Trouble with Prime connection - java

The problem below was given in one of my exams and was asked to solve the following problem using Java only.
The problem is, I got stuck in the part where the program is supposed to return the given non-negative integer as an array of digits. Can anyone provide a solution to this?
Thanks in advance.
Two positive numbers A and B are said to be connected (denoted by "A ↔ B") if one of these conditions holds:
(1) A and B have the same length and differ in exactly one digit; for example, 123 ↔ 173.
(2) Adding one digit to the left of A (or B) makes B (or A); for example, 23 ↔ 223 and 123 ↔ 23.
We call a prime P a 2's relative if there exists a chain of connected primes between 2 and P and no prime in the chain exceeds P.
For example, 127 is a 2's relative. One of the possible chains is shown below:
2 ↔ 3 ↔ 13 ↔ 113 ↔ 103 ↔ 107 ↔ 127
However, 11 and 103 are not 2's relatives.
Let F(N) be the sum of the primes ≤ N which are not 2's relatives.
We can verify that F(103) = 431 and F(104) = 78728.
Find F(107).
Edited: my part
I am sorry I don't carbon copy remember my solution as I don't have my results given to me. But just for the sake of this question, I think the part where it was supposed to return non-negative number, I had something like this -
private static int[] toDigits(int n) {
if (n < 0)
throw new IllegalArgumentException();
int[] temp = new int[10];
int len = 0;
do {
temp[len] = n % 9;
n /= 9;
len++;
} while (n > 0);

import java.util.Arrays;
import java.util.PriorityQueue;
import java.util.Queue;
public final class infinitybyone implements TestSolution {
public static void main(String[] args) {
System.out.println(new infinitybyone().run());
}
private static final int LIMIT = Library.pow(10, 7);
public String run() {
boolean[] isPrime = Library.listPrimality(LIMIT);
int[] pathMax = new int[isPrime.length];
Arrays.fill(pathMax, Integer.MAX_VALUE);
Queue<IntPair> queue = new PriorityQueue<>();
queue.add(new IntPair(2, 2));
while (!queue.isEmpty()) {
IntPair item = queue.remove();
int n = item.b;
int pmax = item.a;
if (pmax >= pathMax[n]) {
continue;
}
pathMax[n] = pmax;
int[] digits = toDigits(n);
int[] tempDigits = digits.clone();
for (int i = 0; i < tempDigits.length; i++) {
for (int j = 0; j < 10; j++) {
tempDigits[i] = j;
int m = toNumber(tempDigits);
int nextPmax = Math.max(m, pmax);
if (m < isPrime.length && isPrime[m] && nextPmax < pathMax[m])
queue.add(new IntPair(nextPmax, m));
}
tempDigits[i] = digits[i];
}
}
long sum = 0;
for (int i = 0; i < isPrime.length; i++) {
if (isPrime[i] && pathMax[i] > i)
sum += i;
}
return Long.toString(sum);
}
private static int[] toDigits(int n) {
if (n < 0)
throw new IllegalArgumentException();
//************This is PROBABLY where you made the error************
int[] temp = new int[11];
int len = 0;
do {
temp[len] = n % 10;
n /= 10;
len++;
} while (n > 0);
int[] result = new int[len + 1];
for (int i = 0; i < result.length; i++)
result[i] = temp[len - i];
return result;
}
private static int toNumber(int[] digits) {
int result = 0;
for (int x : digits)
result = result * 10 + x;
return result;
}
private static class IntPair implements Comparable<IntPair> {
public final int a;
public final int b;
public IntPair(int a, int b) {
this.a = a;
this.b = b;
}
public int compareTo(IntPair other) {
return Integer.compare(a, other.a);
}
}
}
I can't really tell where you messed up but at least from the code you shared, tell me why would you use 10 instead of 11? It should extract base-10 in little endian.

Related

find prime numbers within 1 to N that are mirror to each other

I encountered a problem that I need to find the mirror of the prime numbers within the range of 1 to N. A mirror is like 13 and 31, 17 and 71, etc. I write the solution provided below,
/*
* find prime numbers within 1 to N that is a mirror to each other
*/
public static List<Integer> solution(int N) {
List<Integer> primes = findPrimes(N);
Set<Integer> set = new LinkedHashSet<>();
for (int i = 0; i < primes.size(); i++) {
int prime = primes.get(i);
int mirror = hasMirror(prime, primes);
if (mirror == 0) {
continue;
}
set.add(prime);
set.add(mirror);
}
return new ArrayList<>(set);
}
/*
* find the mirror of a number
* */
private static int findMirror(int P) {
int R = 0;
while (P != 0) {
int D = P % 10;
R = R * 10 + D;
P /= 10;
}
return R;
}
private static int hasMirror(int P, List<Integer> B) {
Integer[] A = B.toArray(new Integer[0]);
int N = A.length;
int R = findMirror(P);
for (int i = N - 1; i >= 0; i--) {
if (A[i] == R) {
return R;
}
}
return 0;
}
public static List<Integer> findPrimes(int N) {
int[] F = new int[N + 1];
List<Integer> result = new ArrayList<>();
for (int i = 2; i <= N; i++) {
if (F[i] == 0) {
// the prime value need to be 2 digit for the mirror image
if (i < 10 || i == findMirror(i)) {
continue;
}
result.add(i);
for (int k = i * i; k <= N; k += i) {
if (F[k] == 0) {
F[k] = 1;
}
}
}
}
return result;
}
}
The solution works, but, is there an option to improve the performance?
One thing you can do to improve performance is, not invoking the hasMirror() for already identified mirrors.
For example, let's say you checked 17 and identified that it has a mirror 71. Then when you reach 71 later on your loop, you can skip checking its mirrors as you have already identified it.
List<Integer> primes = findPrimes(N);
Set<Integer> set = new LinkedHashSet<>();
for (int i = 0; i < primes.size(); i++) {
int prime = primes.get(i);
if (!set.contains(prime)) {
int mirror = hasMirror(prime, primes);
if (mirror == 0) {
continue;
}
set.add(prime);
set.add(mirror);
}
}

Calculate factorial of 50 using array only in java

I'm a total beginner of java.
I have a homework to write a complete program that calculates the factorial of 50 using array.
I can't use any method like biginteger.
I can only use array because my professor wants us to understand the logic behind, I guess...
However, he didn't really teach us the detail of array, so I'm really confused here.
Basically, I'm trying to divide the big number and put it into array slot. So if the first array gets 235, I can divide it and extract the number and put it into one array slot. Then, put the remain next array slot. And repeat the process until I get the result (which is factorial of 50, and it's a huge number..)
I tried to understand what's the logic behind, but I really can't figure it out.. So far I have this on my mind.
import java.util.Scanner;
class Factorial
{
public static void main(String[] args)
{
int n;
Scanner kb = new Scanner(System.in);
System.out.println("Enter n");
n = kb.nextInt();
System.out.println(n +"! = " + fact(n));
}
public static int fact(int n)
{
int product = 1;
int[] a = new int[100];
a[0] = 1;
for (int j = 2; j < a.length; j++)
{
for(; n >= 1; n--)
{
product = product * n;
a[j-1] = n;
a[j] = a[j]/10;
a[j+1] = a[j]%10;
}
}
return product;
}
}
But it doesn't show me the factorial of 50.
it shows me 0 as the result, so apparently, it's not working.
I'm trying to use one method (fact()), but I'm not sure that's the right way to do.
My professor mentioned about using operator / and % to assign the number to the next slot of array repeatedly.
So I'm trying to use that for this homework.
Does anyone have an idea for this homework?
Please help me!
And sorry for the confusing instruction... I'm confused also, so please forgive me.
FYI: factorial of 50 is 30414093201713378043612608166064768844377641568960512000000000000
Try this.
static int[] fact(int n) {
int[] r = new int[100];
r[0] = 1;
for (int i = 1; i <= n; ++i) {
int carry = 0;
for (int j = 0; j < r.length; ++j) {
int x = r[j] * i + carry;
r[j] = x % 10;
carry = x / 10;
}
}
return r;
}
and
int[] result = fact(50);
int i = result.length - 1;
while (i > 0 && result[i] == 0)
--i;
while (i >= 0)
System.out.print(result[i--]);
System.out.println();
// -> 30414093201713378043612608166064768844377641568960512000000000000
Her's my result:
50 factorial - 30414093201713378043612608166064768844377641568960512000000000000
And here's the code. I hard coded an array of 100 digits. When printing, I skip the leading zeroes.
public class FactorialArray {
public static void main(String[] args) {
int n = 50;
System.out.print(n + " factorial - ");
int[] result = factorial(n);
boolean firstDigit = false;
for (int digit : result) {
if (digit > 0) {
firstDigit = true;
}
if (firstDigit) {
System.out.print(digit);
}
}
System.out.println();
}
private static int[] factorial(int n) {
int[] r = new int[100];
r[r.length - 1] = 1;
for (int i = 1; i <= n; i++) {
int carry = 0;
for (int j = r.length - 1; j >= 0; j--) {
int x = r[j] * i + carry;
r[j] = x % 10;
carry = x / 10;
}
}
return r;
}
}
How about:
public static BigInteger p(int numOfAllPerson) {
if (numOfAllPerson < 0) {
throw new IllegalArgumentException();
}
if (numOfAllPerson == 0) {
return BigInteger.ONE;
}
BigInteger retBigInt = BigInteger.ONE;
for (; numOfAllPerson > 0; numOfAllPerson--) {
retBigInt = retBigInt.multiply(BigInteger.valueOf(numOfAllPerson));
}
return retBigInt;
}
Please recall basic level of math how multiplication works?
2344
X 34
= (2344*4)*10^0 + (2344*3)*10^1 = ans
2344
X334
= (2344*4)*10^0 + (2344*3)*10^1 + (2344*3)*10^2= ans
So for m digits X n digits you need n list of string array.
Each time you multiply each digits with m. and store it.
After each step you will append 0,1,2,n-1 trailing zero(s) to that string.
Finally, sum all of n listed string. You know how to do that.
So up to this you know m*n
now it is very easy to compute 1*..........*49*50.
how about:
int[] arrayOfFifty = new int[50];
//populate the array with 1 to 50
for(int i = 1; i < 51; i++){
arrayOfFifty[i-1] = i;
}
//perform the factorial
long result = 1;
for(int i = 0; i < arrayOfFifty.length; i++){
result = arrayOfFifty[i] * result;
}
Did not test this. No idea how big the number is and if it would cause error due to the size of the number.
Updated. arrays use ".length" to measure the size.
I now updated result to long data type and it returns the following - which is obviously incorrect. This is a massive number and I'm not sure what your professor is trying to get at.
-3258495067890909184

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;
}
}

Radix sort in java help

Hi i need some help to improve my code. I am trying to use Radixsort to sort array of 10 numbers (for example) in increasing order.
When i run the program with array of size 10 and put 10 random int numbers in like
70
309
450
279
799
192
586
609
54
657
i get this out:
450
309
192
279
54
192
586
657
54
609
Don´t see where my error is in the code.
class IntQueue
{
static class Hlekkur
{
int tala;
Hlekkur naest;
}
Hlekkur fyrsti;
Hlekkur sidasti;
int n;
public IntQueue()
{
fyrsti = sidasti = null;
}
// First number in queue.
public int first()
{
return fyrsti.tala;
}
public int get()
{
int res = fyrsti.tala;
n--;
if( fyrsti == sidasti )
fyrsti = sidasti = null;
else
fyrsti = fyrsti.naest;
return res;
}
public void put( int i )
{
Hlekkur nyr = new Hlekkur();
n++;
nyr.tala = i;
if( sidasti==null )
f yrsti = sidasti = nyr;
else
{
sidasti.naest = nyr;
sidasti = nyr;
}
}
public int count()
{
return n;
}
public static void radixSort(int [] q, int n, int d){
IntQueue [] queue = new IntQueue[n];
for (int k = 0; k < n; k++){
queue[k] = new IntQueue();
}
for (int i = d-1; i >=0; i--){
for (int j = 0; j < n; j++){
while(queue[j].count() != 0)
{
queue[j].get();
}
}
for (int index = 0; index < n; index++){
// trying to look at one of three digit to sort after.
int v=1;
int digit = (q[index]/v)%10;
v*=10;
queue[digit].put(q[index]);
}
for (int p = 0; p < n; p++){
while(queue[p].count() != 0) {
q[p] = (queue[p].get());
}
}
}
}
}
I am also thinking can I let the function take one queue as an
argument and on return that queue is in increasing order? If so how?
Please help. Sorry if my english is bad not so good in it.
Please let know if you need more details.
import java.util.Random;
public class RadTest extends IntQueue {
public static void main(String[] args)
{
int [] q = new int[10];
Random r = new Random();
int t = 0;
int size = 10;
while(t != size)
{
q[t] = (r.nextInt(1000));
t++;
}
for(int i = 0; i!= size; i++)
{
System.out.println(q[i]);
}
System.out.println("Radad: \n");
radixSort(q,size,3);
for(int i = 0; i!= size; i++)
{
System.out.println(q[i]);
}
}
}
Hope this is what you were talking about...
Thank you for your answer, I will look into it. Not looking for someone to solve the problem for me. Looking for help and Ideas how i can solve it.
in my task it says:
Implement a radix sort function for integers that sorts with queues.
The function should take one queue as an
argument and on return that queue should contain the same values in ascending
order You may assume that the values are between 0 and 999.
Can i put 100 int numbers on my queue and use radixsort function to sort it or do i need to put numbers in array and then array in radixsort function which use queues?
I understand it like i needed to put numbers in Int queue and put that queue into the function but that has not worked.
But Thank for your answers will look at them and try to solve my problem. But if you think you can help please leave comment.
This works for the test cases I tried. It's not entirely well documented, but I think that's okay. I'll leave it to you to read it, compare it to what you're currently doing, and find out why what you have might be different than mine in philosophy. There's also other things that are marked where I did them the "lazy" way, and you should do them a better way.
import java.util.*;
class Radix {
static int[] radixSort(int[] arr) {
// Bucket is only used in this method, so I declare it here
// I'm not 100% sure I recommend doing this in production code
// but it turns out, it's perfectly legal to do!
class Bucket {
private List<Integer> list = new LinkedList<Integer>();
int[] sorted;
public void add(int i) { list.add(i); sorted = null;}
public int[] getSortedArray() {
if(sorted == null) {
sorted = new int[list.size()];
int i = 0;
for(Integer val : list) {
sorted[i++] = val.intValue(); // probably could autobox, oh well
}
Arrays.sort(sorted); // use whatever method you want to sort here...
// Arrays.sort probably isn't allowed
}
return sorted;
}
}
int maxLen = 0;
for(int i : arr) {
if(i < 0) throw new IllegalArgumentException("I don't deal with negative numbers");
int len = numKeys(i);
if(len > maxLen) maxLen = len;
}
Bucket[] buckets = new Bucket[maxLen];
for(int i = 0; i < buckets.length; i++) buckets[i] = new Bucket();
for(int i : arr) buckets[numKeys(i)-1].add(i);
int[] result = new int[arr.length];
int[] posarr = new int[buckets.length]; // all int to 0
for(int i = 0; i < result.length; i++) {
// get the 'best' element, which will be the most appropriate from
// the set of earliest unused elements from each bucket
int best = -1;
int bestpos = -1;
for(int p = 0; p < posarr.length; p++) {
if(posarr[p] == buckets[p].getSortedArray().length) continue;
int oldbest = best;
best = bestOf(best, buckets[p].getSortedArray()[posarr[p]]);
if(best != oldbest) {
bestpos = p;
}
}
posarr[bestpos]++;
result[i] = best;
}
return result;
}
static int bestOf(int a, int b) {
if(a == -1) return b;
// you'll have to write this yourself :)
String as = a+"";
String bs = b+"";
if(as.compareTo(bs) < 0) return a;
return b;
}
static int numKeys(int i) {
if(i < 0) throw new IllegalArgumentException("I don't deal with negative numbers");
if(i == 0) return 1;
//return (i+"").length(); // lame method :}
int len = 0;
while(i > 0) {
len++;
i /= 10;
}
return len;
}
public static void main(String[] args) {
int[] test = {1, 6, 31, 65, 143, 316, 93, 736};
int[] res = radixSort(test);
for(int i : res) System.out.println(i);
}
}
One thing that looks strange:
for (int p = 0; p < n; p++){
while(queue[p].count() != 0) {
q[p] = (queue[p].get());
}
}
Is p supposed to be the index in q, which ranges from 0 to n-1, or in queue, which ranges from 0 to 9? It is unlikely to be both ...
Another:
for (int index = 0; index < n; index++){
// trying to look at one of three digit to sort after.
int v=1;
int digit = (q[index]/v)%10;
v*=10;
queue[digit].put(q[index]);
}
Why are you multiplying v by 10, only to overwrite it by v = 1 in the next iteration? Are you aware than v will always be one, and you will thus look at the same digit in every iteration?
Well I don't think I can help without almost posting the solution (just giving hints is more exhausting and I'm a bit tired, sorry), so I'll just contribute a nice little fuzz test so you can test your solution. How does that sound? :-)
Coming up with a good fuzztester is always a good idea if you're implementing some algorithm. While there's no 100% certainty if that runs with your implementation chances are it'll work (radix sort doesn't have any strange edge cases I'm aware of that only happen extremely rarely)
private static void fuzztest() throws Exception{
Random rnd = new Random();
int testcnt = 0;
final int NR_TESTS = 10000;
// Maximum size of array.
final int MAX_DATA_LENGTH = 1000;
// Maximum value allowed for each integer.
final int MAX_SIZE = Integer.MAX_VALUE;
while(testcnt < NR_TESTS){
int len = rnd.nextInt(MAX_DATA_LENGTH) + 1;
Integer[] array = new Integer[len];
Integer[] radix = new Integer[len];
for(int i = 0; i < len; i++){
array[i] = rnd.nextInt(MAX_SIZE);
radix[i] = new Integer(array[i]);
}
Arrays.sort(array);
sort(radix); // use your own sort function here.
for(int i = 0; i < len; i++){
if(array[i].compareTo(radix[i]) != 0){
throw new Exception("Not sorted!");
}
}
System.out.println(testcnt);
testcnt++;
}

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