Download Summation.java public class Summation { public static void main

Summation.java
public class Summation {
public static void main(String[] args){
long timeBefore = System.nanoTime();
System.out.println(sum(1, 10));
long timeUsed = System.nanoTime() - timeBefore;
System.out.println("Time used " + timeUsed);
timeBefore = System.nanoTime();
System.out.println(sum2(1, 10));
timeUsed = System.nanoTime() - timeBefore;
System.out.println("Time used " + timeUsed);
}
public static int sum (int from, int upto)
{
if(from == upto) //If we have reached to a single number to add then return that
number say the call was sum(5,5)
return upto;
else
return sum(from,((from+upto)/2))+sum((((from+upto)/2)+1),upto); // so we
are
}
public static int sum2 (int from, int upto)
{
int sum = 0;
for(int i = from; i<=upto; i++)
sum = sum + i;
return sum;
}
}
Factorial method only
public static int factorial( int integer)
{
if( integer == 1)
return 1;
else
{
return integer*(factorial(integer-1));
}
}
RecursionExamples.java
import java.util.Scanner;
public class RecursionExamples {
public static void main(String[] args) {
Scanner input = new Scanner(System.in);
System.out.println("Enter an integer value: ");
long number = input.nextLong();
System.out.println("The number of odd digits in the number is " + countOdd(number));
System.out.println("The sum of the digits in the number is " + sumDigits(number));
System.out.println("Enter an integer value, we will compute 10^n: ");
int power = input.nextInt();
System.out.println("10^n is " + tenToThe(power));
int array1[] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
System.out.println("The maximum of the array should be 10, got " + max(array1));
int array7[] = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20};
System.out.println("The sum of 2, 4, 6, 8, 10, 12, 14, 18, 20 is " + sumArray(array7));
for(int i=1; i<=21; i++){
System.out.println("Found " + i + " in location " + trinarySearch(array7, i));
}
System.out.println("The number of vowels in the string" +
"\n \"A is a very nice letter.\" is " + countVowels("A is a very nice letter."));
System.out.println("Removing the vowels from " +
"\n \"A is a very nice letter.\" gives " + removeVowels("A is a very nice letter."));
System.out.println("Doubling each letter from " +
"\n \"A is a very nice letter.\" gives " + doubleEachLetter("A is a very nice letter."));
System.out.println("Reversing the letters from " +
"\n \"A is a very nice letter.\" gives " + reverse("A is a very nice letter."));
}
// recursive countOdd()
public static long countOdd(long number){
long result;
if(number == 0)
// base case
result = 0;
else {
long digit = number % 10;
if(digit < 0)
digit = -1 * digit;
if(digit % 2 == 1)
result = countOdd(number/10) + 1;
else
result = countOdd(number/10);
}
return result;
}
// recursive sumDigits()
public static long sumDigits(long number){
long result;
if(number == 0)
// base case
result = 0;
else {
long digit = number % 10;
if(digit < 0)
digit = -1 * digit;
result = digit + sumDigits(number/10);
}
return result;
}
// recursive tenToThe()
/**
* Precondition: n >= 0.
* Returns 10 to the power n.
*/
public static int tenToThe(int n){
int result;
if(n==0){
result = 1;
} else {
result = tenToThe(n/2);
result = result * result;
if(n%2 == 1){
// n is odd we need to square then multiply by 10
result = result * 10;
}
}
return result;
}
// recursive sumArray()
public static int sumArray(int [] data){
return sumArray(data, data.length-1);
}
public static int sumArray(int [] data, int last){
int result;
if(last < 0)
result = 0; // only one value in the subarray
else{
result = data[last] + sumArray(data, last-1);
}
return result;
}
// recursive max()
public static int max(int [] data){
return max(data, 0, data.length-1);
}
public static int max(int [] data, int first, int last){
int result;
if(first == last)
result = data[first]; // only one value in the subarray
else{
int mid = (last + first)/2;
int max1 = max(data, first, mid);
int max2 = max(data, mid+1, last);
if(max1 > max2)
result = max1;
else
result = max2;
}
return result;
}
// recursive trinaarySeaerch()
public static int trinarySearch(int data[], int target){
return trinarySearch(data, target, 0, data.length-1);
}
//Uses trinary search to search for target in a[first] through
//a[last] inclusive. Returns the index of target if target
//is found. Returns -1 if target is not found.
public static int trinarySearch(int data[], int target, int first, int last) {
int result;
if (first > last)
result = -1;
else {
int mid1 = (2*first + last)/3;
int mid2 = (first + 2*last)/3;
if (target == data[mid1])
result = mid1;
else if (target == data[mid2])
result = mid2;
else if (target < data[mid1])
result = trinarySearch(data, target, first, mid1 - 1);
else if (target < data[mid2])
result = trinarySearch(data, target, mid1 + 1, mid2-1);
else
result = trinarySearch(data, target, mid2 + 1, last);
}
return result;
}
// recursive countVowels()
public static int countVowels(String s){
int result;
if(s.length() == 0)
result = 0;
else {
if(isVowel(s.charAt(0)))
result = 1 + countVowels(s.substring(1));
else
result = countVowels(s.substring(1));
}
return result;
}
public static boolean isVowel(char c){
return c=='a' || c=='e' || c=='i' || c=='o' || c=='u'
|| c=='A' || c=='E' || c=='I' || c=='O' || c=='U';
}
// recursive removeVowels()
public static String removeVowels(String s){
String result;
if(s.length() == 0)
result = "";
else {
if(isVowel(s.charAt(0)))
result = removeVowels(s.substring(1));
else
result = s.charAt(0) + removeVowels(s.substring(1));
}
return result;
}
// recursive doubleEachLetter()
public static String doubleEachLetter(String s){
String result;
if(s.length() == 0)
result = "";
else {
String doubled = "" + s.charAt(0) + s.charAt(0);
result = doubled + doubleEachLetter(s.substring(1));
}
return result;
}
// recursive reverse()
public static String reverse(String s){
String result;
if(s.length() == 0)
result = "";
else {
result = reverse(s.substring(1)) + s.charAt(0);
}
return result;
}
}