Finding the second max element in a binary search tree

Question

I have a problem with finding the second maximum element in a binary search tree. I do not know why but in some cases my programm crashes or gives incorrect answer (I don't know those cases). Help me to find a problem in my algorithm in code below. Thank you.

#include <iostream>
    using namespace std;
    struct Node {
        Node* right;
        Node* left;
        int data;
        Node* parent;
    };

    Node* maximum(Node *root){
        if (root -> right)
            return maximum(root -> right);
        else
            return root;
    }
    void insert(Node *root, Node *a){
        if (root -> left && root -> data > a -> data)
            return insert(root -> left, a);
        if (root -> right && root -> data < a -> data)
            return insert(root -> right, a);
        if (root -> data > a -> data){
            root -> left = a;
            a -> parent = root;
        }
        if (root -> data < a -> data){
            root -> right = a;
            a -> parent = root;
        }
    }
    int main(){
        int j = 0;
        int n = 0;
        Node *root = new Node;
        cin >> j;
        if (j != 0) {
            root -> data = j;
            root -> parent = NULL;
            root -> left = NULL;
            root -> right = NULL;
        } else {cout << "0"; return 0;}
        while (true){
            cin >> j;
            if (j == 0) break;
            Node *a = new Node;
            a -> data = j;
            a -> left = NULL;
            a -> right = NULL;
            a -> parent = NULL;
            insert(root, a);
        }
if(!max -> parent)
    if (max -> left)
        cout << maximum(max -> left) -> data;
    else
        cout << max -> data;
else
    if (max -> left && max -> left > max -> parent)
        cout << maximum(max -> left) -> data;
    else
        cout << max -> parent -> data;

        return 0;
    }

Answer 1

In the following code:

Node* max = maximum(root);

if (max->left){
    if (max->parent->data > max->left->data) cout << max->parent->data;
    else cout << max->left->data;
} else
    cout << max->parent->data;

If your max turns out to be root , then max->parent will be NULL . So you should check for NULL condition before testing it on data .

Answer 2

Check you are following this Logic :-

Second max will be in the left subtree of max or its parent.

If if left-subtree exists then find max of left-subtree which is second highest

If if left-subtree does not exist then parent of max is second highest.

Corner cases

1) root is null ie no element. No need to check all these.

2) Root is the only element ie there is only 1 number. So no second highest as parent of root is null.