tree_min_height.cpp

#include <iostream>
#include <climits>
#include <algorithm>

class Tree {
private:
  struct TreeNode {
    int val;
    TreeNode *l, *r;
    TreeNode(int val, TreeNode *l = nullptr, TreeNode *r = nullptr) :
      val(val), l(l), r(r) {}
  };
  size_t size;
  TreeNode *root;
  TreeNode *__insert(TreeNode *root, TreeNode *node) {
    if(!root)
      return node;
    if(node->val < root->val)
      root->l = __insert(root->l, node);
    else
      root->r = __insert(root->r, node);
    return root;
  }
  size_t __minimal_height(TreeNode *root, size_t current_height) {
    if(!root->l && !root->r)
      return current_height + 1;
    if(!root->l) return __minimal_height(root->r, current_height + 1);
    if(!root->r) return __minimal_height(root->l, current_height + 1);
    return std::min(__minimal_height(root->l, current_height + 1),
                    __minimal_height(root->r, current_height + 1));
  }
public:
  Tree() : size(0), root(nullptr) {}
  void insert(int val) {
    root = __insert(root, new TreeNode(val));
  }
  size_t minimal_height() {
    return __minimal_height(root, 0);
  };
};

int main() {
  Tree t;
  int val;
  while(std::cin >> val) {
    t.insert(val);
  }
  std::cout << t.minimal_height();
}