'প্রযুক্তিতে নতুনের ছোঁয়া'

Copyright Free Audio Tracks

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<span style="font-size: large;"><b>S</b></span>ometimes you need copyright free audio track for your video clip or other tutorial videos for making your Youtube videos, but unfortunately, you are not allowed to used copyright content for making your Youtube video.In this purpose, you can use this copyright free audio track, which means if you use this audio track Youtube will not be able to claim you to violate copyright law.<br />
<br />
Now I'm given you some most popular Youtube channel for copyright free audio tracks.<br />
<span style="font-size: large;"><br /></span> <span style="font-size: large;">1) <a href="https://www.youtube.com/user/NoCopyrightSounds" target="_blank">NCS- NoCopyrightSounds</a></span>
<br />
<iframe width="560" height="315" src="https://www.youtube.com/embed/2UeMLPCL1Cs?list=PLRBp0Fe2GpgmsW46rJyudVFlY6IYjFBIK" frameborder="0" allowfullscreen></iframe>
<br />
<br />
<span style="font-size: large;"><a href="https://www.youtube.com/channel/UCht8qITGkBvXKsR1Byln-wA" target="_blank"><b>2) Audio Library – No Copyright Music</b></a></span><br />
<span style="font-size: large;"><b> </b></span> 
<br />
<iframe width="560" height="315" src="https://www.youtube.com/embed/odCWcV6Jv90?list=PLzCxunOM5WFI6sgbAppnSgLQxxNg_d10L" frameborder="0" allowfullscreen></iframe>
<br />
<br />
<b>note: before use, those tracks </b><b><b>must </b>read carefully their</b> <span style="color: red;"><b>Licence<span style="color: black;">.</span></b></span></div>

Copyright Free Audio Tracks

S ometimes you need copyright free audio track for your video clip or other tutorial videos for making your Youtube videos, but unfortunate...

Bangla Java Tutorial 1 : Getting Started

What is in the video? 1. Introduction 2. What is java? 3. Why should learn Java? 4.History of Java 5. How Java Code works 6. JDK & Ec...

C++ Programming for the Absolute Beginner pdf free download

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<h2>
C++ Programming for the Absolute Beginner</h2>
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Time complexity

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<span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19px;">In computer science, the </span><b style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19px;">time complexity</b><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19px;"> of an algorithm quantifies the amount of </span><b style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19px;">time</b><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19px;"> taken by an algorithm to run as a function of the length of the string representing the input</span><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19px;">. The </span><b style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19px;">time complexity</b><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19px;"> of an algorithm is commonly expressed using big O notation, which excludes coefficients and lower order terms.</span><br />
<span style="color: #222222; font-family: arial, sans-serif;"><span style="line-height: 19px;"><br /></span></span><span style="background-color: white; color: #222222; font-family: arial, sans-serif; font-size: 16px; line-height: 19px;"></span>
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Source : <span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 12.880000114440918px; line-height: 20px; text-align: left;"> </span><span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 12.880000114440918px; line-height: 20px; text-align: left;">Wikipedia</span></div>
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Time complexity

In computer science, the time complexity of an algorithm quantifies the amount of time taken by an algorithm to run as a function of th...

Analysis of Algorithms | (Asymptotic Notations)

Proofs by Induction

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<span class="_Tgc">A <b>proof</b> by <b>induction</b> is just like an ordinary <b>proof</b>
 in which every step must be justified. However it employs a neat trick 
which allows you to prove a statement about an arbitrary number n by 
first proving it is true when n is 1 and then assuming it is true for 
n=k and showing it is true for n=k+1.</span><br />
<br />
<br />
<iframe allowfullscreen="" frameborder="0" height="360" src="https://www.youtube.com/embed/dMn5w4_ztSw" width="640"></iframe>

Proofs by Induction

A proof by induction is just like an ordinary proof in which every step must be justified. However it employs a neat trick which allow...

Binary Search

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<h3 style="text-align: left;">
<span style="font-size: large;">Overview of  Binary Search </span></h3>
The binary search algorithm begins by comparing the target value to the 
value of the middle element of the sorted array. If the target value is 
equal to the middle element's value, then the position is returned and 
the search is finished. If the target value is less than the middle 
element's value, then the search continues on the lower half of the 
array; or if the target value is greater than the middle element's 
value, then the search continues on the upper half of the array. This 
process continues, eliminating half of the elements, and comparing the 
target value to the value of the middle element of the remaining 
elements - until the target value is either found (and its associated 
element position is returned), or until the entire array has been 
searched (and "not found" is returned).<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8S5WHwTR-ZWlYLou_ibWiDiJeNLDddFCx4J9pz2xD1NIhCZGd1sPpZfOocD2VeXXq6PTjzX4ndlhUDSkp28KcWtRjwTam0VjNzBET0trFCyyT2LrTcKqmv1VaAY9lS-TKqSwYEZfxiPwy/s1600/binary_search.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="342" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh8S5WHwTR-ZWlYLou_ibWiDiJeNLDddFCx4J9pz2xD1NIhCZGd1sPpZfOocD2VeXXq6PTjzX4ndlhUDSkp28KcWtRjwTam0VjNzBET0trFCyyT2LrTcKqmv1VaAY9lS-TKqSwYEZfxiPwy/s400/binary_search.gif" width="400" /></a></div>
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Binary search algorithm in C++ relies on a divide and conquer strategy 
to find a value within an already-sorted collection. Binary search 
locates the position of an item in a sorted array. Binary search compare
 an input search key to the middle element of the array and the 
comparison determines whether the element equals the input, less than 
the input or greater. The return value is the element position in the 
array.<br />
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<h3>
<span style="font-size: large;">Binary Search Algorithm complexity</span></h3>
<ul>
<li>Worst case performance O(log n)</li>
<li>Best case performance O(1)</li>
<li>Average case performance O(log n)</li>
<li>Worst case space complexity O(1) </li>
</ul>
The idea of binary search is to use the information that the array is 
sorted and reduce the time complexity to O(Logn). We basically ignore 
half of the elements just after one comparison.<br />
<b>1)</b> Compare x with the middle element.<br />
<b>2) </b>If x matches with middle element, we return the mid index.<br />
<b>3)</b> Else If x is greater than the mid element, then x 
can only lie in right half subarray after the mid element.  So we recur 
for right half.<br />
<b>4)</b> Else (x is smaller) recur for the left half.<br />
<br />
<h2 style="text-align: center;">
 
<b>Iterative </b> implementation of Binary Search</h2>
<br />
<pre class="brush:cpp;"> 
#include<iostream>
using namespace std;

// A iterative binary search function. It returns location of x in
// given array arr[l..r] if present, otherwise -1
int binarySearch(int arr[], int l, int r, int x)
{
  while (l <= r)
  {
    int m = l + (r-l)/2;

if (arr[m] == x) return m;  // Check if x is present at mid

if (arr[m] < x) l = m + 1; // If x greater, ignore left half

else r = m - 1; // If x is smaller, ignore right half
  }
  return -1; // if we reach here, then element was not present
}

int main(void)
{
   int arr[] = {2, 3, 4, 10, 40};
   int n = sizeof(arr)/ sizeof(arr[0]);// calculate array size

int x ;
   //print array
   for (int i=0;i<n;i++)
   {
       cout<<arr[i]<<"\t";
   }
   cout<<"\n\nEnter a number to Search: ";
   cin>>x;
   int result = binarySearch(arr, 0, n-1, x);
   if (result==-1)
   {
       cout<<"\nElement is not found in array"<<endl;
   }
   else
   {
       cout<<"\nElement is found at index:==> "<< result<<endl;
   }

return 0;
}

</pre>
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<h2 style="text-align: center;">
::Output ::</h2>
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<br />
<h2 style="text-align: center;">
<b>Recursive </b> implementation of Binary Search</h2>
<br />
<pre class="brush:cpp;"> 
#include<iostream>
using namespace std;

// A recursive binary search function. It returns location of x in
// given array arr[l..r] is present, otherwise -1
int binarySearch(int arr[], int l, int r, int x)
{
   if (r >= l)
   {
        int mid = l + (r - l)/2;

// If the element is present at the middle itself
        if (arr[mid] == x)  return mid;

// If element is smaller than mid, then it can only be present
        // in left subarray
        if (arr[mid] > x) return binarySearch(arr, l, mid-1, x);

// Else the element can only be present in right subarray
        return binarySearch(arr, mid+1, r, x);
   }

// We reach here when element is not present in array
   return -1;
}

int main(void)
{
   int arr[] = {2, 3, 4, 10, 40};
   int n = sizeof(arr)/ sizeof(arr[0]);// calculate array size

return 0;
} </pre>
</div>
<h2 style="text-align: center;">
::Output ::</h2>
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</div>

Binary Search

Overview of Binary Search The binary search algorithm begins by comparing the target value to the value of the middle element of the s...

MergeSort Using Recursion

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MergeSort is a <a href="https://en.wikipedia.org/wiki/Divide_and_conquer_algorithms" target="_blank">Divide and Conquer</a> algorithm.  It divides input array in two halves, calls itself for the two halves and then merges the two sorted halves. <span id="more-2783"></span> <b>The merg() function</b>
 is used for merging two halves.  The merge(arr, l, m, r) is key process
 that assumes that arr[l..m] and arr[m+1..r] are sorted and merges the 
two sorted sub-arrays into one. See following C implementation for 
details.<br />
<br />
<br />
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOa4EntnLBmEFZZgwLv3oSCQpCmxkrmt5e3o3QAfQdlafr159r62cMWCJordmqxm-sCi4gmEhgItut-Z75cdF-Qw01GiSu_M85JKUlZlREbmTbjeth_3qJr-52bzRVX0rDbPNorFJ2voDP/s1600/Merge_sort_algorithm_diagram.svg.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" height="308" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhOa4EntnLBmEFZZgwLv3oSCQpCmxkrmt5e3o3QAfQdlafr159r62cMWCJordmqxm-sCi4gmEhgItut-Z75cdF-Qw01GiSu_M85JKUlZlREbmTbjeth_3qJr-52bzRVX0rDbPNorFJ2voDP/s320/Merge_sort_algorithm_diagram.svg.png" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><div class="firstHeading" id="firstHeading" lang="en">
Merge sort algorithm diagram</div>
</td></tr>
</tbody></table>
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<br />
<h3 style="text-align: left;">
For  <b>simulation</b> visite <a href="http://www.ee.ryerson.ca/~courses/coe428/sorting/mergesort.html" target="_blank">here</a>

</h3>
<h2 style="text-align: center;">
Implementation in C++</h2>
<pre class="brush:cpp;"> 
#include <iostream>

using namespace std;

void merge(int arr[], int l, int m, int r)
{
    int i, j, k;
    int n1 = m - l + 1;
    int n2 =  r - m;

/* create temp arrays */
    int L[n1], R[n2];

/* Copy data to temp arrays L[] and R[] */
    for(i = 0; i < n1; i++)
        L[i] = arr[l + i];
    for(j = 0; j < n2; j++)
        R[j] = arr[m + 1+ j];

/* Merge the temp arrays back into arr[l..r]*/
    i = 0;
    j = 0;
    k = l;
    while (i < n1 && j < n2)
    {
        if (L[i] <= R[j])
        {
            arr[k] = L[i];
            i++;
        }
        else
        {
            arr[k] = R[j];
            j++;
        }
        k++;
    }

/* Copy the remaining elements of L[], if there are any */
    while (i < n1)
    {
        arr[k] = L[i];
        i++;
        k++;
    }

/* Copy the remaining elements of R[], if there are any */
    while (j < n2)
    {
        arr[k] = R[j];
        j++;
        k++;
    }
}

/* l is for left index and r is right index of the sub-array
  of arr to be sorted */
void mergeSort(int arr[], int l, int r)
{
    if (l < r)
    {
        int m = l+(r-l)/2; //Same as (l+r)/2, but avoids overflow for large l and h
        mergeSort(arr, l, m);
        mergeSort(arr, m+1, r);
        merge(arr, l, m, r);
    }
}

/* Function to print an array */
void printArray(int A[], int size)
{
    int i;
    for (i=0; i < size; i++)
        cout<< A[i]<<endl;

}/* Driver program to test above functions */
int main()
{
    int arr[] = {12, 11, 13, 5, 6, 7};
    int arr_size = sizeof(arr)/sizeof(arr[0]);

cout<<"Given array is \n";
    printArray(arr, arr_size);

mergeSort(arr, 0, arr_size - 1);

cout<<"\nSorted array is \n"<<endl;
    printArray(arr, arr_size);
    return 0;
}

</pre>
<h2 style="text-align: center;">
::Output ::</h2>
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</div>

MergeSort Using Recursion

MergeSort is a Divide and Conquer algorithm. It divides input array in two halves, calls itself for the two halves and then merges the ...

পবিত্র রমজান মাসের উপলক্ষে আমার তৈরী একটি বাংলা ইসলামিক সফটওয়্যার ~'RAMADAN-2015'

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<span style="background-color: white; color: #333333; font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif; font-size: 16px; line-height: 24px;">আসসালামু আলাইকুম কেমন আছেন সবাই? আল্লাহ রহমতে আশা করি এই পবিত্র সিয়াম সাধনার সবাই ভালই আছেন।</span><span style="color: #333333; font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif; font-size: 16px; line-height: 24px;">গত কয়েকদিন আগে চিন্তা করলাম এবার রোজার জন্য একটা সফটওয়্যার বানাবো কানতু কাজ শুরু করতে পারলাম না মিডর্টাম এক্সজামের কারনে। গত দুইদিন আগে মিডর্টাম শেষ হলে কাজ শুরু করি এবং আল্লাহ রহমতে গত দুইদিনের টানা পরিশ্রমে আজ কাজ শেষ করতে পারি তাই সফটওয়্যারটি রিলিজ করি।</span><br />
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RAMADAN-2015 মূলত একটি ইসলামিক সফটওয়্যার। সফটওয়্যারটাতে যেসব ফিচার রয়েছে সেগুলো হলোঃ<br />
# সম্পূর্ণ বাংলা এবং আকর্ষনীয় ইন্টারফেস<br />
# সেহরী ওইফতারের দোয়া<br />
# সেহরী ওইফতারের সময়সূচি<br />
# রমজানের ৩০ রোজার দোয়া<br />
# রোজা ভঙ্গের কারনসমূহ<br />
# লাইলাতুল কদরের ফজিলত ও গুরুত্বপুর্ণ সম্পর্কে আলোচনা<br />
# ৩০ পারা কোরআন তেলোয়াত<br />
# অনলাইনে ইসলামিক ওয়েবসাইট ভিউয়ার<br />
# আপডেট চেকার<br />
# এছাড়াও আরো অন্যান্য গুরুপুর্ণ বিষয় ...</div>
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<img alt="" class="alignnone size-full wp-image-366428" data-mce-src="http://www.techtunes.com.bd/tDrive/tuner/al-maruf-2/366427/Screenshot_1.jpg" height="373" src="http://www.techtunes.com.bd/tDrive/tuner/al-maruf-2/366427/Screenshot_1.jpg" width="700" /></div>
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<img alt="" class="alignnone size-full wp-image-366429" data-mce-src="http://www.techtunes.com.bd/tDrive/tuner/al-maruf-2/366427/Screenshot_2.jpg" height="371" src="http://www.techtunes.com.bd/tDrive/tuner/al-maruf-2/366427/Screenshot_2.jpg" width="700" /></div>
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<img alt="" class="alignnone size-full wp-image-366433" data-mce-src="http://www.techtunes.com.bd/tDrive/tuner/al-maruf-2/366427/Screenshot_11.jpg" height="375" src="http://www.techtunes.com.bd/tDrive/tuner/al-maruf-2/366427/Screenshot_11.jpg" width="700" /></div>
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<img alt="" class="alignnone size-full wp-image-366432" data-mce-src="http://www.techtunes.com.bd/tDrive/tuner/al-maruf-2/366427/Screenshot_3.jpg" height="472" src="http://www.techtunes.com.bd/tDrive/tuner/al-maruf-2/366427/Screenshot_3.jpg" width="700" /></div>
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<img alt="" class="alignnone size-full wp-image-366434" data-mce-src="http://www.techtunes.com.bd/tDrive/tuner/al-maruf-2/366427/Screenshot_6.jpg" height="429" src="http://www.techtunes.com.bd/tDrive/tuner/al-maruf-2/366427/Screenshot_6.jpg" width="700" /></div>
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<b>ডাউনলোড লিংকঃ</b></h3>
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<b>মিডিয়া ফায়ার লিংকঃ</b></div>
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<a data-mce-href="https://www.mediafire.com/?10ggx5sg399uklr" href="https://www.mediafire.com/?10ggx5sg399uklr" target="_blank"><img alt="" class="  wp-image-366439 aligncenter" data-mce-src="http://www.techtunes.com.bd/tDrive/tuner/al-maruf-2/366427/down-button.png" height="111" src="http://www.techtunes.com.bd/tDrive/tuner/al-maruf-2/366427/down-button.png" style="display: block; margin-left: auto; margin-right: auto;" width="434" /></a></div>
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<b>ড্রপবক্স লিংকঃ</b></div>
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<a data-mce-href="https://www.dropbox.com/s/82u86fkrf8a07lh/Setup-Ramadan-2015.exe?dl=0" href="https://www.dropbox.com/s/82u86fkrf8a07lh/Setup-Ramadan-2015.exe?dl=0" target="_blank"><img alt="" class="  wp-image-366437 aligncenter" data-mce-src="http://www.techtunes.com.bd/tDrive/tuner/al-maruf-2/366427/download.png" height="170" src="http://www.techtunes.com.bd/tDrive/tuner/al-maruf-2/366427/download.png" style="display: block; margin-left: auto; margin-right: auto;" width="383" /></a></div>
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<b>মেগাফাইল আপলোড লিংকঃ</b></div>
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<a data-mce-href="http://www.megafileupload.com/4Gyu/Setup-Ramadan-2015.exe" href="http://www.megafileupload.com/4Gyu/Setup-Ramadan-2015.exe" target="_blank"><img alt="" class="  wp-image-366441 aligncenter" data-mce-src="http://www.techtunes.com.bd/tDrive/tuner/al-maruf-2/366427/WOVETKj.png" height="113" src="http://www.techtunes.com.bd/tDrive/tuner/al-maruf-2/366427/WOVETKj.png" style="display: block; margin-left: auto; margin-right: auto;" width="278" /></a></div>
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*সফটওয়্যারটির বেশ কিছু কন্টেন বেশ কিছু ওয়েবসাইট থেকে নেয়া।<br />
এই সফটওয়্যারটিতে কোন ভূল ত্রটি থাকলে আমাকে জানালে আমি অনেক খুশি হবো এবং পরবর্তীতে তা সংশোধন করার চেষ্টা করব।<br />
সর্বোপরি আমার জন্য দোয়া করবেন এবং সফটওয়্যারটি কেমন হয়েছে তা টিউমেন্টের মাধমে অবশ্যই জানাবেন।<br />
সবশেষে সবার সুস্থতা ও সালাম জানিয়ে এবং আল্লাহর কাছে এক মাস সঠিক ভাবে রোজা রাখার তৌফিক চেয়ে আজকের মতো এখানেই বিদায় নিচ্ছি<b> আল্লাহ হাফেজ</b>।।।</div>
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পবিত্র রমজান মাসের উপলক্ষে আমার তৈরী একটি বাংলা ইসলামিক সফটওয়্যার ~'RAMADAN-2015'

আসসালামু আলাইকুম কেমন আছেন সবাই? আল্লাহ রহমতে আশা করি এই পবিত্র সিয়াম সাধনার সবাই ভালই আছেন। গত কয়েকদিন আগে চিন্তা করলাম এবার রোজার জন্য এ...

Binary tree

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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;"><a href="http://upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Binary_tree.svg/300px-Binary_tree.svg.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Binary_tree.svg/300px-Binary_tree.svg.png" /></a></span></div>
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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>
<h2 style="text-align: center;">
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>
<h2 style="text-align: center;">
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>
<br /></div>

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 ...

Tower of Hanoi

<div dir="ltr" style="text-align: left;" trbidi="on">
<h2 style="text-align: center;">
::Tower of Hanoi ::</h2>
<div style="text-align: center;">
<div style="text-align: left;">
The Tower of Hanoi (also called the Tower of Brahma or Lucas' Tower,[1] and sometimes pluralized) is amathematical game or puzzle. It consists of three rods, and a number of disks of different sizes which can slide onto any rod. The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape</div>
</div>
<div style="text-align: center;">
. </div>
<div style="text-align: center;">
<img border="0" height="175" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBg-fJU4k1Ymag-1XXiOBqWCuXfLJv1eziu_z30ddH-EwbnfxO_cb-9zUBltWEps0CZOLNV51dg7TDJhxeioHcoPhvGPnm-aD9E7Q58YGCvEup6El7_bclH8cnUroHKyNOAuQhoeubvY4g/s1600/Tower_of_Hanoi.jpeg" width="400" />

</div>
<div style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; line-height: 22.3999996185303px; margin-bottom: 0.5em; margin-top: 0.5em;">
The objective of the puzzle is to move the entire stack to another rod, obeying the following simple rules:</div>
<ol style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; line-height: 22.3999996185303px; list-style-image: none; margin: 0.3em 0px 0px 3.2em; padding: 0px;">
<li style="margin-bottom: 0.1em;">Only one disk can be moved at a time.</li>
<li style="margin-bottom: 0.1em;">Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack i.e. a disk can only be moved if it is the uppermost disk on a stack.</li>
<li style="margin-bottom: 0.1em;">No disk may be placed on top of a smaller disk.</li>
</ol>
<div style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; line-height: 22.3999996185303px; margin-bottom: 0.5em; margin-top: 0.5em;">
With three disks, the puzzle can be solved in seven moves. The minimum number of moves required to solve a Tower of Hanoi puzzle is 2<sup style="font-size: 11.1999998092651px; line-height: 1;"><i>n</i></sup> - 1, where <i>n</i> is the number of disks.</div>
<div style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; line-height: 22.3999996185303px; margin-bottom: 0.5em; margin-top: 0.5em;">
<br /></div>
<br />
<div style="text-align: center;">
<img border="0" height="155" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqshUUkCwTImb-YMwKx4BMlc_lKXy5KWFt-yS8Tw4s2851AUTB4brJmYs6FaU6mJYzIAQzJSS-UosSR7A-54e-h19bKN0l5xStWpIu3uXJZEx2vHzh2wNgFNT-SpUAuQZVih0rf7Z0Rt8w/s1600/300px-Tower_of_Hanoi_4.gif" width="400" />
</div>
<pre class="brush:cpp;"> 
#include <iostream>
 using namespace std;
void towers(int, char, char, char);

int main()
{
    int num;

cout<<"Enter the number of disks : "<<endl;
    cin>>num;
    cout<<"The sequence of moves of the Tower of Hanoi are :\n"<<endl;
    towers(num, 'A', 'C', 'B');
    return 0;
}
void towers(int num, char A, char B, char C)
{
    if (num == 1)
    {
        cout<<"\nMove disk "<<num<<" from peg "<< A<<" to peg "<< B<<endl;
        return ;
    }
    towers(num - 1, A, C, B);

cout<<"Move disk "<< num <<" from peg "<< A<<" to peg "<<B;
    towers(num - 1, C, B, A);
}

</pre>
<h2 style="text-align: center;">
::Output ::</h2>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-rmgQBwiw0QNRhEWkJCuEoWtW7Gymuu7LEiv-S86nFQSZ3HlbuSwFHsdQypHsm4YAPOrLLQPJqBRiZhc9pDCLOJwTiBOT9vkAQm2WQn6W35AftuNP-QDv7YlwX0AtCtOP_DQ7klfBN5_9/s1600/Screenshot_4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="295" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-rmgQBwiw0QNRhEWkJCuEoWtW7Gymuu7LEiv-S86nFQSZ3HlbuSwFHsdQypHsm4YAPOrLLQPJqBRiZhc9pDCLOJwTiBOT9vkAQm2WQn6W35AftuNP-QDv7YlwX0AtCtOP_DQ7klfBN5_9/s1600/Screenshot_4.png" width="400" /></a></div>
<div>
<br /></div>
</div>