Maximum Element Between Two Nodes of BST in C++

Problem statement

Given an array of N elements and two integers A, B which belongs to the given array. Create a Binary Search Tree by inserting element from arr[0] to arr[n-1]. The task is to find the maximum element in the path from A to B.

Example

If array is {24, 23, 15, 36, 19, 41, 25, 35} the we can form BST as follows −

If we consider A = 19 and B = 41 then maximum element between these two nodes is 41

Algorithm

• Find Lowest Common Ancestor(LCA) of node A and B.
• Find maximum node between LCA and A. Let us call it as max1
• Find maximum node between LCA and B. Let us call it as max2
• Return maximum of max1 and max2

Example

Let us now see an example −

 Live Demo

#include <bits/stdc++.h>
using namespace std;
struct node {
   int data;
   struct node* left;
   struct node* right;
};
node *createNode(int x) {
   node *p = new node();
   p -> data = x;
   p -> left = NULL;
   p -> right = NULL;
   return p;
}
void insertNode(struct node *root, int x) {
   node *p = root, *q = NULL;
   while (p != NULL) {
      q = p;
      if (p -> data < x) {
         p = p -> right;
      } else {
         p = p -> left;
      }
   }
   if (q == NULL) {
      p = createNode(x);
   } else {
      if (q -> data < x) {
         q -> right = createNode(x); } else {
            q -> left = createNode(x);
      }
   }
}
int maxelpath(node *q, int x) {
   node *p = q;
   int mx = INT_MIN;
   while (p -> data != x) {
      if (p -> data > x) {
         mx = max(mx, p -> data);
         p = p -> left;
      } else {
         mx = max(mx, p -> data);
         p = p -> right;
      }
   }
   return max(mx, x);
}
int getMaximumElement(struct node *root, int x, int y) {
   node *p = root;
   while ((x < p -> data && y < p -> data) || (x > p ->
   data && y > p -> data)) {
      if (x < p -> data && y < p -> data) {
         p = p -> left;
      } else if (x > p -> data && y > p -> data) {
         p = p -> right;
      }
   }
   return max(maxelpath(p, x), maxelpath(p, y));
}
int main() {
   int arr[] = {24, 23, 15, 36, 19, 41, 25, 35}; int a = 19, b = 41;
   int n = sizeof(arr) / sizeof(arr[0]);
   struct node *root = createNode(arr[0]);
   for (int i = 1; i < n; i++) insertNode(root, arr[i]);
   cout << "Maximum element = " << getMaximumElement(root, a, b) << endl;
   return 0;
}

Output

Maximum element = 41