We Keep Coding

Perfect Numbers in an ArrayList

This is an exercise.
A perfect number is a number whose sum of divisors without itself is equal to that number
6 is a perfect number because its divisors are: 1,2,3,6 and 1 + 2 + 3 = 6
28 is a perfect number because its divisors are: 1,2,4,7,28 and 1 + 2 + 4 + 7 = 28
Task: write the body of findNPerfectNumbers, which will find n prime perfect numbers and return them as a list
I must use this program:
import java.util.ArrayList;
public class Exercise {
public static ArrayList<Integer> findNPerfectNumbers(int n)
{
return new ArrayList<>();
}
public static void main(String[] args)
{
System.out.println(findNPerfectNumbers(4));
}
}
I create this code to resolve this problem, but I have a problem to return an ArrayList. I don't know how. It should look like this example: 6 = 1,2,3,6 ///// 28 = 1, 2, 4, 7
My idea:
import java.util.ArrayList;
public class Main
{
public static ArrayList<Integer> findNPerfectNumbers(int n)
{
int sum = 0;
ArrayList<Integer> perfectList = new ArrayList<>();
ArrayList<Integer> factorList = new ArrayList<>();
for (int i = 6; i < n; i++)
{
factorList.clear();
for (int j = 1; j <= i / 2; j++)
{
if (i % j == 0)
{
factorList.add(j);
}
}
sum = 0;
for (int h = 0; h < factorList.size(); h++)
{
sum = sum + factorList.get(h);
}
if (sum == i)
{
perfectList.add(i);
}
}
return perfectList;
}
public static void main(String[] args)
{
System.out.println(findNPerfectNumbers(28));
}
}
Anyone have an idea?

The question is as simple as to have the findNPerfectNumbers function return the first N perfect numbers.
The main part for the exercise is probably to do this as efficiently as possible. For example limiting divider check by half like you do in for (int j = 1; j <= i / 2; j++) is one of many options.
The reason your function doesn't return anything though is because your outer for loop is incorrect with the given input of 4 what you'r doing is for (int i = 6; i < 4; i++) which doesn't do any loops because 4 is smaller than 6.
what you probably intended to do issomething like for (int i = 6; perfectList.size() < n; i++) which would loop aslong as you have fewer than N perfect numbers.
example working code:
import java.util.ArrayList;
public class Exercise {
public static ArrayList<Integer> findNPerfectNumbers(int n) {
int sum = 0;
ArrayList<Integer> perfectList = new ArrayList<>();
for (int i = 6; perfectList.size() < n; i++) {
ArrayList<Integer> factorList = new ArrayList<>();
for (int j = 1; j <= i / 2; j++) {
if (i % j == 0) {
factorList.add(j);
}
}
sum = 0;
for (Integer factor : factorList) {
sum += factor;
}
if (sum == i) {
System.out.println("Found perfect number " + i + " with factors " + factorList);
perfectList.add(i);
}
}
return perfectList;
}
public static void main(String[] args) {
System.out.println(findNPerfectNumbers(4));
}
}

If number is less than 10^1500 you can use Euclid's method
public static List<Long> findPerfect(int n){
List<Long> perfectList=new ArrayList<>();
int x=0;
long sum=0;
long last;
while(perfectList.size()!=n){
last= (long) Math.pow(2,x);
sum+=last;
if(isPrime(sum))
perfectList.add(sum*last);
x++;
}
return perfectList;
}
public static boolean isPrime(long x){
if(x==1)
return false;
for (int i = 2; i <= Math.sqrt(x); i++) {
if(x%i==0)
return false;
}
return true;
}

how to find number with most divisor from array in java

I got some problem someone of with really helped me but I got program source code who print all of divisor from array, but I tried to print a number with most divisor for ex. array[1,2,3,4,5] and I want to print that the number with most divisor is 4 (1,2,4)
public static class Main {
public static void main(String[] args) {
System.out.println(getNumWithMaxDivisors(numbers));
}
static int getNumDivisors(int n) {
int noOfDivisors = 0;
for (int i = 1; i <= n / 2; i++) {
if (n % i == 0) {
System.out.print(i + " ");
noOfDivisors++;
}
}
return noOfDivisors;
}
static int getNumWithMaxDivisors(int[] numbers) {
int currentMaxDivisors = 0;
int numWithMaxDivisors = numbers[0];
for (int i = 0; i < numbers.length; i++) {
int numDivisors = getNumDivisors(numbers[i]);
if (numDivisors > currentMaxDivisors) {
numWithMaxDivisors = numbers[i];
}
}
return numWithMaxDivisors;
}
}
Code looks that, do you know where is a problem ?

The problem is that inside of your getNumWithMaxDivisors() method, you are not redefining the current number of max divisors. To fix this, you can update it inside of the if statement as so:
static int getNumWithMaxDivisors(int[] numbers) {
int currentMaxDivisors = 0;
int numWithMaxDivisors = numbers[0];
for (int i = 0; i < numbers.length; i++) {
int numDivisors = getNumDivisors(numbers[i]);
if (numDivisors > currentMaxDivisors) {
currentMaxDivisors = numDivisors; //ADD THIS LINE
numWithMaxDivisors = numbers[i];
}
}
return numWithMaxDivisors;
}
Input:
int[] numbers = {1,2,3,4,5};
System.out.println(getNumWithMaxDivisors(numbers));
Output:
4
Side Note: You could just as well start your for loop at i = 2 in your getNumDivisors() method, since every number is divisible by 1, so there is no point in checking it. This just saves you a bit of time!

add this line of code currentMaxDivisors = numDivisors; inside your if-statement like so:
static int getNumWithMaxDivisors(int[] numbers) {
int currentMaxDivisors = 0;
int numWithMaxDivisors = numbers[0];
for (int i = 0; i < numbers.length; i++) {
int numDivisors = getNumDivisors(numbers[i]);
if (numDivisors > currentMaxDivisors) {
currentMaxDivisors = numDivisors; //here this is missing
numWithMaxDivisors = numbers[i];
}
}
return numWithMaxDivisors;
}

Rolling hash: my codes fails with modulo for long string

I'm trying to solve https://leetcode.com/problems/longest-repeating-substring/
I want to use rolling hash to match strings.
However, my codes don't seem to work when I deal with modulo.
For a string with all same characters, the maximum length of repeating substring should be string.length - 1.
public class Main {
public static void main(String[] args) {
String str = "bbbbbbbbbbbbbbbbbbb";
System.out.println(str.length() - 1);
Solution s = new Solution();
System.out.println(s.longestRepeatingSubstring(str));
}
}
class Solution {
public int longestRepeatingSubstring(String S) {
HashSet<Long> h = new HashSet();
long mod = (long)1e7 + 7;
for(int i = S.length() - 1; i >0; i--){
h = new HashSet();
long c = 0;
int j = 0;
for(; j < i; j ++){
c = (c*26 % mod + S.charAt(j) - 'a')% mod;
}
h.add(c);
for(; j < S.length(); j++){
c -= (S.charAt(j - i ) - 'a') * Math.pow(26,i-1)% mod;
c = (c*26 % mod + S.charAt(j) - 'a')% mod;
if(h.contains(c)){
return i;
}
h.add(c);
}
}
return 0;
}
}
Playground for my codes: https://leetcode.com/playground/F4HkxbFQ

We cannot see your original link, we need a password.
The usage of modulo seems to be really complex.
Why not try something like this
class Scratch {
// "static void main" must be defined in a public class.
public static void main(String[] args) {
String str = "bbaaabbbbccbbbbbbzzzbbbbb";
System.out.println(str.length() - 1);
Solution s = new Solution();
System.out.println(s.longestRepeatingSubstring(str));
}
static class Solution {
public int longestRepeatingSubstring(String s) {
int max = -1;
int currentLength = 1;
char[] array = s.toCharArray();
for (int index = 1; index < array.length; index++) {
if (array[index - 1] == array[index]) {
currentLength++;
max = Math.max(max, currentLength);
} else {
currentLength = 1;
}
}
return max;
}
}
}

Numbers too big for variables

I am to find the last ten digits of 1^1 + 2^2 + 3^3.. + 1000^1000.
Is there any way to find this out with pure logic? I think you can't store a number that big.
This question is from a math competition, but I thought of trying to do this in Java.

You don't need to store number that big, you just need the last ten digits. You can store this in a long.
An efficient way to calculate large powers is to multiply and the squares e.g. 19^19 = 19 * 19^2 * 19 ^ 16 = 19 * 19 ^ 2 * 19^2^2^2^2. When you have value which is greater than 10^10 you can truncate the last 10 digits.
BTW the last ten digits of 1000^1000 is 0000000000 and when your add this to your sum, it's the same as adding zero ;)
Edit: While you don't have to use BigInteger, it is simpler to write.
BigInteger tenDigits = BigInteger.valueOf(10).pow(10);
BigInteger sum = BigInteger.ZERO;
for (int i= 1; i <= 1000; i++) {
BigInteger bi = BigInteger.valueOf(i);
sum = sum.add(bi.modPow(bi, tenDigits));
}
sum = sum.mod(tenDigits);
modPow is more efficient than pow with mod seperately as it doesn't have to calculate very large numbers, only the result of the mod.

You could use BigIntegers...
public static void main(String[] args) {
BigInteger acc = BigInteger.ZERO;
for (int k = 1; k <= 1000; k++) {
BigInteger pow = BigInteger.valueOf(k).pow(k);
acc = acc.add(pow);
}
System.out.println(acc);
}

I believe the problem comes from Project Euler, so it's not just a math problem; it should require some computation as well. I don't know how it could be solved with pencil and paper other than by duplicating the calculations a computer might make. I can't see much in the way of a purely mathematical solution. Mathematics can help us optimize the code, however.
To raise a^n, find the binary expansion of n:
n = n_k x 2^k + n_(k-1) x 2^(k-1) + ... + n_0 x 2^0
where n_i = 0 or 1 are the binary digits of n with the zeroth digit on the right. Then
a^n = a^(n_k x 2^k) x a^(n_(k-1) x 2^(k-1)) x ... x a^(n_0 x 2^0).
We can ignore any factors where n_i = 0, since the factor is then a^0 = 1. The process can be written as an algorithm which is O(log n) time and O(1) space (see below).
Next, as a challenge, in order to avoid the use of BigInteger, we can break the calculation into two parts: finding the answer mod 2^10 and finding the answer mod 5^10. In both cases the numbers in the relevant ranges and products of numbers in the relevant ranges fit into longs. The downside is that we have to use the Chinese Remainder Theorem to recombine the results, but it's not that hard, and it's instructive. The hardest part of using the Chinese Remainder Theorem is finding inverses mod m, but that can be accomplished in a straightforward manner using a modification of the Euclidean algorithm.
Asymptotic running time is O(n log n), space is O(1), and everything fits into a few long variables, no BigInteger or other sophisticated library required.
public class SeriesMod1010 {
public static long pow(long a,long n,long m) { // a^n mod m
long result = 1;
long a2i = a%m; // a^2^i for i = 0, ...
while (n>0) {
if (n%2 == 1) {
result *= a2i;
result %= m;
}
a2i *= a2i;
a2i %= m;
n /= 2;
}
return result;
}
public static long inverse(long a, long m) { // mult. inverse of a mod m
long r = m;
long nr = a;
long t = 0;
long nt = 1;
long tmp;
while (nr != 0) {
long q = r/nr;
tmp = nt; nt = t - q*nt; t = tmp;
tmp = nr; nr = r - q*nr; r = tmp;
}
if (r > 1) return -1; // no inverse
if (t < 0) t += m;
return t;
}
public static void main(String[] args) {
long twoTo10 = 1024;
long sum210 = 0;
for (long i=1; i<=1000; i++) {
sum210 += pow(i,i,twoTo10);
sum210 %= twoTo10;
}
long fiveTo10 = 9_765_625;
long sum510 = 0;
for (long i=1; i<=1000; i++) {
sum510 += pow(i,i,fiveTo10);
sum510 %= fiveTo10;
}
// recombine the numbers with the Chinese remainder theorem
long tenTo10 = 10_000_000_000L;
long answer = sum210 * inverse(fiveTo10,twoTo10) * fiveTo10
+ sum510 * inverse(twoTo10,fiveTo10) * twoTo10;
answer %= tenTo10;
System.out.println(answer);
}
}

use BigIntegers :
import java.math.BigInteger;
public class Program {
public static void main(String[] args) {
BigInteger result = new BigInteger("1");
BigInteger temp = new BigInteger("1");
BigInteger I;
for(int i = 1 ; i < 1001 ; i++){
I = new BigInteger(""+i);
for(int j = 1 ; j < i ; j++){
temp = temp.multiply(I);
}
result = result.multiply(temp);
temp = new BigInteger("1");
}
System.out.println(result);
}
}

It can be solved without BigInteger, because you need to store only 10 last digits on every addition or multiplication operation, using % to avoid overflow:
int n = 1000;
long result = 0;
long tenDigits = 10_000_000_000L;
for (int i = 1; i <= n; i++) {
long r = i;
for (int j = 2; j <= i; j++) {
r = (r * i) % tenDigits;
}
result += r;
}
return result % tenDigits;
Complexity is O(N^2), supposed that multiplication runs in constant time.
Answer: 9110846700.

The decimal base uses 0...9 (10 digits) to represent digits, a number that is in the second position right to left represents Digits * base.length^l2rPosition. Using this logics you can create a class that "pretty much does what your primary school teacher told you to, back when we used paper to calculate stuff, but with a baseN number and base-to-base conversions" I have done this class fully functional in C#, but I don't have time to translate it completely to java, this is about the same logics behind java.math.BigInteger. (with less performance I bet for I used a lot of lists >_>" No time to optimize it now
class IntEx {
ArrayList<Integer> digits = new ArrayList<>();
long baseSize = Integer.MAX_VALUE+1;
boolean negative = false;
public IntEx(int init)
{
set(init);
}
public void set(int number)
{
digits = new ArrayList<>();
int backup = number;
do
{
int index = (int)(backup % baseSize);
digits.add(index);
backup = (int) (backup / baseSize);
} while ((backup) > 0);
}
// ... other operations
private void add(IntEx number)
{
IntEx greater = number.digits.size() > digits.size() ? number : this;
IntEx lesser = number.digits.size() < digits.size() ? number : this;
int leftOvers = 0;
ArrayList<Integer> result = new ArrayList<>();
for (int i = 0; i < greater.digits.size() || leftOvers > 0; i++)
{
int sum;
if (i >= greater.digits.size())
sum = leftOvers;
else if(i >= lesser.digits.size())
sum = leftOvers + greater.digits.get(i);
else
sum = digits.get(i) + number.digits.get(i) + leftOvers;
leftOvers = 0;
if (sum > baseSize-1)
{
while (sum > baseSize-1)
{
sum -= baseSize;
leftOvers += 1;
}
result.add(sum);
}
else
{
result.add(sum);
leftOvers = 0;
}
}
digits = result;
}
private void multiply(IntEx target)
{
ArrayList<IntEx> MultiParts = new ArrayList<>();
for (int i = 0; i < digits.size(); i++)
{
IntEx thisPart = new IntEx(0);
thisPart.digits = new ArrayList<>();
for (int k = 0; k < i; k++)
thisPart.digits.add(0);
int Leftovers = 0;
for (int j = 0; j < target.digits.size(); j++)
{
int multiFragment = digits.get(i) * (int) target.digits.get(j) + Leftovers;
Leftovers = (int) (multiFragment / baseSize);
thisPart.digits.add((int)(multiFragment % baseSize));
}
while (Leftovers > 0)
{
thisPart.digits.add((int)(Leftovers % baseSize));
Leftovers = (int) (Leftovers / baseSize);
}
MultiParts.add(thisPart);
}
IntEx newNumber = new IntEx(0);
for (int i = 0; i < MultiParts.size(); i++)
{
newNumber.add(MultiParts.get(i));
}
digits = newNumber.digits;
}
public long longValue() throws Exception
{
int position = 0;
long multi = 1;
long retValue = 0;
if (digits.isEmpty()) return 0;
if (digits.size() > 16) throw new Exception("The number within IntEx class is too big to fit into a long");
do
{
retValue += digits.get(position) * multi;
multi *= baseSize;
position++;
} while (position < digits.size());
return retValue;
}
public static long BaseConvert(String number, String base)
{
boolean negative = number.startsWith("-");
number = number.replace("-", "");
ArrayList<Character> localDigits = new ArrayList<>();
for(int i = number.toCharArray().length - 1; i >=0; i--) {
localDigits.add(number.charAt(i));
}
// List<>().reverse is missing in this damn java. -_-
long retValue = 0;
long Multi = 1;
char[] CharsBase = base.toCharArray();
for (int i = 0; i < number.length(); i++)
{
int t = base.indexOf(localDigits.get(i));
retValue += base.indexOf(localDigits.get(i)) * Multi;
Multi *= base.length();
}
if (negative)
retValue = -retValue;
return retValue;
}
public static String BaseMult(String a, String b, String Base)
{
ArrayList<String> MultiParts = new ArrayList<>();
// this huge block is a tribute to java not having "Reverse()" method.
char[] x = new char[a.length()];
char[] y = new char[b.length()];
for(int i = 0; i < a.length(); i++) {
x[i] = a.charAt(a.length()-i);
}
for(int i = 0; i < b.length(); i++) {
y[i] = a.charAt(a.length()-i);
}
a = new String(x);
b = new String(y);
// ---------------------------------------------------------------------
for (int i = 0; i < a.length(); i++)
{
ArrayList<Character> thisPart = new ArrayList<>();
for (int k = 0; k < i; k++)
thisPart.add(Base.charAt(0));
int leftOvers = 0;
for (int j = 0; j < b.length(); j++)
{
// Need I say repeated characters in base may cause mayhem?
int MultiFragment = Base.indexOf(a.charAt(i)) * Base.indexOf(b.charAt(j)) + leftOvers;
leftOvers = MultiFragment / Base.length();
thisPart.add(Base.charAt(MultiFragment % Base.length()));
}
while (leftOvers > 0)
{
thisPart.add(Base.charAt(leftOvers % Base.length()));
leftOvers = leftOvers / Base.length();
}
char[] thisPartReverse = new char[thisPart.size()];
for(int z = 0; z < thisPart.size();z++)
thisPartReverse[z] = thisPart.get(thisPart.size()-z);
MultiParts.add(new String(thisPartReverse));
}
String retValue = ""+Base.charAt(0);
for (int i = 0; i < MultiParts.size(); i++)
{
retValue = BaseSum(retValue, MultiParts.get(i), Base);
}
return retValue;
}
public static String BaseSum(String a, String b, String Base)
{
// this huge block is a tribute to java not having "Reverse()" method.
char[] x = new char[a.length()];
char[] y = new char[b.length()];
for(int i = 0; i < a.length(); i++) {
x[i] = a.charAt(a.length()-i);
}
for(int i = 0; i < b.length(); i++) {
y[i] = a.charAt(a.length()-i);
}
a = new String(x);
b = new String(y);
// ---------------------------------------------------------------------
String greater = a.length() > b.length() ? a : b;
String lesser = a.length() < b.length() ? a : b;
int leftOvers = 0;
ArrayList<Character> result = new ArrayList();
for (int i = 0; i < greater.length() || leftOvers > 0; i++)
{
int sum;
if (i >= greater.length())
sum = leftOvers;
else if (i >= lesser.length())
sum = leftOvers + Base.indexOf(greater.charAt(i));
else
sum = Base.indexOf(a.charAt(i)) + Base.indexOf(b.charAt(i)) + leftOvers;
leftOvers = 0;
if (sum > Base.length()-1)
{
while (sum > Base.length()-1)
{
sum -= Base.length();
leftOvers += 1;
}
result.add(Base.charAt(sum));
}
else
{
result.add(Base.charAt(sum));
leftOvers = 0;
}
}
char[] reverseResult = new char[result.size()];
for(int i = 0; i < result.size(); i++)
reverseResult[i] = result.get(result.size() -i);
return new String(reverseResult);
}
public static String BaseConvertItoA(long number, String base)
{
ArrayList<Character> retValue = new ArrayList<>();
boolean negative = false;
long backup = number;
if (negative = (backup < 0))
backup = -backup;
do
{
int index = (int)(backup % base.length());
retValue.add(base.charAt(index));
backup = backup / base.length();
} while ((backup) > 0);
if (negative)
retValue.add('-');
char[] reverseRetVal = new char[retValue.size()];
for(int i = 0; i < retValue.size(); i++)
reverseRetVal[i] = retValue.get(retValue.size()-i);
return new String(reverseRetVal);
}
public String ToString(String base)
{
if(base == null || base.length() < 2)
base = "0123456789";
ArrayList<Character> retVal = new ArrayList<>();
char[] CharsBase = base.toCharArray();
int TamanhoBase = base.length();
String result = ""+base.charAt(0);
String multi = ""+base.charAt(1);
String lbase = IntEx.BaseConvertItoA(baseSize, base);
for (int i = 0; i < digits.size(); i++)
{
String ThisByte = IntEx.BaseConvertItoA(digits.get(i), base);
String Next = IntEx.BaseMult(ThisByte, multi, base);
result = IntEx.BaseSum(result, Next, base);
multi = IntEx.BaseMult(multi, lbase, base);
}
return result;
}
public static void main(String... args) {
int ref = 0;
IntEx result = new IntEx(0);
while(++ref <= 1000)
{
IntEx mul = new IntEx(1000);
for (int i = 0; i < 1000; ++i) {
mul.multiply(new IntEx(i));
}
result.add(mul);
}
System.out.println(result.toString());
}
}
Disclaimer: This is a rough translation/localization from a C# study, there are lots of code omitted. This is "almost" the same logics behind java.math.BigInteger (you can open BigInteger code on your favorite designer and check for yourself. If may I be forgetting a overloaded operator behind not translated to java, have a bit of patience and forgiveness, this example is just for a "maybe" clarification of the theory.
Also, just a sidenote, I know it is "Trying to reinvent the wheel", but considering this question has academic purpose I think its fairly rasonable to share.
One can see the result of this study on gitHub (not localized though), I'm not expanding that C# code here for its very extensive and not the language of this question.

This gives the correct answer without excess calculations. A Long is sufficient.
public String lastTen() {
long answer = 0;
String txtAnswer = "";
int length = 0;
int i = 1;
for(i = 1; i <= 1000; i++) {
answer += Math.pow(i, i);
txtAnswer = Long.toString(answer);
length = txtAnswer.length();
if(length > 9) break;
}
return txtAnswer.substring(length-10);
}

Algorithm to calculate Fibonacci sequence implemented in Java gives weird result

When I run Countdown.class I get the following output:
263845041
-1236909152
-973064111
2084994033
1111929922
-1098043341
13886581
-1084156760
-1070270179
2140540357
Blast Off!
The numbers before "Blast Off!" ought to be the first 10 Fibonacci numbers. My source code is as follows.
public class Fibonacci {
public static long fib(int n) {
if (n <= 1) return 1;
return fib(n-1) + fib(n-2);
}
public static long fastfib(int n) {
int a = 0;
int b = 1;
int c = 0;
for (int i = 0; i <= n; n++) {
c = a + b;
a = b;
b = c;
}
return c;
}
}
and the class that implements the fastfib method is:
public class Countdown {
public static void countdown(int n) {
if (n == 0) System.out.println("Blast Off!");
else {
System.out.println(Fibonacci.fastfib(n));
countdown(n - 1);
}
}
public static void main(String[] args) {
countdown(10);
}
}

Though your fastfib() method returns long, the calculations are done on ints.
You are encountering integer overflow.
Make sure to declare a,b,c as longs and NOT as ints. If you want even larger numbers (that are out of range for longs as well) - you might want to have a look on BigInteger (and use it).
EDIT: As mentioned by #ExtremeCoders in comment, there is another issue in the code in your for loop:
for (int i = 0; i <= n; n++) should be for (int i = 0; i <= n; i++), you want to increase i - not n.

In addition to the other answers,
for (int i = 0; i <= n; n++) {
should be
for (int i = 0; i <= n; i++) {
// ^ that's an i

Change the datatypes of a,b and c to long, and it will start working fine. Your numbers are crossing the limits for int.

You should user BigInteger insted of long
import java.math.BigInteger;
public class Fibonacci {
public static BigInteger fib(BigInteger n) {
int result = n.compareTo(BigInteger.valueOf(1)); // returns -1, 0 or 1 as this BigInteger is numerically less than, equal to, or greater than val.
if (result != 1) return BigInteger.valueOf(1);
return fib(
n.subtract(
BigInteger.valueOf(1).add
(n.subtract
(
BigInteger.valueOf(-2)
)
)
)
);
}
public static BigInteger fastfib(int n) {
BigInteger a = BigInteger.valueOf(0);
BigInteger b = BigInteger.valueOf(1);
BigInteger c = BigInteger.valueOf(0);
for (int i = 1; i < n; i++) {
c = a.add(b);
a = b;
b = c;
}
return c;
}
}