refers to the offer brushing the question] AcWing 46. Post-order traversal sequence of binary search tree (recursion, tree)

ideas

What is a binary search tree

It can be seen that in a binary tree:

• If the left subtree of any node is not empty, the value of all nodes on the left subtree is less than the value of its root node;
• If the right subtree of any node is not empty, then the value of all nodes on the right subtree is greater than the value of its root node;
• The left and right subtrees of any node are also binary search trees respectively;
• There are no nodes with equal keys.

The topic is to judge whether a sequence is a legal post-order traversal sequence of a binary search tree.
Recursion + post-order traversal simulation of tree

topic

Input an integer array to determine whether the array is the result of a post-order traversal of a binary search tree.

Returns true if so, false otherwise.

Suppose any two numbers of the input array are different from each other.
data range

Array length [0,1000]

.
Sample

Input: [4, 8, 6, 12, 16, 14, 10]

output: true

java code

class Solution {
    
    
    
    private int [] seq;
    
    public boolean dfs(int l, int r)
    {
    
    
        if (l >= r) return true;
        int root = seq[r];
        int k = l;
        while (k < r && seq[k] < root) k++;
        
        for (int i = k; i < r; i++)
            if (seq[i] < root)  // 右边应该都比root大
                return false;
                
        // 递归处理左右两边
        return dfs(l, k - 1) && dfs(k, r - 1);
    }
    
    public boolean verifySequenceOfBST(int [] sequence) {
    
    
        seq = sequence;
        return dfs(0, seq.length -1);
    }
}