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<!DOCTYPE html>
<html>
<head>
<title>Algorithm and Complexity</title>
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<ul>
<li><a href="index.html">Main •</a></li>
<li><a href="myvector.html">MyVector •</a></li>
<li><a href="bubble.html">Bubble Sort •</a></li>
<li><a href="merge.html">Merge Sort •</a></li>
<li><a href="insert.html">Insert Sort •</a></li>
<li><a href="quick.html">Quick Sort •</a></li>
<li><a href="graphs.html">Graphs •</a></li>
<li><a href="olsen.html" style="color:red;">Olsen Gang</a></li>
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<h1 id="header">Most efficient way to sort integers</h1>
<p style="margin-left: 24%;"><iframe width="560" height="315" src="https://www.youtube.com/embed/k4RRi_ntQc8" frameborder="0" allowfullscreen></iframe></p>
<div id="main_explanation">
<p><strong>1)</strong>Since we know we’re sorting fixed-size integers, radix sort is much more efficient than any comparison-based sort (quicksort, introsort, merge sort, etc.).</p>
<p ><strong>2)</strong>I implemented quicksort, double-pivot quick sort and radix sorting.After comparing I discover that for sorting 20k numbers (length=4 int) radix sort in 25.5% more efficient than double-pivot quicksort:</p>
<ul >
<li><strong>Double Pivot Quick Sort: 2.25373 s;</strong></li>
<li><strong>Radix sort: 1.67982 s;</strong></li>
</ul>
<p id="centerText">C++ comparing of algorithms with real data you gave (<a href="http://math.uni.lodz.pl/~jakubo/ac16/creditcardnumbers.txt">creditcardnumbers.txt</a>):</p>
<p>/* Have to put in the same folder with olsen.txt file which contain info about credit cards.*/</p>
<!-- generated by C/C++ to HTML Formatter -->
<div style="background-color: rgb(243, 243, 243); font-family: fixed,monospace; border: 1px solid rgb(200, 200, 200); color: RGB(0, 0, 0);"><div style="margin: 10px"><span style="color: rgb(127, 96, 0);">#include <cstdlib></span><br/><span style="color: rgb(127, 96, 0);">#include <ctime></span><br/><span style="color: rgb(127, 96, 0);">#include <iostream></span><br/><span style="color: rgb(127, 96, 0);">#include <windows.h></span><br/><span style="color: rgb(127, 96, 0);">#include <iomanip></span><br/><span style="color: rgb(127, 96, 0);">#include <fstream></span><br/><span style="color: rgb(127, 96, 0);">#include <vector></span><br/><span style="color: rgb(127, 96, 0);">#include <algorithm></span><br/><span style="color: rgb(127, 96, 0);">#include <sstream></span><br/><span style="color: rgb(127, 96, 0);">#include <math.h></span><br/><span style="color: rgb(127, 96, 0);">#include <algorithm></span><br/><br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">using</span> <span style="color: rgb(7, 55, 99); font-weight: bold">namespace</span> std;<br/>
<br/>
<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">double</span> PCFreq = 0.0;<br/>
__int64 CounterStart = 0;<br/>
<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">void</span> StartCounter()<br/>
{<br/>
LARGE_INTEGER li;<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">if</span>(!QueryPerformanceFrequency(&li))<br/>
cout << <span style="color: rgb(204, 0, 0);">"QueryPerformanceFrequency failed!\n"</span>;<br/>
<br/>
PCFreq = <span style="color: rgb(7, 55, 99); font-weight: bold">double</span>(li.QuadPart)/1000.0;<br/>
<br/>
QueryPerformanceCounter(&li);<br/>
CounterStart = li.QuadPart;<br/>
}<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">double</span> GetCounter()<br/>
{<br/>
LARGE_INTEGER li;<br/>
QueryPerformanceCounter(&li);<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">return</span> <span style="color: rgb(7, 55, 99); font-weight: bold">double</span>(li.QuadPart-CounterStart)/PCFreq;<br/>
}<br/>
<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">void</span> changeUp(<span style="color: rgb(7, 55, 99); font-weight: bold">int</span> ar[],<span style="color: rgb(7, 55, 99); font-weight: bold">int</span> cell){<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">int</span> tmp=ar[cell];<br/>
ar[cell]=ar[cell+1];<br/>
ar[cell+1]=tmp;<br/>
}<br/>
<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">void</span> quickSort(<span style="color: rgb(7, 55, 99); font-weight: bold">int</span> arr[], <span style="color: rgb(7, 55, 99); font-weight: bold">int</span> left, <span style="color: rgb(7, 55, 99); font-weight: bold">int</span> right) {<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">int</span> i = left, j = right;<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">int</span> tmp;<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">int</span> pivot = arr[(left + right) / 2];<br/>
<br/>
<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">while</span> (i <= j) {<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">while</span> (arr[i] < pivot)<br/>
i++;<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">while</span> (arr[j] > pivot)<br/>
j--;<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">if</span> (i <= j) {<br/>
tmp = arr[i];<br/>
arr[i] = arr[j];<br/>
arr[j] = tmp;<br/>
i++;<br/>
j--;<br/>
}<br/>
};<br/>
<br/>
<span style="color: rgb(56, 118, 29); font-style: italic">/* recursion */</span><br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">if</span> (left < j)<br/>
quickSort(arr, left, j);<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">if</span> (i < right)<br/>
quickSort(arr, i, right);<br/>
}<br/>
<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">template</span> <<span style="color: rgb(7, 55, 99); font-weight: bold">typename</span> T><br/>
T StringToNumber ( <span style="color: rgb(7, 55, 99); font-weight: bold">const</span> string &Text )<br/>
{<br/>
istringstream ss(Text);<br/>
T result;<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">return</span> ss >> result ? result : 0;<br/>
}<br/>
<br/>
<br/>
<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">void</span> quickSortDualPivot(<span style="color: rgb(7, 55, 99); font-weight: bold">int</span> arr[], <span style="color: rgb(7, 55, 99); font-weight: bold">int</span> low, <span style="color: rgb(7, 55, 99); font-weight: bold">int</span> high)<br/>
{<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">if</span> (low >= high) {<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">return</span>;<br/>
}<br/>
<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">int</span> lt = low + 1, ht = high - 1, i, temp;<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">if</span> (arr[low] > arr[high]) {<br/>
temp = arr[low];<br/>
arr[low] = arr[high];<br/>
arr[high] = temp;<br/>
}<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">if</span> (low + 1 == high) {<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">return</span>;<br/>
}<br/>
<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">for</span> (i = low + 1; i <= high; ++i) {<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">if</span> (i > ht) {<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">break</span>;<br/>
}<br/>
<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">if</span> (arr[i] < arr[low]) {<br/>
temp = arr[lt];<br/>
arr[lt] = arr[i];<br/>
arr[i] = temp;<br/>
++lt;<br/>
} <span style="color: rgb(7, 55, 99); font-weight: bold">else</span> <span style="color: rgb(7, 55, 99); font-weight: bold">if</span> (arr[i] > arr[high]) {<br/>
temp = arr[ht];<br/>
arr[ht] = arr[i];<br/>
arr[i] = temp;<br/>
--ht;<br/>
--i;<br/>
}<br/>
}<br/>
<br/>
++ht;<br/>
temp = arr[ht];<br/>
arr[ht] = arr[high];<br/>
arr[high] = temp;<br/>
--lt;<br/>
temp = arr[lt];<br/>
arr[lt] = arr[low];<br/>
arr[low] = temp;<br/>
<br/>
<span style="color: rgb(56, 118, 29); font-style: italic">// Recursively applying the algorithm to sub-arrays</span><br/>
quickSortDualPivot(arr, low, lt - 1);<br/>
quickSortDualPivot(arr, lt + 1, ht - 1);<br/>
quickSortDualPivot(arr, ht + 1, high);<br/>
}<br/>
<br/>
<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">int</span> getMax(<span style="color: rgb(7, 55, 99); font-weight: bold">int</span> arr[], <span style="color: rgb(7, 55, 99); font-weight: bold">int</span> n)<br/>
{<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">int</span> mx = arr[0];<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">for</span> (<span style="color: rgb(7, 55, 99); font-weight: bold">int</span> i = 1; i < n; i++)<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">if</span> (arr[i] > mx)<br/>
mx = arr[i];<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">return</span> mx;<br/>
}<br/>
<br/>
<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">void</span> countSort(<span style="color: rgb(7, 55, 99); font-weight: bold">int</span> arr[], <span style="color: rgb(7, 55, 99); font-weight: bold">int</span> n, <span style="color: rgb(7, 55, 99); font-weight: bold">int</span> exp)<br/>
{<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">int</span> output[n];<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">int</span> i, count[10] = {0};<br/>
<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">for</span> (i = 0; i < n; i++){<br/>
count[ (arr[i]/exp)%10 ]++;<br/>
}<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">for</span> (i = 1; i < 10; i++){<br/>
count[i] += count[i - 1];<br/>
}<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">for</span> (i = n - 1; i >= 0; i--){<br/>
output[count[ (arr[i]/exp)%10 ] - 1] = arr[i];<br/>
count[ (arr[i]/exp)%10 ]--;<br/>
}<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">for</span> (i = 0; i < n; i++)<br/>
arr[i] = output[i];<br/>
}<br/>
<br/>
<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">void</span> radixsort(<span style="color: rgb(7, 55, 99); font-weight: bold">int</span> arr[], <span style="color: rgb(7, 55, 99); font-weight: bold">int</span> n)<br/>
{<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">int</span> m = getMax(arr, n);<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">for</span> (<span style="color: rgb(7, 55, 99); font-weight: bold">int</span> exp = 1; m/exp > 0; exp *= 10)<br/>
countSort(arr, n, exp);<br/>
}<br/>
<br/>
<br/>
<br/>
<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">int</span> main(){<br/>
srand(time(0));<br/>
vector<string>numbers;<br/>
vector<string>codes;<br/>
ifstream file(<span style="color: rgb(204, 0, 0);">"olsen.txt"</span>);<br/>
string numb;<br/>
string code;<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">int</span> length=0;<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">while</span>(file >> numb >> code){<br/>
numbers.push_back(numb);<br/>
codes.push_back(code);<br/>
length++;<br/>
}<br/>
<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">int</span> Result;<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">int</span> *codesArray=<span style="color: rgb(7, 55, 99); font-weight: bold">new</span> <span style="color: rgb(7, 55, 99); font-weight: bold">int</span>[codes.size()];<br/>
<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">for</span>(<span style="color: rgb(7, 55, 99); font-weight: bold">int</span> x = 0 ; x < codes.size(); x++){<br/>
codesArray[x]=StringToNumber<<span style="color: rgb(7, 55, 99); font-weight: bold">int</span>>(codes[x]);<br/>
}<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">int</span> x=2;<span style="color: rgb(56, 118, 29); font-style: italic">// x=1 -> QuickSort, x=2-> Double-Pivot , x=3 -> Radix Sort</span><br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">if</span>(x==1){<br/>
StartCounter();<br/>
quickSort(codesArray,0,codes.size());<br/>
cout<<GetCounter()<<endl;<br/>
}<span style="color: rgb(7, 55, 99); font-weight: bold">else</span> <span style="color: rgb(7, 55, 99); font-weight: bold">if</span>(x==2){<br/>
StartCounter();<br/>
quickSortDualPivot(codesArray,0,codes.size());<br/>
cout<<GetCounter();<br/>
}<span style="color: rgb(7, 55, 99); font-weight: bold">else</span> <span style="color: rgb(7, 55, 99); font-weight: bold">if</span>(x==3){<br/>
StartCounter();<br/>
radixsort(codesArray,codes.size());<br/>
cout<<GetCounter();<br/>
}<br/>
<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">for</span>(<span style="color: rgb(7, 55, 99); font-weight: bold">int</span> x=0 ; x<codes.size();x++){ <span style="color: rgb(56, 118, 29); font-style: italic">//Here i am showing that array was sorted successfully</span><br/>
cout<<codesArray[x]<<endl;<br/>
}<br/>
<br/>
<br/>
<br/>
<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">delete</span> [] codesArray;<br/>
<span style="color: rgb(7, 55, 99); font-weight: bold">return</span> 0;<br/>
}<br/>
</div></div>
<!-- end of generated code -->
</div>
<div id="bottom">
<ul>
<li><a href="index.html">Main </a></li>
<li><a href="myvector.html">MyVector </a></li>
<li><a href="bubble.html">Bubble Sort </a></li>
<li><a href="merge.html">Merge Sort </a></li>
<li><a href="insert.html">Insert Sort </a></li>
<li><a href="quick.html">Quick Sort </a></li>
<li><a href="olsen.html" >Olsen Gang</a></li>
</ul>
</div>
</div>
</body>
</html>