'প্রযুক্তিতে নতুনের ছোঁয়া'

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 />
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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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<br />
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 />
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<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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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzVfwdtXs0KUsEtgWfF0WeIZIYWeU7LnM7Z6KmAM2BtmYW6IoF8vosllHpvmllHK_XsjQeFW0m_2RkEwg1cRUcvuGvXlHTdVEubHukIDEn5pBM43aNFl1IX05AQwUCrofUOK-GaroODeYM/s1600/Screenshot_3.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="143" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzVfwdtXs0KUsEtgWfF0WeIZIYWeU7LnM7Z6KmAM2BtmYW6IoF8vosllHpvmllHK_XsjQeFW0m_2RkEwg1cRUcvuGvXlHTdVEubHukIDEn5pBM43aNFl1IX05AQwUCrofUOK-GaroODeYM/s400/Screenshot_3.png" width="400" /></a></div>
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<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>
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<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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<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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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjssPd7EzyxCFHs8HnszpZrbKMC4VVey8XaBsvm-O4g2s6R7K9bn82HqBYPMKTFdRIiJ71_AwjCXn1V1EBMKVQ2xUQ6vSPGy7e4kOkEAuFkuHhdufqwq-3A_zkyG5967Ke2Sf1uN4lmrAzV/s1600/Screenshot_2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="176" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjssPd7EzyxCFHs8HnszpZrbKMC4VVey8XaBsvm-O4g2s6R7K9bn82HqBYPMKTFdRIiJ71_AwjCXn1V1EBMKVQ2xUQ6vSPGy7e4kOkEAuFkuHhdufqwq-3A_zkyG5967Ke2Sf1uN4lmrAzV/s320/Screenshot_2.png" width="320" /></a></div>
</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 />
<div style="color: #333333; font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif; font-size: 16px; line-height: 24px;">
<img alt="" class="  wp-image-366444 aligncenter" data-mce-src="http://www.techtunes.com.bd/tDrive/tuner/al-maruf-2/366427/Screenshot_7.jpg" height="376" src="http://www.techtunes.com.bd/tDrive/tuner/al-maruf-2/366427/Screenshot_7.jpg" style="display: block; margin-left: auto; margin-right: auto;" width="640" /></div>
<div style="color: #333333; font-family: Georgia, 'Times New Roman', 'Bitstream Charter', Times, serif; font-size: 16px; line-height: 24px;">
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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