【剑指Offer】33. 二叉搜索树的后序遍历序列

 

题目描述

输入一个整数数组，判断该数组是不是某二叉搜索树的后序遍历的结果。假设输入的数组的任意两个数字都互不相同。

例如，下图是后序遍历序列 1,3,2 所对应的二叉搜索树。

public class Solution {
    public boolean VerifySquenceOfBST(int [] sequence) {
        if(sequence == null || sequence.length == 0)
            return false;
        return verify(sequence, 0, sequence.length-1);
    }
    private boolean verify(int[] sequence, int first, int last) {
        // 终止
        if(last-first <= 1)
            return true;
        
        int curIndex = first;
        int root = sequence[last];
        
        // 树左
        while(curIndex<last && sequence[curIndex]<=root) 
            curIndex++;
        
        // 树右
        for(int i=curIndex; i<last; i++) {
            if(sequence[i]<root)
                return false;
        }
        
        // 递归
        return verify(sequence, first, curIndex-1) && verify(sequence, curIndex, last-1);
    }
}

public class Solution {
    public boolean VerifySquenceOfBST(int [] sequence) {
        if(sequence == null || sequence.length == 0) return false;
        return dfs(sequence, 0, sequence.length-1);
    }
    
    private boolean dfs(int [] arr, int l, int r) {
        // 临界判断
        if(l >= r) return true;
        
        int p = l;
        int root = arr[r];
        
        // 左
        while(arr[p] < root) p++;
        int m = p;
        
        // 右
        while(arr[p] > root) p++;
        
        return (p == r) && dfs(arr, l, m-1) && dfs(arr, m, r-1);
    }
}