'প্রযুক্তিতে নতুনের ছোঁয়া'

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Binary tree</h2>
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<span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;">In </span><a href="http://en.wikipedia.org/wiki/Computer_science" style="background: none rgb(255, 255, 255); color: #0b0080; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px; text-decoration: none;" title="Computer science">computer science</a><span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;">, a </span><b style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; line-height: 22.3999996185303px;">binary tree</b><span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;"> is a </span><a href="http://en.wikipedia.org/wiki/Tree_structure" style="background: none rgb(255, 255, 255); color: #0b0080; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px; text-decoration: none;" title="Tree structure">tree</a><span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;"> </span><a href="http://en.wikipedia.org/wiki/Data_structure" style="background: none rgb(255, 255, 255); color: #0b0080; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px; text-decoration: none;" title="Data structure">data structure</a><span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;"> in which each node has at most two </span><a class="mw-redirect" href="http://en.wikipedia.org/wiki/Child_node" style="background: none rgb(255, 255, 255); color: #0b0080; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px; text-decoration: none;" title="Child node">children</a><span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;">, which are referred to as the </span><i style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;">left</i><span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;"> child and the </span><i style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;">right</i><span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;"> child. A </span><a href="http://en.wikipedia.org/wiki/Recursive_definition" style="background: none rgb(255, 255, 255); color: #0b0080; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px; text-decoration: none;" title="Recursive definition">recursive definition</a><span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;"> using just </span><a href="http://en.wikipedia.org/wiki/Set_theory" style="background: none rgb(255, 255, 255); color: #0b0080; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px; text-decoration: none;" title="Set theory">set theory</a><span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;"> notions is that a (non-empty) binary tree is a </span><a href="http://en.wikipedia.org/wiki/Tuple" style="background: none rgb(255, 255, 255); color: #0b0080; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px; text-decoration: none;" title="Tuple">triple</a><span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;"> (</span><i style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;">L</i><span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;">, </span><i style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;">S</i><span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;">,</span><i style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;">R</i><span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;">), where </span><i style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;">L</i><span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;"> and </span><i style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;">R</i><span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;"> are binary trees or the </span><a href="http://en.wikipedia.org/wiki/Empty_set" style="background: none rgb(255, 255, 255); color: #0b0080; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px; text-decoration: none;" title="Empty set">empty set</a><span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;"> and </span><i style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;">S</i><span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;"> is a </span><a class="mw-redirect" href="http://en.wikipedia.org/wiki/Singleton_set" style="background: none rgb(255, 255, 255); color: #0b0080; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px; text-decoration: none;" title="Singleton set">singleton set</a><span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;">.</span><span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; font-weight: normal; line-height: 22.3999996185303px;">Some authors allow the binary tree to be the empty set as well.       </span>
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<span style="background-color: white;">For more understanding visit this <a href="http://algs4.cs.princeton.edu/32bst/" target="_blank">link</a> </span></div>
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<span style="background-color: white;"><span style="color: #252525; font-family: sans-serif; font-size: 14px; line-height: 22.3999996185303px;">For </span><span style="color: #252525; font-family: sans-serif;"><span style="font-size: 14px; line-height: 22.3999996185303px;">visualization </span></span><span style="color: #252525; font-family: sans-serif; font-size: 14px; line-height: 22.3999996185303px;">visit this</span><span style="color: #252525; font-family: sans-serif; line-height: 22.3999996185303px;"> </span><a href="https://www.cs.usfca.edu/~galles/visualization/BST.html" target="_blank">link</a></span></div>
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<h2 style="text-align: center;">
Node.h</h2>
<pre class="brush:cpp;">#include <iostream>

using namespace std;

class Node {
public:
 Node ();
 Node (int a);
 ~Node ();
 void SetValue (int a);
 int GetValue ();
 void SetLeft (Node* L);
 Node* GetLeft ();
 void SetRight (Node* R);
 Node* GetRight ();
private:
 int Value;
 Node* Left;
 Node* Right;
};

Node :: Node () {
 Value = 0;
 Left = NULL;
 Right = NULL;
}

Node :: Node (int a) {
 Value = a;
 Left = NULL;
 Right = NULL;

}

Node :: ~Node () {
 delete Left;
 delete Right;
}

void Node :: SetValue (int a) {
 Value = a;
}

int Node :: GetValue () {
 return Value;
}

void Node :: SetLeft (Node* L) {
 Left = L;
}

Node* Node :: GetLeft () {
 return Left;
}

void Node :: SetRight (Node* R) {
 Right = R;
}

Node* Node :: GetRight () {
 return Right;
}

</pre>
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BT.h</h2>
<pre class="brush:cpp;">#include "Node.h"

class BT {
public:
 BT ();
 ~BT ();
 void SetRoot(Node* R);
 Node* GetRoot ();
 void Insert (int a);
 void PreOrder (Node* N);
 Node* FindMin (Node* N);
 Node* Delete (Node* N, int a);
private:
 Node* Root;
};

BT :: BT () {
 Root = NULL;
}

BT :: ~BT () {
 delete Root;
}

void BT :: SetRoot(Node* R) {
 Root = R;
}

Node* BT :: GetRoot () {
 return Root;
}

void BT :: Insert (int a) {
 if (GetRoot () == NULL) {
  Node* NN = new Node (a);
  SetRoot (NN);
 }
 else {
  Node *p, *q;
  p = q = GetRoot();
  while (p->GetValue() != a && q != NULL ) {
   p = q;
   if (p->GetValue() < a)
    q = p->GetRight();
   else
    q = p->GetLeft();
  }

if (p->GetValue() == a)
   cout << "Duplicate Value" << endl;
  else if (p->GetValue() < a) {
   Node* NN = new Node(a);
   p->SetRight(NN);
  }
  else {
   Node* NN = new Node(a);
   p->SetLeft(NN);
  }
 }
}

void BT :: PreOrder (Node* N) {
 if (N != NULL) {
  cout << N->GetValue() << endl;
  PreOrder(N->GetLeft());
  PreOrder (N->GetRight());
 }
}

Node* BT :: FindMin (Node* N) {
 if (N == NULL) return N;
 else if (N->GetLeft() == NULL) return N;
 else FindMin (N->GetLeft());
}

Node* BT :: Delete (Node* N, int a) {
 Node *NN;
 if (a < N->GetValue()) {
  NN = Delete(N->GetLeft(), a);
  N->SetLeft(NN);
 }
 else if (a > N->GetValue()) {
  NN = Delete(N->GetRight(), a);
  N->SetRight(NN);
 }
 else if (N->GetLeft() != NULL && N->GetRight() != NULL) {
  Node* MN = FindMin (N->GetRight());
  N->SetValue (MN->GetValue());
  NN = Delete (N->GetRight(), MN->GetValue());
  N->SetRight(NN);
 }
 else {
  if (N->GetRight() == NULL) {
   N = N->GetLeft();
  }
  else if (N->GetLeft() == NULL) {
   N = N->GetRight();
  }
  else N = NULL;
 }
 return N;
}

</pre>
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main.cpp</h2>
<pre class="brush:cpp;">#include "BT.h"

int main () {
 BT ob;
 ob.Insert(25);
 ob.Insert(86);
 ob.Insert(69);
 ob.Insert(25);
 ob.PreOrder(ob.GetRoot());
 cout << (ob.FindMin(ob.GetRoot()))->GetValue() << endl;
 cout << (ob.FindPreviousNode(69))->GetValue() << endl;
 ob.delete(ob.GetRoot(),86);
 return 0;
}

</pre>
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Binary tree

Binary tree In computer science, a binary tree is a tree data structure in which each node has at most two children, which are referred to as the left child and the right child. A recursive definitio…

Binary tree

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