Find the closest element in Binary Search Tree in C++

Suppose we have one binary search tree (BST) and another target value; we have to find k values in that given BST that are closest to the target. Here the target value is a floating-point number. We can assume k is always valid, and k ≤ total nodes.

So, if the input is like

target = 3.714286, and k = 2, then the output will be [4,3]

To solve this, we will follow these steps −

• Define a function pushSmaller(), this will take node,stack st, and target,

• while node is not present, do −

  • if val of node < target, then −

    • insert node into st

    • node := right of node

  • Otherwise

    • node := left of node

• Define a function pushLarger(), this will take node, stack st, target,

• while node is empty, do −

  • if val of node >= target, then −

    • insert node into st

    • node := left of node

  • Otherwise

    • node := right of node

• From the main method do the following −

• Define an array ret

• Define one stack smaller

• Define one stack larger

• pushLarger(root, larger, target)

• pushSmaller(root, smaller, target)

• while k is non-zero, decrease k in each step, do −

  • if smaller is not empty and (larger is empty or |target - value of top element of smaller| < |target - top element of larger|)

    • curr = top element of smaller

    • delete element from smaller

    • insert val of curr at the end of ret

    • pushSmaller(left of curr, smaller, target)

  • Otherwise

    • curr = top element of larger

    • delete element from larger

    • insert val of curr at the end of ret

    • pushSmaller(right of curr, larger, target)

• return ret

Example 

Let us see the following implementation to get better understanding −

 Live Demo

#include <bits/stdc++.h>
using namespace std;
void print_vector(vector<auto> v){
   for(int i = 0; i<v.size(); i++){
      cout << v[i] << ", ";
   }
   cout << "]"<<endl;
}
class TreeNode{
   public:
      int val;
      TreeNode *left, *right;
      TreeNode(int data){
         val = data;
         left = NULL;
         right = NULL;
      }
};
void insert(TreeNode **root, int val){
   queue<TreeNode*> q;
   q.push(*root);
   while(q.size()){
      TreeNode *temp = q.front();
      q.pop();
      if(!temp->left){
         if(val != NULL)
            temp->left = new TreeNode(val);
         else
            temp->left = new TreeNode(0);
         return;
      }
      else{
         q.push(temp->left);
      }
      if(!temp->right){
         if(val != NULL)
            temp->right = new TreeNode(val);
         else
            temp->right = new TreeNode(0);
         return;
      }
      else{
         q.push(temp->right);
      }
   }
}
TreeNode *make_tree(vector<int> v){
   TreeNode *root = new TreeNode(v[0]);
   for(int i = 1; i<v.size(); i++){
      insert(&root, v[i]);
   }
   return root;
}
class Solution {
   public:
   vector<int> closestKValues(TreeNode* root, double target, int k){
      vector<int> ret;
      stack<TreeNode*> smaller;
      stack<TreeNode*> larger;
      pushLarger(root, larger, target);
      pushSmaller(root, smaller, target);
      while (k--) {
         if (!smaller.empty() && (larger.empty() || (abs(target - smaller.top()->val) < abs(target - larger.top()->val)))) {
            TreeNode* curr = smaller.top();
            smaller.pop();
            ret.push_back(curr->val);
            pushSmaller(curr->left, smaller, target);
         }
         else {
            TreeNode* curr = larger.top();
            larger.pop();
            ret.push_back(curr->val);
            pushLarger(curr->right, larger, target);
      }
   }
   return ret;
}
void pushSmaller(TreeNode* node, stack <TreeNode*>& st, double target){
   while (node) {
      if (node->val < target) {
         st.push(node);
         node = node->right;
      }
      else {
         node = node->left;
      }
   }
}
void pushLarger(TreeNode* node, stack <TreeNode*>& st, double target){
   while (node) {
      if (node->val >= target) {
         st.push(node);
         node = node->left;
      }
      else
         node = node->right;
      }
   }
};
main(){
   Solution ob;
   vector<int> v = {4,2,5,1,3};
   TreeNode *root = make_tree(v);
   print_vector(ob.closestKValues(root, 3.7142, 2));
}

Input

{4,2,5,1,3}, 3.7142, 2

Output

[4, 3, ]