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kth smallest and MAX_MIN added
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‎Graph Generated/KthSmallest Element.png

25.8 KB
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‎Graph Generated/MIN-MAX Element.png

17.3 KB
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‎Java Program for Complexity Analysis/KthSmallest.java

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import java.io.BufferedWriter;
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import java.io.File;
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import java.io.FileWriter;
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import java.io.IOException;
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import java.util.Arrays;
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import java.util.List;
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import java.util.Random;
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public class KthSmallest {
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public static void main(String[] args) throws IOException {
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File f=new File("D:\\Algorithm time Complexity analysis\\kthSmallest_comp_analysis.txt");
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BufferedWriter bw=new BufferedWriter(new FileWriter(f,false),2);
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//50000,75000,100000,125000,150000,175000,200000
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List<Integer> TestCase=Arrays.asList(50000,75000,100000,125000,150000,175000,200000);
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int[] best;
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int[] worst;
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int[] avg;
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int t=0;
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bw.write("Number_of_Input\t\t\tNumber_of_comparisions\n");
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while(t < TestCase.size()) {
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int arrSize=TestCase.get(t);
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best=new int[arrSize];
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worst=new int[arrSize];
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avg=new int[arrSize];
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Random rand=new Random(); // To Generate Random Numbers...
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for(int i=0;i<arrSize;i++) {
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avg[i]=rand.nextInt(arrSize*10); //Filling Numbers in the range of (0, arrSize*10-1) in array of size arrSize
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}
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for(int i=0;i<arrSize;i++) {
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best[i]=avg[i];
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}
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Arrays.sort(best); // To make a sorted array... which we will use for best case..
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for(int i=0;i<arrSize;i++) {
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worst[i]=best[arrSize-1-i]; // To make reverse order of the Best case ... to Check worst case..
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}
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int k=arrSize/3;
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CountComparisons=0;
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int kthSmallest=kthSmallest(best,0,best.length-1,arrSize/3);
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bw.write(String.format("Best_case\t\t\t%d\t\t\t%d\n",arrSize,CountComparisons));
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System.out.println(k+" "+kthSmallest+" "+CountComparisons);
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CountComparisons=0;
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//it will be the worst case
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kthSmallest=kthSmallest(worst,0,worst.length-1,arrSize/3);
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bw.write(String.format("Worst_case\t\t\t%d\t\t\t%d\n",arrSize,CountComparisons));
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System.out.println(k+" "+kthSmallest+" "+CountComparisons);
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CountComparisons=0;
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//Avg case.....
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kthSmallest=kthSmallest(avg,0,avg.length-1,arrSize/3);
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bw.write(String.format("Avg_case\t\t\t%d\t\t\t%d\n",arrSize,CountComparisons));
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System.out.println(k+" "+kthSmallest+" "+CountComparisons);
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// For TESTING only...
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//
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// if(t==0) {
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// for(int i=0;i<arrSize;i++) {
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// System.out.print(best[i] +" ");
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// }
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// System.out.println();
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//
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// for(int i=0;i<arrSize;i++) {
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// System.out.print(worst[i] +" ");
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// }
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// System.out.println();
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//
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// for(int i=0;i<arrSize;i++) {
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// System.out.print(avg[i] +" ");
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// }
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// System.out.println();
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// }
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//
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t++;
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System.out.println("Success");
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}
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bw.close();
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}
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static int CountComparisons;
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static int kthSmallest(int arr[], int l, int r, int k)
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{
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if (k > 0 && k <= r - l + 1)
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{
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int n = r - l + 1 ;
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int i;
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int []median = new int[(n + 4) / 5];
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for (i = 0; i < n/5; i++)
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median[i] = getMedian(arr,l + i * 5, 5);
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if (i*5 < n)
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{
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median[i] = getMedian(arr,l + i * 5, n % 5);
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i++;
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}
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int medOfMed = (i == 1)? median[i - 1]:
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kthSmallest(median, 0, i - 1, i / 2);
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int pos = partition(arr, l, r, medOfMed);
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if (pos-l == k - 1)
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return arr[pos];
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if (pos-l > k - 1)
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return kthSmallest(arr, l, pos - 1, k);
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return kthSmallest(arr, pos + 1, r, k - pos + l - 1);
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}
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return Integer.MAX_VALUE;
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}
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private static int getMedian(int[] arr, int l, int r) {
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Arrays.sort(arr,l,l+r);
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CountComparisons+=r;
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return arr[l+(r)/2];
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}
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static int partition(int arr[], int low, int high,int pivot)
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{
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int i;
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for(i = low; i < high; i++)
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if (arr[i] == pivot)
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break;
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swap(arr, i, high);
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i = low;
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for(int j = low; j <= high - 1; j++)
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{
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if (arr[j] <= pivot)
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{
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CountComparisons++;
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swap(arr, i, j);
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i++;
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}
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}
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swap(arr, i, high);
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return i;
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}
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private static void swap(int[] arr, int i, int j) {
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int temp=arr[i];
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arr[i]=arr[j];
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arr[j]=temp;
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}
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}

‎Java Program for Complexity Analysis/MinMax.java

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import java.io.BufferedWriter;
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import java.io.File;
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import java.io.FileWriter;
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import java.io.IOException;
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import java.util.Arrays;
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import java.util.List;
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import java.util.Random;
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public class MinMax {
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public static void main(String[] args) throws IOException {
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File f=new File("D:\\Algorithm time Complexity analysis\\min_max_comp_analysis.txt");
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BufferedWriter bw=new BufferedWriter(new FileWriter(f,false),2);
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//50000,75000,100000,125000,150000,175000,200000
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List<Integer> TestCase=Arrays.asList(50000,75000,100000,125000,150000,175000,200000);
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int[] arr;
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int k=0;
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bw.write("Number_of_Input\t\t\tNumber_of_comparisions\n");
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while(k < TestCase.size()) {
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int arrSize=TestCase.get(k);
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arr=new int[arrSize];
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Random rand=new Random(); // To Generate Random Numbers...
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for(int i=0;i<arrSize;i++) {
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arr[i]=rand.nextInt(arrSize*10); //Filling Numbers in the range of (0, arrSize*10-1) in array of size arrSize
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}
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CountComparisons=0;
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//Avg case.....
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Pair minmax=minMax(arr,0,arr.length-1);
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bw.write(String.format("%d\t\t\t%d\n",arrSize,CountComparisons));
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// System.out.println(minmax.min+" "+minmax.max+" "+CountComparisons);
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k++;
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System.out.println("Success");
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}
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bw.close();
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}
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static int CountComparisons;
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static class Pair{
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int min;
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int max;
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Pair(int min,int max){
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this.min=min;
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this.max=max;
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}
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}
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// By Tournament Method
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private static Pair minMax(int[] arr, int l,int h) {
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if(l==h) {
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return new Pair(arr[l],arr[h]);
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}
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else if(l==h-1) {
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CountComparisons++;
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if(arr[l]>arr[h]) {
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return new Pair(arr[h],arr[l]);
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}else {
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return new Pair(arr[l],arr[h]);
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}
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}
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int mid=l+(h-l)/2;
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Pair minmaxl=minMax(arr,l,mid);
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Pair minmaxr=minMax(arr,mid+1,h);
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int localmin,localmax;
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CountComparisons+=2;
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if(minmaxl.min < minmaxr.min) {
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localmin=minmaxl.min;
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}else {
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localmin=minmaxr.min;
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}
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if(minmaxl.max > minmaxr.max) {
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localmax=minmaxl.max;
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}else {
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localmax=minmaxr.max;
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}
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return new Pair(localmin,localmax);
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}
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}

‎Pdf for analysis Chart/DAA_Exp_5_1804310039_Raveet_kumar.pdf

151 KB
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‎kthSmallest_comp_analysis.txt

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Number_of_Input Number_of_comparisions
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Best_case 50000 242502
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Worst_case 50000 244439
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Avg_case 50000 243101
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Best_case 75000 363602
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Worst_case 75000 364801
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Avg_case 75000 365326
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Best_case 100000 488609
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Worst_case 100000 490781
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Avg_case 100000 489150
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Best_case 125000 608491
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Worst_case 125000 614225
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Avg_case 125000 613707
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Best_case 150000 731024
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Worst_case 150000 736832
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Avg_case 150000 735973
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Best_case 175000 852674
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Worst_case 175000 856175
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Avg_case 175000 861939
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Best_case 200000 982516
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Worst_case 200000 985837
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Avg_case 200000 986009

‎min_max_comp_analysis.txt

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Number_of_Input Number_of_comparisions
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50000 82766
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75000 117230
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100000 165534
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125000 190534
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150000 234462
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175000 284462
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200000 331070

‎python program for plotting graphs/CountingAndRadix.py

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import pandas as pd
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import matplotlib.pyplot as mp
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df=pd.read_csv("D:\Algorithm time Complexity analysis\\Radix_sort_analysis.txt",sep="\t")
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df=pd.read_csv("D:\Algorithm time Complexity analysis\\min_max_comp_analysis.txt",sep="\t\t\t")
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best=[]
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worst=[]
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avg=[]
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print(df)
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for i in range(df.shape[0]):
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if i%3==0:
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best.append([df.iloc[i,1],df.iloc[i,2]])
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if i%3==1:
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worst.append([df.iloc[i,1],df.iloc[i,2]])
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if i%3==2:
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avg.append([df.iloc[i,1],df.iloc[i,2]])
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avg.append([df.iloc[i,0],df.iloc[i,1]])
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mp.plot([i[0] for i in best],[i[1] for i in best],'bs--',label="bestcase(sorted)")
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mp.plot([i[0] for i in worst],[i[1] for i in worst],'m^--',label="worst case(reverse)")
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mp.plot([i[0] for i in avg],[i[1] for i in avg],'go--',label="averagecase(random)")
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mp.plot([i[0] for i in avg],[i[1] for i in avg],'go--')
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mp.xlabel("Number of Input")
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mp.ylabel("Time Taken")
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mp.title("Radix Sort")
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mp.ylabel("Number of Comparsions")
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mp.title("MIN-MAX Element")
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mp.legend()
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mp.grid(True,color='k')

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