255.Verify Preorder Sequence in Binary Search Tree

    /*
     * 255.Verify Preorder Sequence in Binary Search Tree 
     * Given an array of numbers,
     * verify whether it is the correct preorder traversal sequence of a binary
     * search tree. 
     * 11.21 By Mingyang
     * Time complexity O(n^2), space complexity O(1). 
     */
      public boolean verifyPreorder(int[] preorder) {
            if (preorder == null || preorder.length <= 1) {
                return true;
            }         
            return dfs(preorder, 0, preorder.length - 1);
        }     
        private boolean dfs(int[] preorder, int low, int hi) {
            if (low >= hi) {
                return true;
            }      
            int root = preorder[low];
            int i = low + 1;
            while (i <= hi && preorder[i] < root) {
                i++;
            }         
            int j = i;
            while (j <= hi && preorder[j] > root) {
                j++;
            }        
            if (j <= hi) {
                return false;
            }        
            return dfs(preorder, low + 1, i - 1) && dfs(preorder, i, hi);
        }

    /*
     * 自己的代码，写的几乎一模一样，很高兴！
     * 唯一没想到的就是if (start >= end)都应该返回true
     * 因为2，3两个数的情况时，最后一个return的返回，第一个就是start>end的情况，这应该返回true
     */
    public static boolean verifyPreorder(int[] preorder) {
        int len = preorder.length;
        if (preorder == null || len == 0)
            return true;
        return verifyHelper(preorder, 0, len - 1);
    }
    public static boolean verifyHelper(int[] preorder, int start, int end) {
        if (start >= end)
            return true;
        int val = preorder[start];
        int index = -1;
        for (int i = start + 1; i <= end; i++) {
            if (preorder[i] > val && index == -1) {
                index = i;
            }
            if (preorder[i] < val && index != -1)
                return false;
        }
        if (index != -1)
            return verifyHelper(preorder, start + 1, end);
        return verifyHelper(preorder, start + 1, index - 1) && verifyHelper(preorder, index, end);        
    }