Trees: Terminology, Traversals & Representation

9. Practice Problems

প্রতিটি প্রশ্নে runnable C++ answer দেওয়া হয়েছে। আগে নিজে চেষ্টা করুন।

1. Write a function that returns the height of a binary tree.
   একটি binary tree-এর height return করুন।
   ✨ Show Answer

   height.cpp

   #include <bits/stdc++.h>
   using namespace std;
   struct N{int v;N*l,*r;N(int x):v(x),l(nullptr),r(nullptr){}};
   int height(N* r){ return r? 1+max(height(r->l),height(r->r)) : 0; }
   int main(){
       N* r=new N(1); r->l=new N(2); r->r=new N(3); r->l->l=new N(4);
       cout << "Height = " << height(r);
   }

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   Height বলতে এখানে node-সংখ্যা ধরা হয়েছে (অনেক বইয়ে edge-সংখ্যা ধরা হয় — দুটিই বৈধ, প্রশ্ন বুঝে ব্যবহার করুন)।

2. Count total nodes and number of leaves in a binary tree.
   মোট node ও leaf-এর সংখ্যা গুনুন।
   ✨ Show Answer

   count.cpp

   #include <bits/stdc++.h>
   using namespace std;
   struct N{int v;N*l,*r;N(int x):v(x),l(nullptr),r(nullptr){}};
   int cntNodes(N* r){ return r? 1+cntNodes(r->l)+cntNodes(r->r) : 0; }
   int cntLeaves(N* r){
       if(!r) return 0;
       if(!r->l && !r->r) return 1;
       return cntLeaves(r->l)+cntLeaves(r->r);
   }
   int main(){
       N* r=new N(1); r->l=new N(2); r->r=new N(3); r->l->l=new N(4); r->l->r=new N(5);
       cout << "Nodes=" << cntNodes(r) << " Leaves=" << cntLeaves(r);
   }

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3. Check whether a binary tree is height-balanced (|left height − right height| ≤ 1 for every node).
   প্রতিটি node-এ left ও right height-এর পার্থক্য ≤ 1 কিনা পরীক্ষা করুন।
   ✨ Show Answer

   balanced.cpp

   #include <bits/stdc++.h>
   using namespace std;
   struct N{int v;N*l,*r;N(int x):v(x),l(nullptr),r(nullptr){}};
   // returns height; sets bal=false if unbalanced anywhere
   int chk(N* r, bool& bal){
       if(!r) return 0;
       int a=chk(r->l,bal), b=chk(r->r,bal);
       if(abs(a-b)>1) bal=false;
       return 1+max(a,b);
   }
   int main(){
       N* r=new N(1); r->l=new N(2); r->l->l=new N(3);
       bool b=true; chk(r,b);
       cout << (b? "Balanced" : "NOT balanced");
   }

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4. Mirror (invert) a binary tree.
   একটি binary tree-এর mirror তৈরি করুন।
   ✨ Show Answer

   mirror.cpp

   #include <bits/stdc++.h>
   using namespace std;
   struct N{int v;N*l,*r;N(int x):v(x),l(nullptr),r(nullptr){}};
   void mirror(N* r){ if(!r) return; swap(r->l,r->r); mirror(r->l); mirror(r->r); }
   void in(N* r){ if(!r)return; in(r->l); cout<<r->v<<' '; in(r->r); }
   int main(){
       N* r=new N(1); r->l=new N(2); r->r=new N(3); r->l->l=new N(4);
       cout << "Before: "; in(r); cout << '\n';
       mirror(r);
       cout << "After : "; in(r);
   }

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5. Print level-order in a zig-zag pattern (left→right, then right→left, alternating).
   Zig-zag level order — এক level বাঁ থেকে ডান, পরের level ডান থেকে বাঁ।
   ✨ Show Answer

   zigzag.cpp

   #include <bits/stdc++.h>
   using namespace std;
   struct N{int v;N*l,*r;N(int x):v(x),l(nullptr),r(nullptr){}};
   void zz(N* root){
       if(!root) return;
       deque<N*> dq; dq.push_back(root);
       bool ltr=true;
       while(!dq.empty()){
           int sz=dq.size();
           while(sz--){
               if(ltr){
                   N* n=dq.front(); dq.pop_front();
                   cout<<n->v<<' ';
                   if(n->l) dq.push_back(n->l);
                   if(n->r) dq.push_back(n->r);
               } else {
                   N* n=dq.back(); dq.pop_back();
                   cout<<n->v<<' ';
                   if(n->r) dq.push_front(n->r);
                   if(n->l) dq.push_front(n->l);
               }
           }
           cout<<'\n'; ltr=!ltr;
       }
   }
   int main(){
       N* r=new N(1); r->l=new N(2); r->r=new N(3);
       r->l->l=new N(4); r->l->r=new N(5); r->r->l=new N(6); r->r->r=new N(7);
       zz(r);
   }

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6. Iterative inorder traversal using an explicit stack.
   Recursion ছাড়া, explicit stack দিয়ে inorder।
   ✨ Show Answer

   iter_in.cpp

   #include <bits/stdc++.h>
   using namespace std;
   struct N{int v;N*l,*r;N(int x):v(x),l(nullptr),r(nullptr){}};
   void iterIn(N* root){
       stack<N*> st; N* cur=root;
       while(cur || !st.empty()){
           while(cur){ st.push(cur); cur=cur->l; }
           cur=st.top(); st.pop();
           cout<<cur->v<<' ';
           cur=cur->r;
       }
   }
   int main(){
       N* r=new N(4); r->l=new N(2); r->r=new N(6);
       r->l->l=new N(1); r->l->r=new N(3);
       iterIn(r);
   }

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7. Serialize and deserialize a binary tree using pre-order with NULL markers.
   Pre-order ও NULL marker দিয়ে serialize/deserialize করুন।
   ✨ Show Answer

   serialize.cpp

   #include <bits/stdc++.h>
   using namespace std;
   struct N{int v;N*l,*r;N(int x):v(x),l(nullptr),r(nullptr){}};
   void ser(N* r, string& s){
       if(!r){ s+="# "; return; }
       s+=to_string(r->v)+' '; ser(r->l,s); ser(r->r,s);
   }
   N* des(stringstream& ss){
       string t; if(!(ss>>t)) return nullptr;
       if(t=="#") return nullptr;
       N* n=new N(stoi(t));
       n->l=des(ss); n->r=des(ss);
       return n;
   }
   void in(N* r){ if(!r)return; in(r->l); cout<<r->v<<' '; in(r->r); }
   int main(){
       N* r=new N(1); r->l=new N(2); r->r=new N(3); r->r->l=new N(4);
       string s; ser(r,s);
       cout << "Serial: " << s << '\n';
       stringstream ss(s); N* r2=des(ss);
       cout << "Inorder of rebuilt: "; in(r2);
   }

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