Develop Reference

Java Basics - Extract digits from a number

I'm new to Java, so still trying to figure out the syntax and code execution,
I'm working on a very simple algorithm which is basically to return/print true or false statement if a number is divisible by the sum of its digits.
public class Main {
public static void main(String[] args) {
divisableNumber();
}
static void divisableNumber() {
int num = 2250;
int sumOfDigits = 0;
while (num > 0) {
System.out.println(num);
int remainder = num %10 ;
sumOfDigits += remainder;
System.out.println("line17");
System.out.println(sumOfDigits);
num = num /10;
}
System.out.println(num);
// if(num % sumOfDigits == 0) {
// System.out.println( num);
// } else {
// System.out.println(num + "is not divisable by sum of digits");
// }
}
//*****Explanation*********
// java divides by 10 without remainder.
// Hence, can see that with each iteration number is losing its unit digit( it happens end of each loop line21)
// basically with each iteration we are checking what is the remainder of the input divided by 10
// Eventually, we are adding the remainder ( which is the unit digit at each iteration)
}
``
I don't understand why the loop zeros out the variable and how to overcome it ( i could have written another variable inside the loop , but it seems not clean ).
Can anyone help ?
[enter image description here][1]
[1]: https://i.stack.imgur.com/rZbOW.png

Your code prints 0 every time since it divides the number to 10 until it becomes 0 inside the while loop. Remember that any positive number below 10 divided by 10 gives the result 0 in Java.
You calculated the sum of digits correctly but did not check if it divides the number correctly. In order to achieve that, you need to store a copy of number at the start and check if it is divisible by sumOfDigits.
You can achieve the solution with the following code, it is very similar but structured a little better.
class Main
{
// Function to check if the
// given number is divisible
// by sum of its digits
static String divisableNumber(long n)
{
long temp = n; // store a copy of number
// Find sum of digits
int sum = 0;
while (n != 0)
{
int k = (int) n % 10; // get remainder of division of 10
sum += k; // add digit sum
n /= 10; // divide number by 10
}
// check if sum of digits divides n
if (temp % sum == 0)
return "YES";
return "NO";
}
// This is where the execution begins always (main function)
public static void main(String []args)
{
long n = 123; // better to declare number here and give it as a parameter to function
System.out.println(isDivisible(n)); // print the result of divisible or not
}
}

Java find second-leading digit in int

I am working on a Java problem in which I need to check if the second-leading digit of an int (ex: the '2' in 123, or the '8' in 58347) of any size is a particular digit (such as a '2' or a '5'), and then assign true to a Boolean, if it is that digit. I am trying to do the modulo/divisor method, but I am not able to extract the second-leading digit if the number is large.
I searched Stack Overflow, and found a very similar question. However, the solution for that question works if the number is hard-coded as being two digits. I know there is a way by converting int to String, and I tried that method successfully, but I need to use int/modulo/division method. I tried doing (n%100)/10; but it got me second-to-last digit (ex: the '7' in 4562374), not second-after-first digit.
// n is a number such as 123, or 25, or 52856.
while (n > 0) {
int i=((n%10)/10);
if( (i==2)||(i==3) || (i==5)|| (i==7) )
{ secondDigit=true; }
else { secondDigit= false; } }
System.out.println(secondDigit);

Just keep dividing by 10 until the number is < 100 then do modulo 10, example:
class Main {
public static void main(String[] args) {
int n = 58347;
while (n >= 100) {
n /= 10;
}
System.out.println(n % 10); // prints 8
}
}

Not certain about the efficiency of this method, however its easy to read.
Integer.parseInt(String.valueOf(Math.abs(initial_value)).charAt(1)+"")
However, you have to ensure that the number has more than 1 digit.

Instead of repeatedly dividing the number you have until it's small enough for you to handle, how about finding out how big the number is so you only need to do a single division?
What I mean is that you should consider using logarithms to find out the magnitude of your number. Finding the base 10 logarithm of your number gets you its magnitude. For 100 the log_10 is 2, so you can do the following:
long magnitude = Math.log10(number);
long divisor = Math.pow(10, magnitude - 1);
long smallNumber = number / divisor;
int digit = smallNumber % 10;

I have a program that calculates the first 200 prime numbers, but I do not understand a formula in it

I need to write a code which should calculate the first 200 prime numbers, but I can't hand it in as long as I can't explain everything. I used a piece of code from the internet as reference (http://crab.rutgers.edu/~dhong/cs325/chapter3/PrimeNumber.java).
Whole code:
public class Opdracht3 {
public static void main(String[] args) {
int limiet = 200;
int counter = 1;
int testpriem = 3;
boolean isPriem;
while (counter <= limiet) {
isPriem = true;
for (int i = 2; i <= testpriem / 2; i++) {
if (testpriem % i == 0) {
isPriem = false;
break;
}
}
if (isPriem) {
System.out.println(counter + ": " + testpriem);
counter++;
}
testpriem++;
}
}
}
Below part of code verifies if the number is a composite. If testpriem is composite, then comes out of the loop and starts over. Otherwise, it continues and prints the prime number testpriem.
The problem is here:
for (int i = 2; i <= testpriem / 2; i++) {
if (testpriem % i == 0) {
isPriem = false;
break;
}
}
I tested what happens to i, and one way or another it recognizes the divisor needed to calculate the composite. (With 4 divisor is 2, with 9 divisor is 3, with 221 divisor is 13) But I am flabbergasted as of why.
Any ideas?.

the % or ("remainder") operator in Java divides one operand by another and returns the remainder as its result. And of course if integer x is evenly divisible by another integer y (meaning x/y = some integer z with a remainder of zero), then x can not be prime.

First remember every number able to divide by its half or less. Consider number 7 it is possible divided by 1,2,3 because after 3, if try to divide number by 4 means 4x2 = 8 that is greater than 7. so it is optimum way to find divisor in this way. One more thing every number divided by 1 and number itself. so if number number is divided by 1 or itself then it is called prime so i starts from 2.
now consider testpriem =7 so you will get loop like
for (int i = 2; i <= 7 / 2(i.e 3); i++)
{
if(7 % i == 0)
{
isPriem = false;
break;
}
so first time it checks 7%2=1 so condition false. again check for 7%3 = 1 again condition false. and now this condition full fills here i <= 7 / 2(i.e 3) so loop stopped and it result 7 number is prime

Well, if testpriem % i == 0, it means that i divides testpriem, which means that testpriem is not a prime a number and i, is its first divider. % is the modulo operation, which is the rest of the division.
https://en.wikipedia.org/wiki/Modulo_operation

The break stops the for loop and moves to the next position in the while loop. So it does not restart the for loop for the current tested number.
The break is used for efficiency reasons. You could remove it and the algorithm would still work correctly but slower.

How to find prime factorization of number using loop?

I'm supposed to find the prime factorization of this number: 600851475.
Prime factorization, according to my teacher and this website, http://www.mathsisfun.com/prime-factorization.html, are prime numbers that multiplied give you that number. So for example 12, even though its factors are 2,3,4,6, the prime factors WON'T be just 2 & 3, but 2,2,3.
I have the algorithm to find a prime factor allready, but I can't find a way to loop so that it keeps finding the rest until there are no more prime factors.
This is what i got:
public class primeFactors {
public static void main(String[] args) {
int d= 600851475;
int i = 2;
if (d%i!=0) {i++;}
if (d%i==0) {d=d/i;}
System.out.println(i);
}
}
and it prints this: 3.
If i copy paste it multiple times it does print different things:
public class primeFactors {
public static void main(String[] args) {
int d= 600851475;
int i = 2;
if (d%i!=0) {i++;}
if (d%i==0) {d=d/i;}
System.out.println(i);
if (d%i!=0) {i++;}
if (d%i==0) {d=d/i;}
System.out.println(i);
if (d%i!=0) {i++;}
if (d%i==0) {d=d/i;}
System.out.println(i);
if (d%i!=0) {i++;}
if (d%i==0) {d=d/i;}
System.out.println(i);
}
}
That one prints: 3, 3, 4, 5, 5.
How can I do this with loops? I tried with do while loops( do { if section} while (d>i) {print i} ), but it doesn't work. I also tried with for loop (i=2;i<=d;i++) & it doesn't work. It gives me composite numbers too.
HELP PLEASE!!

Since this is an assignment, the most I'll give you is a general direction: the easiest way to write this will be to try candidate divisors and reduce. For example:
130 - try 2, it divides, so reduce
65 - maybe there's another 2 in there? try 2 again. It doesn't divide, so move on
65 - try 3 - no. 4? no. 5? yes, it divides, so reduce.
13 - Is there another 5 in there? no. try 6, 7, 8, 9, 10, 11, 12. Okay, you're done.
So you need to try candidate divisors in a loop, and you need an inner loop to make sure you cast out any repeated factors (for example, 525 will have the prime factors 3, 5, and 7 but you still want to get rid of that second 5). That should get you on the right track.
Clearly, there will be more efficient ways to write this, but if you're stuck, start with the simplest possible thing that could work, and get that working.

You only need something like this (Perhaps this is not the most efficient way but it was pretty straight forward and easier to understand) :
int d= 600851475;
for (int i = 2 ; i < (d / 2) ; i++){
if(isPrime(i)){
if(d % i ==0){
System.out.println(i + "Is a prime factor of " + d);
}
}
}
But first you will need to have this method that check if it is a prime number or not
public static boolean isPrime(int n){
for(int i = 2 ; i < n ; i++){
if(n % i == 0){
return false;
}
}
return true;
}

Try to use a for loop.
for (int i = 2; i <= d; i++)
{
//implement if statement here
}
This should point you in the right direction.

You have the right idea. You need to divide each factor until it no longer divides.
// this will print all prime divisors for n
for (int i = 2; n != 1; i++)
{
while (n % i == 0)
{
System.out.println (i);
n /= i;
}
}

How to find the prime factorization of a number?
Here is what I tried:
def p_factorization(n):
#Finding the factors of n.
num=[i for i in range(1,n+1) if n%i==0]
#Finding the prime factors of n.
#Now prime_num checks to see if any of the factors of 36 have more than two "subfactors".
prime_num=[i for i in range(2,max(num)) if len([j for j in range(1,i+1) if i%j==0])<=2 and max(num)%i==0]
return prime_num
#Explanation:
#The num list is self-explanatory. It finds all of the factors of the number n.
#The prime_num list comprehension is where it gets complicated:
#The i represents all of the numbers in the range of the original factors that we found,
#then we know that a number is prime if it has two or fewer factors, hence the if condition
#applying to the len of the factors of i, which is being iterated through.
#For example, 4 is not a prime number because the length of the list of factors is
#3 [1,2,4].
And of course, we still need max(num) to be divisible by i.
You are very welcome!

Prime Factorization Program in Java

I am working on a prime factorization program implemented in Java.
The goal is to find the largest prime factor of 600851475143 (Project Euler problem 3).
I think I have most of it done, but I am getting a few errors.
Also my logic seems to be off, in particular the method that I have set up for checking to see if a number is prime.
public class PrimeFactor {
public static void main(String[] args) {
int count = 0;
for (int i = 0; i < Math.sqrt(600851475143L); i++) {
if (Prime(i) && i % Math.sqrt(600851475143L) == 0) {
count = i;
System.out.println(count);
}
}
}
public static boolean Prime(int n) {
boolean isPrime = false;
// A number is prime iff it is divisible by 1 and itself only
if (n % n == 0 && n % 1 == 0) {
isPrime = true;
}
return isPrime;
}
}
Edit
public class PrimeFactor {
public static void main(String[] args) {
for (int i = 2; i <= 600851475143L; i++) {
if (isPrime(i) == true) {
System.out.println(i);
}
}
}
public static boolean isPrime(int number) {
if (number == 1) return false;
if (number == 2) return true;
if (number % 2 == 0) return false;
for (int i = 3; i <= number; i++) {
if (number % i == 0) return false;
}
return true;
}
}

Why make it so complicated? You don't need do anything like isPrime(). Divide it's least divisor(prime) and do the loop from this prime. Here is my simple code :
public class PrimeFactor {
public static int largestPrimeFactor(long number) {
int i;
for (i = 2; i <= number; i++) {
if (number % i == 0) {
number /= i;
i--;
}
}
return i;
}
/**
* #param args
*/
public static void main(String[] args) {
System.out.println(largestPrimeFactor(13195));
System.out.println(largestPrimeFactor(600851475143L));
}
}

edit: I hope this doesn't sound incredibly condescending as an answer. I just really wanted to illustrate that from the computer's point of view, you have to check all possible numbers that could be factors of X to make sure it's prime. Computers don't know that it's composite just by looking at it, so you have to iterate
Example: Is X a prime number?
For the case where X = 67:
How do you check this?
I divide it by 2... it has a remainder of 1 (this also tells us that 67 is an odd number)
I divide it by 3... it has a remainder of 1
I divide it by 4... it has a remainder of 3
I divide it by 5... it has a remainder of 2
I divide it by 6... it has a remainder of 1
In fact, you will only get a remainder of 0 if the number is not prime.
Do you have to check every single number less than X to make sure it's prime? Nope. Not anymore, thanks to math (!)
Let's look at a smaller number, like 16.
16 is not prime.
why? because
2*8 = 16
4*4 = 16
So 16 is divisible evenly by more than just 1 and itself. (Although "1" is technically not a prime number, but that's technicalities, and I digress)
So we divide 16 by 1... of course this works, this works for every number
Divide 16 by 2... we get a remainder of 0 (8*2)
Divide 16 by 3... we get a remainder of 1
Divide 16 by 4... we get a remainder of 0 (4*4)
Divide 16 by 5... we get a remainder of 1
Divide 16 by 6... we get a remainder of 4
Divide 16 by 7... we get a remainder of 2
Divide 16 by 8... we get a remainder of 0 (8*2)
We really only need one remainder of 0 to tell us it's composite (the opposite of "prime" is "composite").
Checking if 16 is divisible by 2 is the same thing as checking if it's divisible by 8, because 2 and 8 multiply to give you 16.
We only need to check a portion of the spectrum (from 2 up to the square-root of X) because the largest number that we can multiply is sqrt(X), otherwise we are using the smaller numbers to get redundant answers.
Is 17 prime?
17 % 2 = 1
17 % 3 = 2
17 % 4 = 1 <--| approximately the square root of 17 [4.123...]
17 % 5 = 2 <--|
17 % 6 = 5
17 % 7 = 3
The results after sqrt(X), like 17 % 7 and so on, are redundant because they must necessarily multiply with something smaller than the sqrt(X) to yield X.
That is,
A * B = X
if A and B are both greater than sqrt(X) then
A*B will yield a number that is greater than X.
Thus, one of either A or B must be smaller than sqrt(X), and it is redundant to check both of these values since you only need to know if one of them divides X evenly (the even division gives you the other value as an answer)
I hope that helps.
edit: There are more sophisticated methods of checking primality and Java has a built-in "this number is probably prime" or "this number is definitely composite" method in the BigInteger class as I recently learned via another SO answer :]

You need to do some research on algorithms for factorizing large numbers; this wikipedia page looks like a good place to start. In the first paragraph, it states:
When the numbers are very large, no efficient integer factorization algorithm is publicly known ...
but it does list a number of special and general purpose algorithms. You need to pick one that will work well enough to deal with 12 decimal digit numbers. These numbers are too large for the most naive approach to work, but small enough that (for example) an approach based on enumerating the prime numbers starting from 2 would work. (Hint - start with the Sieve of Erasthones)

Here is very elegant answer - which uses brute force (not some fancy algorithm) but in a smart way - by lowering the limit as we find primes and devide composite by those primes...
It also prints only the primes - and just the primes, and if one prime is more then once in the product - it will print it as many times as that prime is in the product.
public class Factorization {
public static void main(String[] args) {
long composite = 600851475143L;
int limit = (int)Math.sqrt(composite)+1;
for (int i=3; i<limit; i+=2)
{
if (composite%i==0)
{
System.out.println(i);
composite = composite/i;
limit = (int)Math.sqrt(composite)+1;
i-=2; //this is so it could check same prime again
}
}
System.out.println(composite);
}
}

You want to iterate from 2 -> n-1 and make sure that n % i != 0. That's the most naive way to check for primality. As explained above, this is very very slow if the number is large.

To find factors, you want something like:
long limit = sqrt(number);
for (long i=3; i<limit; i+=2)
if (number % i == 0)
print "factor = " , i;
In this case, the factors are all small enough (<7000) that finding them should take well under a second, even with naive code like this. Also note that this particular number has other, smaller, prime factors. For a brute force search like this, you can save a little work by dividing out the smaller factors as you find them, and then do a prime factorization of the smaller number that results. This has the advantage of only giving prime factors. Otherwise, you'll also get composite factors (e.g., this number has four prime factors, so the first method will print out not only the prime factors, but the products of various combinations of those prime factors).
If you want to optimize that a bit, you can use the sieve of Eratosthenes to find the prime numbers up to the square root, and then only attempt division by primes. In this case, the square root is ~775'000, and you only need one bit per number to signify whether it's prime. You also (normally) only want to store odd numbers (since you know immediately that all even numbers but two are composite), so you need ~775'000/2 bits = ~47 Kilobytes.
In this case, that has little real payoff though -- even a completely naive algorithm will appear to produce results instantly.

I think you're confused because there is no iff [if-and-only-if] operator.
Going to the square root of the integer in question is a good shortcut. All that remains is checking if the number within that loop divides evenly. That's simply [big number] % i == 0. There is no reason for your Prime function.
Since you are looking for the largest divisor, another trick would be to start from the highest integer less than the square root and go i--.
Like others have said, ultimately, this is brutally slow.

private static boolean isPrime(int k) throws IllegalArgumentException
{
int j;
if (k < 2) throw new IllegalArgumentException("All prime numbers are greater than 1.");
else {
for (j = 2; j < k; j++) {
if (k % j == 0) return false;
}
}
return true;
}
public static void primeFactorsOf(int n) {
boolean found = false;
if (isPrime(n) == true) System.out.print(n + " ");
else {
int i = 2;
while (found == false) {
if ((n % i == 0) && (isPrime(i))) {
System.out.print(i + ", ");
found = true;
} else i++;
}
primeFactorsOf(n / i);
}
}

For those answers which use a method isPrime(int) : boolean, there is a faster algorithm than the one previously implemented (which is something like)
private static boolean isPrime(long n) { //when n >= 2
for (int k = 2; k < n; k++)
if (n % k == 0) return false;
return true;
}
and it is this:
private static boolean isPrime(long n) { //when n >= 2
if (n == 2 || n == 3) return true;
if (n % 2 == 0 || n % 3 == 0) return false;
for (int k = 1; k <= (Math.floor(Math.sqrt(n)) + 1) / 6; k++)
if (n % (6 * k + 1) == 0 || n % (6 * k - 1) == 0) return false;
return true;
}
I made this algorithm using two facts:
We only need to check for n % k == 0 up to k <= Math.sqrt(n). This is true because for anything higher, factors merely "flip" ex. consider the case n = 15, where 3 * 5 = 5 * 3, and 5 > Math.sqrt(15). There is no need for this overlap of checking both 15 % 3 == 0 and 15 % 5 == 0, when we could just check one of these expressions.
All primes (excluding 2 and 3) can be expressed in the form (6 * k) + 1 or (6 * k) - 1, because any positive integer can be expressed in the form (6 * k) + n, where n = -1, 0, 1, 2, 3, or 4 and k is an integer <= 0, and the cases where n = 0, 2, 3, and 4 are all reducible.
Therefore, n is prime if it is not divisible by 2, 3, or some integer of the form 6k ± 1 <= Math.sqrt(n). Hence the above algorithm.
--
Wikipedia article on testing for primality
--
Edit: Thought I might as well post my full solution (*I did not use isPrime(), and my solution is nearly identical to the top answer, but I thought I should answer the actual question):
public class Euler3 {
public static void main(String[] args) {
long[] nums = {13195, 600851475143L};
for (num : nums)
System.out.println("Largest prime factor of " + num + ": " + lpf(num));
}
private static lpf(long n) {
long largestPrimeFactor = 1;
long maxPossibleFactor = n / 2;
for (long i = 2; i <= maxPossibleFactor; i++)
if (n % i == 0) {
n /= i;
largestPrimeFactor = i;
i--;
}
return largestPrimeFactor;
}
}

To find all prime factorization
import java.math.BigInteger;
import java.util.Scanner;
public class BigIntegerTest {
public static void main(String[] args) {
BigInteger myBigInteger = new BigInteger("65328734260653234260");//653234254
BigInteger originalBigInteger;
BigInteger oneAddedOriginalBigInteger;
originalBigInteger=myBigInteger;
oneAddedOriginalBigInteger=originalBigInteger.add(BigInteger.ONE);
BigInteger index;
BigInteger countBig;
for (index=new BigInteger("2"); index.compareTo(myBigInteger.add(BigInteger.ONE)) <0; index = index.add(BigInteger.ONE)){
countBig=BigInteger.ZERO;
while(myBigInteger.remainder(index) == BigInteger.ZERO ){
myBigInteger=myBigInteger.divide(index);
countBig=countBig.add(BigInteger.ONE);
}
if(countBig.equals(BigInteger.ZERO)) continue;
System.out.println(index+ "**" + countBig);
}
System.out.println("Program is ended!");
}
}

I got a very similar problem for my programming class. In my class it had to calculate for an inputted number. I used a solution very similar to Stijak. I edited my code to do the number from this problem instead of using an input.
Some differences from Stijak's code are these:
I considered even numbers in my code.
My code only prints the largest prime factor, not all factors.
I don't recalculate the factorLimit until I have divided all instances of the current factor off.
I had all the variables declared as long because I wanted the flexibility of using it for very large values of number. I found the worst case scenario was a very large prime number like 9223372036854775783, or a very large number with a prime number square root like 9223371994482243049. The more factors a number has the faster the algorithm runs. Therefore, the best case scenario would be numbers like 4611686018427387904 (2^62) or 6917529027641081856 (3*2^61) because both have 62 factors.
public class LargestPrimeFactor
{
public static void main (String[] args){
long number=600851475143L, factoredNumber=number, factor, factorLimit, maxPrimeFactor;
while(factoredNumber%2==0)
factoredNumber/=2;
factorLimit=(long)Math.sqrt(factoredNumber);
for(factor=3;factor<=factorLimit;factor+=2){
if(factoredNumber%factor==0){
do factoredNumber/=factor;
while(factoredNumber%factor==0);
factorLimit=(long)Math.sqrt(factoredNumber);
}
}
if(factoredNumber==1)
if(factor==3)
maxPrimeFactor=2;
else
maxPrimeFactor=factor-2;
else
maxPrimeFactor=factoredNumber;
if(maxPrimeFactor==number)
System.out.println("Number is prime.");
else
System.out.println("The largest prime factor is "+maxPrimeFactor);
}
}

public class Prime
{
int i;
public Prime( )
{
i = 2;
}
public boolean isPrime( int test )
{
int k;
if( test < 2 )
return false;
else if( test == 2 )
return true;
else if( ( test > 2 ) && ( test % 2 == 0 ) )
return false;
else
{
for( k = 3; k < ( test/2 ); k += 2 )
{
if( test % k == 0 )
return false;
}
}
return true;
}
public void primeFactors( int factorize )
{
if( isPrime( factorize ) )
{
System.out.println( factorize );
i = 2;
}
else
{
if( isPrime( i ) && ( factorize % i == 0 ) )
{
System.out.print( i+", " );
primeFactors( factorize / i );
}
else
{
i++;
primeFactors( factorize );
}
}
public static void main( String[ ] args )
{
Prime p = new Prime( );
p.primeFactors( 649 );
p.primeFactors( 144 );
p.primeFactors( 1001 );
}
}