memory management for linked list and tree programs in c++

I solve algoritm questions from sites like leetcode, hacker rank or cracking the coding interview. I do most if the questions in c++. So for most of them i have a node struct as below

struct Node {
   Node* next;
   //for tree
   Node* left;
   Node* right;
   int data; 
   //ctor
   Node(int val) : left(nullptr);.....
}; 

then i have a function(s) which implements the algorithm

bool someAlgorithm(Node* root) {
  //do stuff
}

and finally i create the nodes in the main

int main() {
  auto root = new  Node(4);
  root->left = new .. 
  root->left->left = new ..
}

I want to incorporate memory management in this kind of solutions. If i use c++11 shared_ptr do i need to provide a destructor ? if yes what should i write in the destructor ? But i found that shared_ptr makes code overly complex and un-understandbale for such small programs.

In general what is the best way to make solving such questions memory safe ?