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BigNumber.java
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BigNumber.java
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package com.ap.project.number;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Random;
public class BigNumber {
private static final BigNumber ZERO = new BigNumber(0);
private static final BigNumber ONE = new BigNumber(1);
private static final BigNumber TWO = new BigNumber(2);
private static final BigNumber THREE = new BigNumber(3);
private static final BigNumber FOUR = new BigNumber(4);
private static final BigNumber FIVE = new BigNumber(5);
private static final BigNumber SIX = new BigNumber(6);
private static final BigNumber SEVEN = new BigNumber(7);
private static final BigNumber EIGHT = new BigNumber(8);
private static final BigNumber NINE = new BigNumber(9);
private final byte[] digits;
private boolean sign; //true means negative, false means positive
public BigNumber(String str) {
str = clean(str); //Removing Spaces and leading zeros
//Validation -> Only numbers are allowed
for(int i = 0; i < str.length(); i++) {
if(i == 0 && str.charAt(i) == '-') { continue; } //If the number is negative it can have a - character
if(str.charAt(i) < '0' || str.charAt(i) > '9') {
throw new IllegalArgumentException(" Input not allowed " + str);
}
}
//Detect the sign of the number
if(str.charAt(0) == '-') {
sign = true;
digits = new byte[str.length() - 1]; //We dont include - character in the digits array so we dont need space for it
int i = 0; //Index of the digits array
for(int digitIndex = 0; digitIndex < digits.length; digitIndex++) {
if(digitIndex == str.length() - 1) { continue; } //Skip the '-' character
int ch = (str.charAt(str.length() - digitIndex - 1) - 48); //Store the digits in reverse order in digits array
digits[i++] = (byte) ch;
}
} else {
digits = new byte[str.length()];
for(int digitIndex = 0; digitIndex < digits.length; digitIndex++) {
int ch = (str.charAt(str.length() - digitIndex - 1) - 48);
digits[digitIndex] = (byte) ch;
}
}
}
public BigNumber(long longNumber) {
this(Long.toString(longNumber));
}
public BigNumber(){
this(0);
}
public static BigNumber fromLong(long longNumber) {
return new BigNumber(longNumber);
}
public static BigNumber fromString(String stringNumber) {
return new BigNumber(stringNumber);
}
//To clean spaces before and after number & clean leading zeros
public static String clean(String str) {
//To remove spaces from before and after of the input number
str = str.trim();
//If all characters are spaces throw an exception
if(str.length() == 0) { throw new IllegalArgumentException(" No numbers entered"); }
//Return 0 if user entered only zeros
int zeroCount = 0;
for(int i = 0; i < str.length(); i++) {
if(str.charAt(i) == '0') { zeroCount++; }
}
if(zeroCount == str.length()) { return "0"; }
StringBuilder digits = new StringBuilder(str.length());
boolean isLeadingZero = true;
//Removing leading zeros
for(int i = 0; i < str.length(); i++) {
if(str.charAt(i) != '0') {
isLeadingZero = false;
}
if(isLeadingZero) {
continue;
}
digits.append(str.charAt(i));
}
return digits.toString();
}
//The returned string includes - character if it is a negative number
public String toString() {
StringBuilder strBuilder = new StringBuilder(digits.length);
for(byte digit : digits) {
strBuilder.append(digit);
}
//If the number is negative we need a - before number
if(sign) {
strBuilder.append('-');
}
return strBuilder.reverse().toString();
}
//The returned string does not contain - character even if the number is negative
private String toStringWithoutDash() {
StringBuilder strBuilder = new StringBuilder(digits.length);
for(byte digit : digits) {
strBuilder.append(digit);
}
return strBuilder.reverse().toString();
}
public int length() {
return digits.length;
}
public boolean equals(Object object) {
if(this == object) { return true; }
if(object == null || getClass() != object.getClass()) { return false; }
BigNumber number = (BigNumber) object;
//if sign of the numbers are not same, numbers are not same
if(sign != number.sign) { return false; }
return Arrays.equals(digits, number.digits);
}
//This method includes sign of the numbers as well
public boolean isGreaterThan(BigNumber secondNumber) {
if(sign && secondNumber.sign) {
if(length() > secondNumber.length()) { return false; }
if(length() < secondNumber.length()) { return true; }
for(int i = digits.length - 1; i >= 0; i--) {
if(digits[i] > secondNumber.digits[i]) { return false; }
if(digits[i] < secondNumber.digits[i]) { return true; }
}
}
if(sign && !secondNumber.sign) {
return false;
}
if(!sign && secondNumber.sign) {
return true;
}
if(!sign) {
return isGreaterThanWithoutSign(secondNumber);
}
return false;
}
//This method does not consider sign of the numbers
public boolean isGreaterThanWithoutSign(BigNumber secondNumber) {
if(length() > secondNumber.length()) { return true; }
if(length() < secondNumber.length()) { return false; }
for(int i = digits.length - 1; i >= 0; i--) {
if(digits[i] > secondNumber.digits[i]) { return true; }
if(digits[i] < secondNumber.digits[i]) { return false; }
}
return false;
}
//Compare two StringBuilder values. 1 if greater, -1 if smaller, 0 if equal
private static int compareStringBuilder(StringBuilder str1, StringBuilder str2) {
String str3 = str1.toString();
String str4 = str2.toString();
//Clean spaces and leading zeros
str3 = clean(str3);
str4 = clean(str4);
//Delete all characters from str1 & str2
str1.delete(0, str1.length());
str2.delete(0, str2.length());
//Append clean strings to empty str1 & str2
str1.append(str3);
str2.append(str4);
//Compare str1 & str2
if(str1.length() > str2.length()) { return 1; }
if(str2.length() > str1.length()) { return -1; }
for(int i = 0; i < str1.length(); i++) {
if(str1.charAt(i) > str2.charAt(i)) { return 1; }
if(str2.charAt(i) > str1.charAt(i)) { return -1; }
}
return 0; //If the strings are equal
}
private boolean compareArray(byte[] a, byte[] b) {
if(a.length > b.length) { return true; }
if(a.length < b.length) { return false; }
for(int i = a.length - 1; i >= 0; i--) {
if(a[i] > b[i]) { return true; }
if(a[i] < b[i]) { return false; }
}
return true;
}
private static BigNumber random(int length) {
Random rnd = new Random();
StringBuilder randomNumber = new StringBuilder();
int[] odds = {1, 3, 7, 9}; //The random number must not be an even number and must not be divisible by 5
int digitSum = 0;
int randomDigit;
for (int i = 1; i <= length; i++) {
randomDigit = rnd.nextInt(10);
//The most significant digit cant be 0
if (i == 1) {
randomDigit = rnd.nextInt(9) + 1;
}
//The least significant digit must be one of odds arrays elements
if (i == length) {
randomDigit = odds[rnd.nextInt(4)];
}
digitSum = digitSum + randomDigit;
randomNumber.append(randomDigit);
}
StringBuilder tempRandom1 = new StringBuilder();
tempRandom1.append(randomNumber);
StringBuilder tempRandom2 = new StringBuilder();
tempRandom2.append(randomNumber);
StringBuilder tempRandom3 = new StringBuilder();
tempRandom3.append(randomNumber);
StringBuilder tempRandom4 = new StringBuilder();
tempRandom4.append(randomNumber);
//Random number must not be divisible to 3, 7, 13, 17, 19
if (digitSum % 3 == 0) { random(length); }
if((fromString(tempRandom1.delete(randomNumber.length() - 1, randomNumber.length()).toString()).subtract(fromLong(2 * (randomNumber.charAt(randomNumber.length() - 1) - 48))).mod(SEVEN).equals(ZERO))) { random(length); }
if((fromString(tempRandom2.delete(randomNumber.length() - 1, randomNumber.length()).toString()).add(fromLong(4 * (randomNumber.charAt(randomNumber.length() - 1) - 48))).mod(fromLong(13)).equals(ZERO))) { random(length); }
if((fromString(tempRandom3.delete(randomNumber.length() - 1, randomNumber.length()).toString()).subtract(fromLong(5 * (randomNumber.charAt(randomNumber.length() - 1) - 48))).mod(fromLong(17)).equals(ZERO))) { random(length); }
if((fromString(tempRandom4.delete(randomNumber.length() - 1, randomNumber.length()).toString()).add(fromLong(2 * (randomNumber.charAt(randomNumber.length() - 1) - 48))).mod(fromLong(19)).equals(ZERO))) { random(length); }
return fromString(randomNumber.toString());
}
//Listing all prime numbers less than square root of the given number
private ArrayList<BigNumber> sieve(BigNumber number) {
int squareRootOfNumber = (int) Math.sqrt(Long.parseLong(number.toString()));
boolean[] isNotPrime = new boolean[squareRootOfNumber + 1];
ArrayList<BigNumber> primeNumbers = new ArrayList<>();
for(int i = 2; i <= squareRootOfNumber; i++) {
if(!isNotPrime[i]) {
for(int j = i * i; j <= squareRootOfNumber; j += i) {
isNotPrime[j] = true;
}
}
}
for(int i = 2; i <= squareRootOfNumber; i++) {
if(!isNotPrime[i]) {
primeNumbers.add(new BigNumber(i));
}
}
return primeNumbers;
}
public ArrayList<BigNumber> primeFactorization() {
//Validation -> only numbers with 9 digits are supported
if(this.length() > 9) {
throw new IllegalArgumentException(" Only 9 digits are supported for prime factorization");
}
ArrayList<BigNumber> primeFactors = new ArrayList<>();
ArrayList<BigNumber> primeNumbers = sieve(this);
BigNumber number = new BigNumber(this.toStringWithoutDash());
for(BigNumber primeNumber : primeNumbers) {
if(primeNumber.isGreaterThan(number)) {
break;
}
while(number.mod(primeNumber).equals(ZERO)) {
primeFactors.add(primeNumber);
number = number.divide(primeNumber);
}
}
if(number.isGreaterThan(ONE)) {
primeFactors.add(number);
}
return primeFactors;
}
public BigNumber add(BigNumber secondNumber) {
StringBuilder strBuilder = new StringBuilder();
if(sign && !secondNumber.sign) {
sign = false;
BigNumber result = new BigNumber(secondNumber.subtract(this).toString());
sign = true;
return result;
}
if(!sign && secondNumber.sign) {
secondNumber.sign = false;
BigNumber result = new BigNumber(this.subtract(secondNumber).toString());
secondNumber.sign = true;
return result;
}
if(sign) {
simpleAdder(secondNumber, strBuilder);
strBuilder.append('-');
return fromString(strBuilder.reverse().toString());
}
simpleAdder(secondNumber, strBuilder);
return BigNumber.fromString(strBuilder.reverse().toString());
}
private void simpleAdder(BigNumber secondNumber, StringBuilder strBuilder) {
int carrier = 0;
for(int i = 0; i < Math.max(length(), secondNumber.length()); i++) {
byte firstNumberDigit = i < length() ? digits[i] : 0;
byte secondNumberDigit = i < secondNumber.length() ? secondNumber.digits[i] : 0;
byte digitSum = (byte) (firstNumberDigit + secondNumberDigit + carrier);
strBuilder.append(digitSum % 10);
carrier = digitSum / 10;
}
if(carrier > 0) {
strBuilder.append(carrier);
}
}
public BigNumber subtract(BigNumber secondNumber) {
StringBuilder strBuilder = new StringBuilder();
if(!sign && !secondNumber.sign) {
if(!compareArray(digits, secondNumber.digits)) {
String result = '-' + secondNumber.subtract(this).toString();
return fromString(result);
} else {
return simpleSubtract(secondNumber, strBuilder);
}
}
if(sign && !secondNumber.sign) {
simpleAdder(secondNumber, strBuilder);
strBuilder.append('-');
return fromString(strBuilder.reverse().toString());
}
if(sign) {
if(compareArray(digits, secondNumber.digits)) {
String a = '-' + simpleSubtract(secondNumber, strBuilder).toString();
return fromString(a);
} else {
return secondNumber.simpleSubtract(this, strBuilder);
}
}
simpleAdder(secondNumber, strBuilder);
return fromString(strBuilder.reverse().toString());
}
private BigNumber simpleSubtract(BigNumber secondNumber, StringBuilder strBuilder) {
BigNumber tempFirstNumber = new BigNumber(this.toString());
for(int i = 0; i < Math.max(tempFirstNumber.length(), secondNumber.length()); i++) {
byte firstNumberDigit = i < tempFirstNumber.length() ? tempFirstNumber.digits[i] : 0;
byte secondNumberDigit = i < secondNumber.length() ? secondNumber.digits[i] : 0;
byte digitSubtract;
if(firstNumberDigit >= secondNumberDigit) {
digitSubtract = (byte) (firstNumberDigit - secondNumberDigit);
strBuilder.append(digitSubtract);
}
if(firstNumberDigit < secondNumberDigit) {
firstNumberDigit += 10;
tempFirstNumber.digits[i + 1]--;
digitSubtract = (byte) (firstNumberDigit - secondNumberDigit);
strBuilder.append(digitSubtract);
}
}
return fromString(strBuilder.reverse().toString());
}
public BigNumber multiply(BigNumber secondNumber) {
StringBuilder firstNumberStr = new StringBuilder();
StringBuilder secondNumberStr = new StringBuilder();
if(sign) {
firstNumberStr.append(this.toStringWithoutDash());
} else {
firstNumberStr.append(this.toString());
}
if(secondNumber.sign) {
secondNumberStr.append(secondNumber.toStringWithoutDash());
} else {
secondNumberStr.append(secondNumber.toString());
}
int firstNumberLength = firstNumberStr.length();
int secondNumberLength = secondNumberStr.length();
int[] result = new int[firstNumberLength + secondNumberLength];
int firstNumberIndex = 0;
int secondNumberIndex;
for(int digit1 = firstNumberLength - 1; digit1 >= 0; digit1--) {
int carry = 0;
int firstNumberDigit = firstNumberStr.charAt(digit1) - '0';
secondNumberIndex = 0;
for(int digit2 = secondNumberLength - 1; digit2 >= 0; digit2--) {
int secondNumberDigit = secondNumberStr.charAt(digit2) - '0';
int sum = (firstNumberDigit * secondNumberDigit) + result[firstNumberIndex + secondNumberIndex] + carry;
carry = sum / 10;
result[firstNumberIndex + secondNumberIndex] = sum % 10;
secondNumberIndex++;
}
if(carry > 0) {
result[firstNumberIndex + secondNumberIndex] += carry;
}
firstNumberIndex++;
}
int i = result.length - 1;
while(i >= 0 && result[i] == 0) {
i--;
}
if(i == -1) { return ZERO; } //If there was only zeroes
StringBuilder resultString = new StringBuilder();
if((sign && !secondNumber.sign) || !sign && secondNumber.sign)
resultString.append('-');
while(i >= 0) {
resultString.append(result[i]);
i--;
}
return fromString(resultString.toString());
}
public BigNumber divide(BigNumber secondNumber) {
String result;
if(sign && !secondNumber.sign) {
BigNumber positiveFirstNumber = new BigNumber(this.toStringWithoutDash());
if(secondNumber.isGreaterThan(positiveFirstNumber)) {
return BigNumber.ZERO;
}
result = '-' + positiveFirstNumber.simpleDivide(secondNumber).toString();
return fromString(result);
}
if(!sign && secondNumber.sign) {
BigNumber positiveSecondNumber = new BigNumber(secondNumber.toStringWithoutDash());
if(positiveSecondNumber.isGreaterThan(this))
return BigNumber.ZERO;
result = '-' + this.simpleDivide(positiveSecondNumber).toString();
return fromString(result);
}
if(sign) {
BigNumber positiveFirstNumber = new BigNumber(this.toStringWithoutDash());
BigNumber positiveSecondNumber = new BigNumber(secondNumber.toStringWithoutDash());
if(positiveSecondNumber.isGreaterThan(positiveFirstNumber))
return BigNumber.ZERO;
result = positiveFirstNumber.simpleDivide(positiveSecondNumber).toString();
return fromString(result);
}
return this.simpleDivide(secondNumber);
}
private BigNumber simpleDivide(BigNumber secondNumber) {
//Validation -> If second number is 0, the division is meaningless
if(secondNumber.equals(ZERO)) {
throw new ArithmeticException(" Second operand is 0");
}
//If second number is larger than first number, result of division is 0
if(secondNumber.isGreaterThan(this)) {
return ZERO;
}
String firstNumberStr = this.toString();
String secondNumberStr = secondNumber.toString();
StringBuilder secondNumberStrBuilder = new StringBuilder(secondNumber.toString());
StringBuilder portionStr;
int index; //Index of digits from first number which have been participated in multiplication
//Pick exact portion of second number from first number from left
//if the portion is still smaller than second number, pick one more digit
if(firstNumberStr.substring(0, secondNumber.length()).compareTo(secondNumberStr) >= 0) {
portionStr = new StringBuilder(firstNumberStr.substring(0, secondNumber.length()));
index = secondNumber.length() - 1;
} else {
portionStr = new StringBuilder(firstNumberStr.substring(0, secondNumber.length() + 1));
index = secondNumber.length();
}
//Make temporary big number from picked portion
BigNumber portionBigNumber = new BigNumber(portionStr.toString());
StringBuilder result = new StringBuilder();
while(index < firstNumberStr.length()) {
int i = 1;
BigNumber multiplier;
while(i <= 9) {
multiplier = new BigNumber(i);
if(secondNumber.multiply(multiplier).isGreaterThan(portionBigNumber)) {
result.append(--i);
break;
}
i++;
}
if(i == 10) {
multiplier = new BigNumber(--i);
result.append(i);
} else {
multiplier = new BigNumber(i);
}
portionStr.delete(0, index + 1);
portionStr.append((portionBigNumber.subtract(secondNumber.multiply(multiplier))).toString());
if(index < firstNumberStr.length() - 1) {
portionStr.append(firstNumberStr.charAt(index + 1));
index++;
} else { index++; }
while(compareStringBuilder(portionStr, secondNumberStrBuilder) < 0 && index < firstNumberStr.length() - 1) {
portionStr.append(firstNumberStr.charAt(index + 1));
result.append(0);
index++;
}
portionBigNumber = new BigNumber(portionStr.toString());
}
return fromString(result.toString());
}
public BigNumber mod(BigNumber secondNumber) {
return this.subtract(this.divide(secondNumber).multiply(secondNumber));
}
public BigNumber pow(BigNumber secondNumber) {
//Validation -> If exponent is negative throw exception
if(secondNumber.sign) {
throw new IllegalArgumentException(" Exponent can't be negative");
}
BigNumber tempSecondNumber = new BigNumber(secondNumber.toString());
BigNumber result = new BigNumber(1);
while(tempSecondNumber.isGreaterThanWithoutSign(BigNumber.ZERO)) {
result = result.multiply(this);
tempSecondNumber = tempSecondNumber.subtract(BigNumber.ONE);
}
return result;
}
public boolean isEven() {
return this.mod(TWO).equals(ZERO);
}
public boolean isPrime(int accuracy) {
if(!this.isGreaterThan(ONE)) {
return false;
}
if(this.equals(TWO)) {
return true;
}
if(this.mod(TWO).equals(ZERO)) {
return false;
}
BigNumber numberMinusOne = this.subtract(ONE);
while(numberMinusOne.isEven()) {
numberMinusOne = numberMinusOne.divide(TWO);
}
for(int i = 0; i < accuracy; i++) {
if(!rabinMiller(numberMinusOne, this)) {
return false;
}
}
return true;
}
private static boolean rabinMiller(BigNumber d, BigNumber number) {
BigNumber numberMinusOne = number.subtract(ONE);
Random rnd = new Random();
BigNumber randomLongNumber = new BigNumber(Math.abs(rnd.nextLong()));
BigNumber randomNumberInRange = randomLongNumber.mod(number.subtract(FOUR)).add(TWO); //Random number must be in range of (2, number - 2)
BigNumber modPowResult = modPow(randomNumberInRange, d, number); //(randomNumberInRange ^ d) % number
if(modPowResult.equals(ONE) || modPowResult.equals(numberMinusOne)) {
return true;
}
while(!d.equals(numberMinusOne)) {
modPowResult = modPowResult.multiply(modPowResult).mod(number);
d = d.multiply(TWO);
if(modPowResult.equals(ONE)) {
return false;
}
if(modPowResult.equals(numberMinusOne)) {
return true;
}
}
return false;
}
private static BigNumber modPow(BigNumber base, BigNumber exponent, BigNumber number) {
BigNumber result = ONE;
base = base.mod(number);
while(exponent.isGreaterThan(ZERO)) {
if(!exponent.isEven()) {
result = (result.multiply(base)).mod(number);
}
exponent = exponent.divide(TWO);
base = (base.multiply(base)).mod(number);
}
return result;
}
public static BigNumber primeGenerator(int length) {
while(true) {
BigNumber randomNumber = random(length);
if(randomNumber.isPrime(10)) {
return randomNumber;
}
}
}
}