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Data structures: how do I draw recursion trees?

I have a question which I'm not sure how to begin. Can someone explain how to do this recursion tree? And is there anyway to do it on Java?
For the recursive method fnc(n,k) defined below, draw the recursion tree of the call fnc(3,5).
Your diagram should include the return values for all calls to method
fnc(n,k).
public static int fnc(int n, int k) {
if ( (n <= 1) || (k <= 1) ) {
return n+k; } else {
return fnc(n-1,k) + fnc(n,k-2);
}
}

If I understand correctly, you just need to keep track of the level at which the recursion is and use that to control the indenting...
Single entry single exit would probably help here so only need one print statement for the return
String.format() quite handy for output multiple values
pad() method to create repeated string - see Simple way to repeat a String in java for alternatives
Example
static int fnc(int n, int k, int level) {
System.out.println(String.format("%sfnc(%d, %d)", pad(level), n, k));
int result;
if ((n <= 1) || (k <= 1)) {
result = n + k;
} else {
result = fnc(n - 1, k, level + 1) + fnc(n, k - 2, level + 1);
}
System.out.println(String.format("%s<== %d", pad(level), result));
return result;
}
private static String pad(int level) {
String pad = "";
for (int i = 0; i < level; i++) {
pad += " ";
}
return pad;
}
public static void main(String[] args) {
fnc(3, 5, 0);
}
Output
fnc(3, 5)
fnc(2, 5)
fnc(1, 5)
<== 6
fnc(2, 3)
fnc(1, 3)
<== 4
fnc(2, 1)
<== 3
<== 7
<== 13
fnc(3, 3)
fnc(2, 3)
fnc(1, 3)
<== 4
fnc(2, 1)
<== 3
<== 7
fnc(3, 1)
<== 4
<== 11
<== 24

How to split an Integer into an Array using Java?

I apologise if this has already been asked before, but I was unable to find a conclusive answer after some extensive searching, so I thought I would ask here. I am a beginner to Java (to coding, in general) and was tasked with writing a program that takes a user-inputted 3 digit number, and adds those three digits.
Note: I cannot use loops for this task, and the three digits must all be inputted at once.
String myInput;
myInput =
JOptionPane.showInputDialog(null,"Hello, and welcome to the ThreeDigit program. "
+ "\nPlease input a three digit number below. \nThreeDigit will add those three numbers and display their sum.");
int threedigitinput;
threedigitinput = Integer.parseInt(myInput);

There are a number of ways, one of which would be...
String ss[] = "123".split("");
int i =
Integer.parseInt(ss[0]) +
Integer.parseInt(ss[1]) +
Integer.parseInt(ss[2]);
System.out.println(i);
another would be...
String s = "123";
int i =
Character.getNumericValue(s.charAt(0)) +
Character.getNumericValue(s.charAt(1)) +
Character.getNumericValue(s.charAt(2));
System.out.println(i);
and still another would be...
String s = "123";
int i =
s.charAt(0) +
s.charAt(1) +
s.charAt(2) -
(3 * 48);
System.out.println(i);
BUT hard coding for 3 numbers isn't very useful beyond this simple case. So how about recursion??
public static int addDigis(String s) {
if(s.length() == 1)
return s.charAt(0) - 48;
return s.charAt(0) - 48 + addDigis(s.substring(1, s.length()));
}
Output for each example: 6

you can use integer math to come up with the three numbers seperately
int first = threedigitinput / 100;
int second = (threedigitinput % 100) / 10;
int third = threedigitinput % 10;

If I understand your question, you could use Character.digit(char,int) to get the value for each character with something like -
int value = Character.digit(myInput.charAt(0), 10)
+ Character.digit(myInput.charAt(1), 10)
+ Character.digit(myInput.charAt(2), 10);

Classic example of using divmod:
public class SumIntegerDigits {
public static void main(String[] args) {
System.out.println(sumOfDigitsSimple(248)); // 14
System.out.println(sumOfDigitsIterative(248)); // 14
System.out.println(sumOfDigitsRecursive(248)); // 14
}
// Simple, non-loop solution
public static final int sumOfDigitsSimple(int x) {
int y = x % 1000; // Make sure that the value has no more than 3 digits.
return divmod(y,100)[0]+divmod(divmod(y,100)[1],10)[0]+divmod(y,10)[1];
}
// Iterative Solution
public static final int sumOfDigitsIterative(int x) {
int sum = 0;
while (x > 0) {
int[] y = divmod(x, 10);
sum += y[1];
x = y[0];
}
return sum;
}
// Tail-recursive Solution
public static final int sumOfDigitsRecursive(int x) {
if (x <= 0) {
return 0;
}
int[] y = divmod(x, 10);
return sumOfDigitsRecursive(y[0]) + y[1];
}
public static final int[] divmod(final int x, int m) {
return new int[] { (x / m), (x % m) };
}
}

How can I get my program to return -1/4 and NOT 1/-4? [closed]

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\Help! My homework is due by 12am tonight and I can't seem to get my program to output a negative number as -1/4 rather than 1/-4! It's frustrating me because the thing is, I cannot just place a "-" in front of my numbers (which as you can see in my program below, I have commented out).
My attempt at getting fraction to be -1/4 (just using this fraction as an example) is under the "public RationalNumber(int...) { line: you see the part where I have *-1 written? Where did I go wrong in that step that led me to get 1/-4? This is frustrating me... Thanks in advance.
private int n;
private int d;
public RationalNumber(int numerator, int denominator) {
if (denominator == 0) {
throw new IllegalArgumentException();
}
if (denominator < 0) {
denominator = denominator * -1;
numerator = numerator * -1;
}
n = numerator;
d = denominator;
simplified();
}
public RationalNumber add(RationalNumber rn) {
int comDenom = d * rn.getDenominator();
int num1 = n * rn.d;
int num2 = rn.n * d;
d = comDenom;
return new RationalNumber(num1 + num2, d);
}
public RationalNumber subtract(RationalNumber rn) {
int num1 = n * rn.d;
int num2 = rn.n * d;
return new RationalNumber(num1 - num2, d);
}
public RationalNumber multiply(RationalNumber rn) {
int numer = n * rn.n;
int denom = d * rn.d;
return new RationalNumber(numer, denom);
}
public RationalNumber divide(RationalNumber rn) {
int numer = n * rn.d;
int denom = d * rn.n;
return new RationalNumber(numer, denom);
}
public RationalNumber() {
n = 0;
d = 1;
}
public boolean equals(RationalNumber o) {
return (n == o.getNumerator() && d == o.getDenominator());
}
public int getDenominator() {
return d;
}
public int getNumerator() {
return n;
}
public String toString() { //Prints everything here.
if (d == 1) {
return "" + n;
}
if (n == 0) {
return "0";
}
/*if ((n < 0) || (d < 0)) {
return "-" + Math.abs(n) + "/" + Math.abs(d);
}*/
return n + "/" + d;
}
private void simplified() {
if (n != 0) {
int cDenom = gcd(n, d);
n = n / cDenom;
d = d / cDenom;
}
}
private int gcd(int gcdNum1, int gcdNum2) {
while (gcdNum1 != 0 && gcdNum2 != 0) {
int tempNum = gcdNum2;
gcdNum2 = gcdNum1 % gcdNum2;
gcdNum1 = tempNum;
}
return gcdNum1 + gcdNum2;
}

Because this is homework, it is in your best interest to find and fix the problem yourself.
Here are a couple of hints to get you started:
Figure out what the values of n and d are before and after the constructor calls simplified().
You could do this with your Java IDE's debugger, or by using trace prints; i.e. calls to System.out.println(...)

You could put back in the commented out section of your toString method, just make it an XOR (^) rather than OR (||)

The problem is that the gcd() method may return a negative result. When you call the simplified() method, you divide n and c with a possibly negative number, and you change their sign. To fix it, you can change the gcd() method to return always a positive result.
Change this line:
return gcdNum1 + gcdNum2;
to
if (gcdNum1 + gcdNum2 < 0) {
return -(gcdNum1 + gcdNum2);
} else {
return gcdNum1 + gcdNum2;
}
And then check if you get the correct results.

return n + "/" + d;
Change to:
return ((n>=0 && d>=0) || (n<0 && d<0))?(""):("-")+Math.abs(n)+"/"+Math.abs(d);
Just a simple work around.

Find the largest palindrome made from the product of two 3-digit numbers

package testing.project;
public class PalindromeThreeDigits {
public static void main(String[] args) {
int value = 0;
for(int i = 100;i <=999;i++)
{
for(int j = i;j <=999;j++)
{
int value1 = i * j;
StringBuilder sb1 = new StringBuilder(""+value1);
String sb2 = ""+value1;
sb1.reverse();
if(sb2.equals(sb1.toString()) && value<value1) {
value = value1;
}
}
}
System.out.println(value);
}
}
This is the code that I wrote in Java... Is there any efficient way other than this.. And can we optimize this code more??

We suppose the largest such palindrome will have six digits rather than five, because 143*777 = 111111 is a palindrome.
As noted elsewhere, a 6-digit base-10 palindrome abccba is a multiple of 11. This is true because a*100001 + b*010010 + c*001100 is equal to 11*a*9091 + 11*b*910 + 11*c*100. So, in our inner loop we can decrease n by steps of 11 if m is not a multiple of 11.
We are trying to find the largest palindrome under a million that is a product of two 3-digit numbers. To find a large result, we try large divisors first:
We step m downwards from 999, by 1's;
Run n down from 999 by 1's (if 11 divides m, or 9% of the time) or from 990 by 11's (if 11 doesn't divide m, or 91% of the time).
We keep track of the largest palindrome found so far in variable q. Suppose q = r·s with r <= s. We usually have m < r <= s. We require m·n > q or n >= q/m. As larger palindromes are found, the range of n gets more restricted, for two reasons: q gets larger, m gets smaller.
The inner loop of attached program executes only 506 times, vs the ~ 810000 times the naive program used.
#include <stdlib.h>
#include <stdio.h>
int main(void) {
enum { A=100000, B=10000, C=1000, c=100, b=10, a=1, T=10 };
int m, n, p, q=111111, r=143, s=777;
int nDel, nLo, nHi, inner=0, n11=(999/11)*11;
for (m=999; m>99; --m) {
nHi = n11; nDel = 11;
if (m%11==0) {
nHi = 999; nDel = 1;
}
nLo = q/m-1;
if (nLo < m) nLo = m-1;
for (n=nHi; n>nLo; n -= nDel) {
++inner;
// Check if p = product is a palindrome
p = m * n;
if (p%T==p/A && (p/B)%T==(p/b)%T && (p/C)%T==(p/c)%T) {
q=p; r=m; s=n;
printf ("%d at %d * %d\n", q, r, s);
break; // We're done with this value of m
}
}
}
printf ("Final result: %d at %d * %d inner=%d\n", q, r, s, inner);
return 0;
}
Note, the program is in C but same techniques will work in Java.

What I would do:
Start at 999, working my way backwards to 998, 997, etc
Create the palindrome for my current number.
Determine the prime factorization of this number (not all that expensive if you have a pre-generated list of primes.
Work through this prime factorization list to determine if I can use a combination of the factors to make 2 3 digit numbers.
Some code:
int[] primes = new int[] {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,
73,79,83,89,97,101,103,107,109,113,,127,131,137,139,149,151,157,163,167,173,
179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,
283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,
419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,
547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,
661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,
811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,
947,953,967,971,977,983,991,997};
for(int i = 999; i >= 100; i--) {
String palstr = String.valueOf(i) + (new StringBuilder().append(i).reverse());
int pal = Integer.parseInt(pal);
int[] factors = new int[20]; // cannot have more than 20 factors
int remainder = pal;
int facpos = 0;
primeloop:
for(int p = 0; p < primes.length; i++) {
while(remainder % p == 0) {
factors[facpos++] = p;
remainder /= p;
if(remainder < p) break primeloop;
}
}
// now to do the combinations here
}

We can translate the task into the language of mathematics.
For a short start, we use characters as digits:
abc * xyz = n
abc is a 3-digit number, and we deconstruct it as 100*a+10*b+c
xyz is a 3-digit number, and we deconstruct it as 100*x+10*y+z
Now we have two mathematical expressions, and can define a,b,c,x,y,z as € of {0..9}.
It is more precise to define a and x as of element from {1..9}, not {0..9}, because 097 isn't really a 3-digit number, is it?
Ok.
If we want to produce a big number, we should try to reach a 9......-Number, and since it shall be palindromic, it has to be of the pattern 9....9. If the last digit is a 9, then from
(100*a + 10*b + c) * (100*x + 10*y + z)
follows that z*c has to lead to a number, ending in digit 9 - all other calculations don't infect the last digit.
So c and z have to be from (1,3,7,9) because (1*9=9, 9*1=9, 3*3=9, 7*7=49).
Now some code (Scala):
val n = (0 to 9)
val m = n.tail // 1 to 9
val niners = Seq (1, 3, 7, 9)
val highs = for (a <- m;
b <- n;
c <- niners;
x <- m;
y <- n;
z <- niners) yield ((100*a + 10*b + c) * (100*x + 10*y + z))
Then I would sort them by size, and starting with the biggest one, test them for being palindromic. So I would omit to test small numbers for being palindromic, because that might not be so cheap.
For aesthetic reasons, I wouldn't take a (toString.reverse == toString) approach, but a recursive divide and modulo solution, but on todays machines, it doesn't make much difference, does it?
// Make a list of digits from a number:
def digitize (z: Int, nums : List[Int] = Nil) : List[Int] =
if (z == 0) nums else digitize (z/10, z%10 :: nums)
/* for 342243, test 3...==...3 and then 4224.
Fails early for 123329 */
def palindromic (nums : List[Int]) : Boolean = nums match {
case Nil => true
case x :: Nil => true
case x :: y :: Nil => x == y
case x :: xs => x == xs.last && palindromic (xs.init) }
def palindrom (z: Int) = palindromic (digitize (z))
For serious performance considerations, I would test it against a toString/reverse/equals approach. Maybe it is worse. It shall fail early, but division and modulo aren't known to be the fastest operations, and I use them to make a List from the Int. It would work for BigInt or Long with few redeclarations, and works nice with Java; could be implemented in Java but look different there.
Okay, putting the things together:
highs.filter (_ > 900000) .sortWith (_ > _) find (palindrom)
res45: Option[Int] = Some(906609)
There where 835 numbers left > 900000, and it returns pretty fast, but I guess even more brute forcing isn't much slower.
Maybe there is a much more clever way to construct the highest palindrom, instead of searching for it.
One problem is: I didn't knew before, that there is a solution > 900000.
A very different approach would be, to produce big palindromes, and deconstruct their factors.

public class Pin
{
public static boolean isPalin(int num)
{
char[] val = (""+num).toCharArray();
for(int i=0;i<val.length;i++)
{
if(val[i] != val[val.length - i - 1])
{
return false;
}
}
return true;
}
public static void main(String[] args)
{
for(int i=999;i>100;i--)
for(int j=999;j>100;j--)
{
int mul = j*i;
if(isPalin(mul))
{
System.out.printf("%d * %d = %d",i,j,mul);
return;
}
}
}
}

package ex;
public class Main {
public static void main(String[] args) {
int i = 0, j = 0, k = 0, l = 0, m = 0, n = 0, flag = 0;
for (i = 999; i >= 100; i--) {
for (j = i; j >= 100; j--) {
k = i * j;
// System.out.println(k);
m = 0;
n = k;
while (n > 0) {
l = n % 10;
m = m * 10 + l;
n = n / 10;
}
if (m == k) {
System.out.println("pal " + k + " of " + i + " and" + j);
flag = 1;
break;
}
}
if (flag == 1) {
// System.out.println(k);
break;
}
}
}
}

A slightly different approach that can easily calculate the largest palindromic number made from the product of up to two 6-digit numbers.
The first part is to create a generator of palindrome numbers. So there is no need to check if a number is palindromic, the second part is a simple loop.
#include <memory>
#include <iostream>
#include <cmath>
using namespace std;
template <int N>
class PalindromeGenerator {
unique_ptr <int []> m_data;
bool m_hasnext;
public :
PalindromeGenerator():m_data(new int[N])
{
for(auto i=0;i<N;i++)
m_data[i]=9;
m_hasnext=true;
}
bool hasNext() const {return m_hasnext;}
long long int getnext()
{
long long int v=0;
long long int b=1;
for(int i=0;i<N;i++){
v+=m_data[i]*b;
b*=10;
}
for(int i=N-1;i>=0;i--){
v+=m_data[i]*b;
b*=10;
}
auto i=N-1;
while (i>=0)
{
if(m_data[i]>=1) {
m_data[i]--;
return v;
}
else
{
m_data[i]=9;
i--;
}
}
m_hasnext=false;
return v;
}
};
template<int N>
void findmaxPalindrome()
{
PalindromeGenerator<N> gen;
decltype(gen.getnext()) minv=static_cast<decltype(gen.getnext())> (pow(10,N-1));
decltype(gen.getnext()) maxv=static_cast<decltype(gen.getnext())> (pow(10,N)-1);
decltype(gen.getnext()) start=11*(maxv/11);
while(gen.hasNext())
{
auto v=gen.getnext();
for (decltype(gen.getnext()) i=start;i>minv;i-=11)
{
if (v%i==0)
{
auto r=v/i;
if (r>minv && r<maxv ){
cout<<"done:"<<v<<" "<<i<< "," <<r <<endl;
return ;
}
}
}
}
return ;
}
int main(int argc, char* argv[])
{
findmaxPalindrome<6>();
return 0;
}

You can use the fact that 11 is a multiple of the palindrome to cut down on the search space. We can get this since we can assume the palindrome will be 6 digits and >= 111111.
e.g. ( from projecteuler ;) )
P= xyzzyx = 100000x + 10000y + 1000z + 100z + 10y +x
P=100001x+10010y+1100z
P=11(9091x+910y+100z)
Check if i mod 11 != 0, then the j loop can be subtracted by 11 (starting at 990) since at least one of the two must be divisible by 11.

You can try the following which prints
999 * 979 * 989 = 967262769
largest palindrome= 967262769 took 0.015
public static void main(String... args) throws IOException, ParseException {
long start = System.nanoTime();
int largestPalindrome = 0;
for (int i = 999; i > 100; i--) {
LOOP:
for (int j = i; j > 100; j--) {
for (int k = j; k > 100; k++) {
int n = i * j * k;
if (n < largestPalindrome) continue LOOP;
if (isPalindrome(n)) {
System.out.println(i + " * " + j + " * " + k + " = " + n);
largestPalindrome = n;
}
}
}
}
long time = System.nanoTime() - start;
System.out.printf("largest palindrome= %d took %.3f seconds%n", largestPalindrome, time / 1e9);
}
private static boolean isPalindrome(int n) {
if (n >= 100 * 1000 * 1000) {
// 9 digits
return n % 10 == n / (100 * 1000 * 1000)
&& (n / 10 % 10) == (n / (10 * 1000 * 1000) % 10)
&& (n / 100 % 10) == (n / (1000 * 1000) % 10)
&& (n / 1000 % 10) == (n / (100 * 1000) % 10);
} else if (n >= 10 * 1000 * 1000) {
// 8 digits
return n % 10 == n / (10 * 1000 * 1000)
&& (n / 10 % 10) == (n / (1000 * 1000) % 10)
&& (n / 100 % 10) == (n / (100 * 1000) % 10)
&& (n / 1000 % 10) == (n / (10 * 1000) % 10);
} else if (n >= 1000 * 1000) {
// 7 digits
return n % 10 == n / (1000 * 1000)
&& (n / 10 % 10) == (n / (100 * 1000) % 10)
&& (n / 100 % 10) == (n / (10 * 1000) % 10);
} else throw new AssertionError();
}

i did this my way , but m not sure if this is the most efficient way of doing this .
package problems;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
public class P_4 {
/**
* #param args
* #throws IOException
*/
static int[] arry = new int[6];
static int[] arry2 = new int[6];
public static boolean chk()
{
for(int a=0;a<arry.length;a++)
if(arry[a]!=arry2[a])
return false;
return true;
}
public static void main(String[] args) throws IOException {
// TODO Auto-generated method stub
InputStreamReader ir = new InputStreamReader(System.in);
BufferedReader br = new BufferedReader(ir);
int temp,z,i;
for(int x=999;x>100;x--)
for(int y=999;y>100;y--)
{
i=0;
z=x*y;
while(z>0)
{
temp=z%10;
z=z/10;
arry[i]=temp;
i++;
}
for(int k = arry.length;k>0;k--)
arry2[arry.length- k]=arry[k-1];
if(chk())
{
System.out.print("pelindrome = ");
for(int l=0;l<arry2.length;l++)
System.out.print(arry2[l]);
System.out.println(x);
System.out.println(y);
}
}
}
}

This is code in C, a little bit long, but gets the job done.:)
#include <stdio.h>
#include <stdlib.h>
/*
A palindromic number reads the same both ways. The largest palindrome made from the product of two
2-digit numbers is 9009 = 91 99.
Find the largest palindrome made from the product of two 3-digit numbers.*/
int palndr(int b)
{
int *x,*y,i=0,j=0,br=0;
int n;
n=b;
while(b!=0)
{
br++;
b/=10;
}
x=(int *)malloc(br*sizeof(int));
y=(int *)malloc(br*sizeof(int));
int br1=br;
while(n!=0)
{
x[i++]=y[--br]=n%10;
n/=10;
}
int ind = 1;
for(i=0;i<br1;i++)
if(x[i]!=y[i])
ind=0;
free(x);
free(y);
return ind;
}
int main()
{
int i,cek,cekmax=1;
int j;
for(i=100;i<=999;i++)
{
for(j=i;j<=999;j++)
{
cek=i*j;
if(palndr(cek))
{
if(pp>cekmax)
cekmax=cek;
}
}
}
printf("The largest palindrome is: %d\n\a",cekmax);
}

You can actually do it with Python, it's easy just take a look:
actualProduct = 0
highestPalindrome = 0
# Setting the numbers. In case it's two digit 10 and 99, in case is three digit 100 and 999, etc.
num1 = 100
num2 = 999
def isPalindrome(number):
number = str(number)
reversed = number[::-1]
if number==reversed:
return True
else:
return False
a = 0
b = 0
for i in range(num1,num2+1):
for j in range(num1,num2+1):
actualProduct = i * j
if (isPalindrome(actualProduct) and (highestPalindrome < actualProduct)):
highestPalindrome = actualProduct
a = i
b = j
print "Largest palindrome made from the product of two %d-digit numbers is [ %d ] made of %d * %d" % (len(str(num1)), highestPalindrome, a, b)

Since we are not cycling down both iterators (num1 and num2) at the same time, the first palindrome number we find will be the largest. We don’t need to test to see if the palindrome we found is the largest. This significantly reduces the time it takes to calculate.
package testing.project;
public class PalindromeThreeDigits {
public static void main(String[] args) {
int limit = 99;
int max = 999;
int num1 = max, num2, prod;
while(num1 > limit)
{
num2 = num1;
while(num2 > limit)
{
total = num1 * num2;
StringBuilder sb1 = new StringBuilder(""+prod);
String sb2 = ""+prod;
sb1.reverse();
if( sb2.equals(sb1.toString()) ) { //optimized here
//print and exit
}
num2--;
}
num1--;
}
}//end of main
}//end of class PalindromeThreeDigits

I tried the solution by Tobin joy and vickyhacks and both of them produce the result 580085 which is wrong here is my solution, though very clumsy:
import java.util.*;
class ProjEu4
{
public static void main(String [] args) throws Exception
{
int n=997;
ArrayList<Integer> al=new ArrayList<Integer>();
outerloop:
while(n>100){
int k=reverse(n);
int fin=n*1000+k;
al=findfactors(fin);
if(al.size()>=2)
{
for(int i=0;i<al.size();i++)
{
if(al.contains(fin/al.get(i))){
System.out.println(fin+" factors are:"+al.get(i)+","+fin/al.get(i));
break outerloop;}
}
}
n--;
}
}
private static ArrayList<Integer> findfactors(int fin)
{
ArrayList<Integer> al=new ArrayList<Integer>();
for(int i=100;i<=999;i++)
{
if(fin%i==0)
al.add(i);
}
return al;
}
private static int reverse(int number)
{
int reverse = 0;
while(number != 0){
reverse = (reverse*10)+(number%10);
number = number/10;
}
return reverse;
}
}

Most probably it is replication of one of the other solution but it looks simple owing to pythonified code ,even it is a bit brute-force.
def largest_palindrome():
largest_palindrome = 0;
for i in reversed(range(1,1000,1)):
for j in reversed(range(1, i+1, 1)):
num = i*j
if check_palindrome(str(num)) and num > largest_palindrome :
largest_palindrome = num
print "largest palindrome ", largest_palindrome
def check_palindrome(term):
rev_term = term[::-1]
return rev_term == term

What about : in python
>>> for i in range((999*999),(100*100), -1):
... if str(i) == str(i)[::-1]:
... print i
... break
...
997799
>>>

I believe there is a simpler approach: Examine palindromes descending from the largest product of two three digit numbers, selecting the first palindrome with two three digit factors.
Here is the Ruby code:
require './palindrome_range'
require './prime'
def get_3_digit_factors(n)
prime_factors = Prime.factors(n)
rf = [prime_factors.pop]
rf << prime_factors.shift while rf.inject(:*) < 100 || prime_factors.inject(:*) > 999
lf = prime_factors.inject(:*)
rf = rf.inject(:*)
lf < 100 || lf > 999 || rf < 100 || rf > 999 ? [] : [lf, rf]
end
def has_3_digit_factors(n)
return !get_3_digit_factors(n).empty?
end
pr = PalindromeRange.new(0, 999 * 999)
n = pr.downto.find {|n| has_3_digit_factors(n)}
puts "Found #{n} - Factors #{get_3_digit_factors(n).inspect}, #{Prime.factors(n).inspect}"
prime.rb:
class Prime
class<<self
# Collect all prime factors
# -- Primes greater than 3 follow the form of (6n +/- 1)
# Being of the form 6n +/- 1 does not mean it is prime, but all primes have that form
# See http://primes.utm.edu/notes/faq/six.html
# -- The algorithm works because, while it will attempt non-prime values (e.g., (6 *4) + 1 == 25),
# they will fail since the earlier repeated division (e.g., by 5) means the non-prime will fail.
# Put another way, after repeatedly dividing by a known prime, the remainder is itself a prime
# factor or a multiple of a prime factor not yet tried (e.g., greater than 5).
def factors(n)
square_root = Math.sqrt(n).ceil
factors = []
while n % 2 == 0
factors << 2
n /= 2
end
while n % 3 == 0
factors << 3
n /= 3
end
i = 6
while i < square_root
[(i - 1), (i + 1)].each do |f|
while n % f == 0
factors << f
n /= f
end
end
i += 6
end
factors << n unless n == 1
factors
end
end
end
palindrome_range.rb:
class PalindromeRange
FIXNUM_MAX = (2**(0.size * 8 -2) -1)
def initialize(min = 0, max = FIXNUM_MAX)
#min = min
#max = max
end
def downto
return enum_for(:downto) unless block_given?
n = #max
while n >= #min
yield n if is_palindrome(n)
n -= 1
end
nil
end
def each
return upto
end
def upto
return enum_for(:downto) unless block_given?
n = #min
while n <= #max
yield n if is_palindrome(n)
n += 1
end
nil
end
private
def is_palindrome(n)
s = n.to_s
i = 0
j = s.length - 1
while i <= j
break if s[i] != s[j]
i += 1
j -= 1
end
i > j
end
end

public class ProjectEuler4 {
public static void main(String[] args) {
int x = 999; // largest 3-digit number
int largestProduct = 0;
for(int y=x; y>99; y--){
int product = x*y;
if(isPalindormic(x*y)){
if(product>largestProduct){
largestProduct = product;
System.out.println("3-digit numbers product palindormic number : " + x + " * " + y + " : " + product);
}
}
if(y==100 || product < largestProduct){y=x;x--;}
}
}
public static boolean isPalindormic(int n){
int palindormic = n;
int reverse = 0;
while(n>9){
reverse = (reverse*10) + n%10;
n=n/10;
}
reverse = (reverse*10) + n;
return (reverse == palindormic);
}
}

Print an integer in binary format in Java

I have a number and I want to print it in binary. I don't want to do it by writing an algorithm.
Is there any built-in function for that in Java?

Assuming you mean "built-in":
int x = 100;
System.out.println(Integer.toBinaryString(x));
See Integer documentation.
(Long has a similar method, BigInteger has an instance method where you can specify the radix.)

Here no need to depend only on binary or any other format... one flexible built in function is available That prints whichever format you want in your program.. Integer.toString(int, representation)
Integer.toString(100,8) // prints 144 --octal representation
Integer.toString(100,2) // prints 1100100 --binary representation
Integer.toString(100,16) //prints 64 --Hex representation

System.out.println(Integer.toBinaryString(343));

I needed something to print things out nicely and separate the bits every n-bit. In other words display the leading zeros and show something like this:
n = 5463
output = 0000 0000 0000 0000 0001 0101 0101 0111
So here's what I wrote:
/**
* Converts an integer to a 32-bit binary string
* #param number
* The number to convert
* #param groupSize
* The number of bits in a group
* #return
* The 32-bit long bit string
*/
public static String intToString(int number, int groupSize) {
StringBuilder result = new StringBuilder();
for(int i = 31; i >= 0 ; i--) {
int mask = 1 << i;
result.append((number & mask) != 0 ? "1" : "0");
if (i % groupSize == 0)
result.append(" ");
}
result.replace(result.length() - 1, result.length(), "");
return result.toString();
}
Invoke it like this:
public static void main(String[] args) {
System.out.println(intToString(5463, 4));
}

public static void main(String[] args)
{
int i = 13;
short s = 13;
byte b = 13;
System.out.println("i: " + String.format("%32s",
Integer.toBinaryString(i)).replaceAll(" ", "0"));
System.out.println("s: " + String.format("%16s",
Integer.toBinaryString(0xFFFF & s)).replaceAll(" ", "0"));
System.out.println("b: " + String.format("%8s",
Integer.toBinaryString(0xFF & b)).replaceAll(" ", "0"));
}
Output:
i: 00000000000000000000000000001101
s: 0000000000001101
b: 00001101

Old school:
int value = 28;
for(int i = 1, j = 0; i < 256; i = i << 1, j++)
System.out.println(j + " " + ((value & i) > 0 ? 1 : 0));
Output (least significant bit is on 0 position):
0 0
1 0
2 1
3 1
4 1
5 0
6 0
7 0

check out this logic can convert a number to any base
public static void toBase(int number, int base) {
String binary = "";
int temp = number/2+1;
for (int j = 0; j < temp ; j++) {
try {
binary += "" + number % base;
number /= base;
} catch (Exception e) {
}
}
for (int j = binary.length() - 1; j >= 0; j--) {
System.out.print(binary.charAt(j));
}
}
OR
StringBuilder binary = new StringBuilder();
int n=15;
while (n>0) {
if((n&1)==1){
binary.append(1);
}else
binary.append(0);
n>>=1;
}
System.out.println(binary.reverse());

This is the simplest way of printing the internal binary representation of an integer.
For Example: If we take n as 17 then the output will be: 0000 0000 0000 0000 0000 0000 0001 0001
void bitPattern(int n) {
int mask = 1 << 31;
int count = 0;
while(mask != 0) {
if(count%4 == 0)
System.out.print(" ");
if((mask&n) == 0)
System.out.print("0");
else
System.out.print("1");
count++;
mask = mask >>> 1;
}
System.out.println();
}

Simple and pretty easiest solution.
public static String intToBinaryString(int integer, int numberOfBits) {
if (numberOfBits > 0) { // To prevent FormatFlagsConversionMismatchException.
String nBits = String.format("%" + numberOfBits + "s", // Int to bits conversion
Integer.toBinaryString(integer))
.replaceAll(" ","0");
return nBits; // returning the Bits for the given int.
}
return null; // if the numberOfBits is not greater than 0, returning null.
}

Solution using 32 bit display mask,
public static String toBinaryString(int n){
StringBuilder res=new StringBuilder();
//res= Integer.toBinaryString(n); or
int displayMask=1<<31;
for (int i=1;i<=32;i++){
res.append((n & displayMask)==0?'0':'1');
n=n<<1;
if (i%8==0) res.append(' ');
}
return res.toString();
}
System.out.println(BitUtil.toBinaryString(30));
O/P:
00000000 00000000 00000000 00011110

Simply try it. If the scope is only printing the binary values of the given integer value. It can be positive or negative.
public static void printBinaryNumbers(int n) {
char[] arr = Integer.toBinaryString(n).toCharArray();
StringBuilder sb = new StringBuilder();
for (Character c : arr) {
sb.append(c);
}
System.out.println(sb);
}
input
5
Output
101

There are already good answers posted here for this question. But, this is the way I've tried myself (and might be the easiest logic based → modulo/divide/add):
int decimalOrBinary = 345;
StringBuilder builder = new StringBuilder();
do {
builder.append(decimalOrBinary % 2);
decimalOrBinary = decimalOrBinary / 2;
} while (decimalOrBinary > 0);
System.out.println(builder.reverse().toString()); //prints 101011001

Binary representation of given int x with left padded zeros:
org.apache.commons.lang3.StringUtils.leftPad(Integer.toBinaryString(x), 32, '0')

You can use bit mask (1<< k) and do AND operation with number!
1 << k has one bit at k position!
private void printBits(int x) {
for(int i = 31; i >= 0; i--) {
if((x & (1 << i)) != 0){
System.out.print(1);
}else {
System.out.print(0);
}
}
System.out.println();
}

The question is tricky in java (and probably also in other language).
A Integer is a 32-bit signed data type, but Integer.toBinaryString() returns a string representation of the integer argument as an unsigned integer in base 2.
So, Integer.parseInt(Integer.toBinaryString(X),2) can generate an exception (signed vs. unsigned).
The safe way is to use Integer.toString(X,2); this will generate something less elegant:
-11110100110
But it works!!!

I think it's the simplest algorithm so far (for those who don't want to use built-in functions):
public static String convertNumber(int a) {
StringBuilder sb=new StringBuilder();
sb.append(a & 1);
while ((a>>=1) != 0) {
sb.append(a & 1);
}
sb.append("b0");
return sb.reverse().toString();
}
Example:
convertNumber(1) --> "0b1"
convertNumber(5) --> "0b101"
convertNumber(117) --> "0b1110101"
How it works: while-loop moves a-number to the right (replacing the last bit with second-to-last, etc), gets the last bit's value and puts it in StringBuilder, repeats until there are no bits left (that's when a=0).

for(int i = 1; i <= 256; i++)
{
System.out.print(i + " "); //show integer
System.out.println(Integer.toBinaryString(i) + " "); //show binary
System.out.print(Integer.toOctalString(i) + " "); //show octal
System.out.print(Integer.toHexString(i) + " "); //show hex
}

Try this way:
public class Bin {
public static void main(String[] args) {
System.out.println(toBinary(0x94, 8));
}
public static String toBinary(int a, int bits) {
if (--bits > 0)
return toBinary(a>>1, bits)+((a&0x1)==0?"0":"1");
else
return (a&0x1)==0?"0":"1";
}
}
10010100

Enter any decimal number as an input. After that we operations like modulo and division to convert the given input into binary number.
Here is the source code of the Java Program to Convert Integer Values into Binary and the bits number of this binary for his decimal number.
The Java program is successfully compiled and run on a Windows system. The program output is also shown below.
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int integer ;
String binary = ""; // here we count "" or null
// just String binary = null;
System.out.print("Enter the binary Number: ");
integer = sc.nextInt();
while(integer>0)
{
int x = integer % 2;
binary = x + binary;
integer = integer / 2;
}
System.out.println("Your binary number is : "+binary);
System.out.println("your binary length : " + binary.length());
}
}

Since no answer is accepted, maybe your question was about how to store an integer in an binary-file.
java.io.DataOutputStream might be what you're looking for: https://docs.oracle.com/javase/8/docs/api/java/io/DataOutputStream.html
DataOutputStream os = new DataOutputStream(outputStream);
os.writeInt(42);
os.flush();
os.close();

Integer.toString(value,numbersystem) --- syntax to be used
and pass value
Integer.toString(100,8) // prints 144 --octal
Integer.toString(100,2) // prints 1100100 --binary
Integer.toString(100,16) //prints 64 --Hex

This is my way to format an output of the Integer.toBinaryString method:
public String toBinaryString(int number, int groupSize) {
String binary = Integer.toBinaryString(number);
StringBuilder result = new StringBuilder(binary);
for (int i = 1; i < binary.length(); i++) {
if (i % groupSize == 0) {
result.insert(binary.length() - i, " ");
}
}
return result.toString();
}
The result for the toBinaryString(0xABFABF, 8) is "10101011 11111010 10111111"
and for the toBinaryString(0xABFABF, 4) is "1010 1011 1111 1010 1011 1111"

It works with signed and unsigned values used powerful bit manipulation and generates the first zeroes on the left.
public static String representDigits(int num) {
int checkBit = 1 << (Integer.SIZE * 8 - 2 ); // avoid the first digit
StringBuffer sb = new StringBuffer();
if (num < 0 ) { // checking the first digit
sb.append("1");
} else {
sb.append("0");
}
while(checkBit != 0) {
if ((num & checkBit) == checkBit){
sb.append("1");
} else {
sb.append("0");
}
checkBit >>= 1;
}
return sb.toString();
}

`
long k=272214023L;
String long =
String.format("%64s",Long.toBinaryString(k)).replace(' ','0');
String long1 = String.format("%64s",Long.toBinaryString(k)).replace(' ','0').replaceAll("(\d{8})","$1 ");
`
print :
0000000000000000000000000000000000000000000
00000000 00000000 00000000 00000000 0000000