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find if given pack of coins can make a given value - coin row problem

given array of coins (int) and an int n the function need to return true if there is atleast one solution to the coin-change problem.
meaning: for array of ints> 0: [c(0) ,c(1) ,c(2) ,c(3) ,...... ,c(k)]. check if there is a solution for
the eqauation: a(0)*c(0)+ a(1)*c(1)+.....+ a(k)*c(k)= n. //n is the money we need to change
given c(0),c(1),....,c(n) >0 and a(0),a(1),....,a(n) =>0 both integers.
so I managed to make this code: the problem is that its algorithmic efficiency sucks, and this should be running on high values, and big coins array, so I need a code that is able to do this quicker.
public static boolean change(int[] coins, int n) {
boolean ans = false;
//loop running in recursion till founds ans/ passing limit
for (int i = 0; i < coins.length & (!ans); i = i + 1) {
if (n % coins[i] == 0) {
return true;
}
if (n >= coins[i]) {
ans = change(coins, n - coins[i]);
}
}
return ans;
}//O(n*k^n) solution for false ans , very bad :(
for example: for coins = {2,4,8} and n= 4111; I should get false, but the program unable to run this.
btw I would prefer this function to use recursion, but any solution/ guidnes is good :)
this is an other try doing this better but still not running as wanted.
//trying to use binary search and using divisions instead of minus
public static int iscashable(int[] coins, int n, int min, int max)
{
int check=(max+min)/2;
if(check == coins.length-1 | check == 0)
return check;
if(n/coins[check] > n% coins[check])
{
return (iscashable(coins,n,check,max));
}
else
{
return check;
}
}
public static int canchange(int[] coins, int n, int count)
{
int x=0;
int check= iscashable(coins,n,0,coins.length-count);
if(n%coins[check]==0)
{
return 0;
}
if(check==0)
{
return n;
}
if(n/coins[check] > n% coins[check])
{
x= (n/coins[check]) - (n% coins[check]);
int k= n-(coins[check]*x);
return canchange(coins, k, count+1);
}
else
{
return canchange(coins,n-coins[check],count+1);
}
}
the problem is both about runtime and number of recursion calls (with big number given, every recursion layer is coins.length^(num of layers));
I really thank you for your help!

lowest value for given number

I recently gave a codility test. There was a this question which I couldn't solve. Now that I'm trying at home, I would like to get help. I don't remember the complete question language, but I do remember the output how would the program respond. Here we go.
"write a java program, for a given number N, need to find the lowest number for the given N. N could be a billion number too."
{this may not be the exact one, Sorry about that}
For Example:
N=1 then o/p is 0.
N=123 then o/p is 100
N=1234 then o/p is 1000 and so on.
My Solution: --just a workaround, this isn't actual logic.
class Solution {
public int solution(int N) {
int pointer=0;
if (N == 1) {
return 0;
} else {
String digitsCount = Integer.toString(N);
for(int i = 0; i < digitsCount.length(); i++) {
pointer++;
}
StringBuffer subString = new StringBuffer();
int count=0;
while(count < pointer-1) {
subString.append("0");
count++;
}
subString = subString.insert(0, "1");
return Integer.parseInt(subString.toString());
}
}
}

Using math library, should be good for about 16 digits.
long getLow(long in) {
if (in <= 1) return 0; // see note below
return (long)(Math.pow(10, Math.floor(Math.log10(in))));
}
The calculation is undefined for in < 1; we return 0. For in = 1 we return 0 per original code, though returning 1 would surely be more consistent: 2,3,...9 return 1, so why not 1 returns 1?

Your solution seems to work fine. The only thing it doesn't take into account is the fact that N can be a very large number. int only has a max value of about 2 billion.
Here is my solution:
public static long getLowestNumberWithSameNumberOfDigits(long input) {
if (input < 10) { // special case
return 0;
}
long trial = 10;
while (input / trial >= 10) {
trial *= 10;
}
return trial;
}

Thank You! Guys. All the suggestions were helpful. Infact, every suggestion has a learning. Here is the updated code. Please accept if you think its good enough.
private static long solution(long N) {
if (N == 1) {
return 0;
} else {
String digitsCount = Long.toString(N);
int pointer=digitsCount.length();
StringBuilder subString = new StringBuilder();
subString.append("1");
for(int i=0; i<pointer-1; i++) {
subString.append("0");
}
return Long.parseLong(subString.toString());
}
}

Using IsPrime method in Java [closed]

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This is my code to use IsPrime method to determine total number of primes between 0 and 1000 and print the total number of primes at last. Can anyone tell what's wrong with the code.
public static void main(String[] args) {
int z=0;
// z is the variable that holds total number of primes
//n is divisor
//i is dividend
if (isPrime(i)) {
z++;
}
System.out.print(z+"\n");
}
public static boolean isPrime(int n){
{
for(i=0; i<1000; i++)
{
for(n=0; n<i; n++)
if(i%n==0)
return false;
else
return true;
}
}
}
Thanks in advance

Formatting it might help you discover the error.
I see a few things that's wrong with your code:
From what I can see, you have an extra open curly bracket in your isPrime method.
i isn't declared in your main method.
You need to wrap your if(isPrime(i)) statement inside a for loop that goes from 0 to 1000. Like the following:
for (int i = 0; i <= 1000; i++) {
if (isPrime(i))
z++;
}
That way, it will be actually checking all the prime numbers from 0 to 1000
For good coding practices, I would name your z variable to be something like counter so that it's clear what that variable is supposed to be doing. i in for-loop is okay since that's a common way to index through the loop.
You can also use several tactics to optimize your code. You can use Math.sqrt() function, as well as start your for loop from 3 and go up by increment of 2 (since any even number will be dividable by 2) and initialize your counter from 1 since 2 will already be a prime number.

public static boolean isPrime(int n){
int factors = 0;
for(int i = 1; i <= n; i++){
if(n % i == 0) // ensure that you mod n not i
factors++;
}
// if factors count is equals to 2 then it is prime number else it's not prime number
if(factors == 2)
return true;
else
return false;
}
Check this modified code once for your reference.

I think you had a few things turned around.
Why not loop from 1 to 1000 in your primary function and then use the isPrime function to determine if each number is prime.
In the isPrime function, you count from 2 to 1/2 the value of the number and do the divisions to determine if it is prime. Return False if it is divisible.
public static void main(String[] args) {
int z=0;
for (i=1;i<=1000;i++) {
if (isPrime(i))
{
z++;
}
}
System.out.print(z+"\n");
}
public static boolean isPrime(int n){
for(i=2; i<=n/2; i++)
{
if(n%i==0) return false;
}
return true;
}

This will count the number of primes based on this link and your original answer...
public static void main(String[] args) {
int isPrimeCount = 0;
for(i=0; i<1000; i++)
{
if(Check_Prime(i))
{
isPrimeCount++;
}
System.out.println(isPrimeCount);
}
}
private static boolean Check_Prime(int number) {
int i;
for (i = 2; i <= number - 1; i++)
{
if (number % i == 0)
{
return false;
}
}
if (i == number)
{
return true;
}
return false;
}

You need to define the variable "i" before you pass it to the isPrime() method in main(). It seems as though whoever wrote the code did not fully understand what a prime number was. According to wikipedia "A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. " With this in mind you need to make sure that the value you pass to the isPrime() method is greater than 1. After look at your code I made some changes. I made the isPrime() method return false if the input value is <=1. Also, I made the isPrime() method return true if the input value is 2. I made other changes in the code that would make the for statement operate n-1 times because that is all that is needed to find out if the number is prime because all numbers are divisible by themselves. Also the for statement starts at the value 2. Your if-then-else return statements within the for loop is illogical because it will return a value without going through the entire loop. You did not need the inner for loop.
Here's a link on prime numbers
Here is the new code:
public class AreaComparison {
/**
* Starts the program.
*
* #param command line arguments
*/
public static void main(String[] args) {
int z = 0;
int i = 2;
// z is the variable that holds total number of primes
//n is divisor
//i is dividend
if (isPrime(i)) {
z++;
}
System.out.print(z + "\n");
}
public static boolean isPrime(int n) {
if (n <= 1) {
return false;
}
if(n == 2){
return true;
}
for (int i = 2; i < n; i++) {
if (n % i == 0) {
return false;
}
}
return true;
}
}

Junit Test for algorithm

I try to solve this problem:
Write a function, persistence, that takes in a positive parameter num and returns its multiplicative persistence, which is the number of times you must multiply the digits in num until you reach a single digit
This is the code that I wrote:
public class Hello {
static int counter = 0;
public static int persistence(long n) {
int digits = digit_count(n);
if (digits <= 1) {
return 0;
}
persistence(product(n));
counter++;
return counter;
}
public static int product(long n) {
int productValue = 1;
while (n != 0) {
productValue *= n % 10;
n /= 10;
}
return productValue;
}
public static int digit_count(long n) {
int count = 0;
while (n > 0) {
n /= 10;
count++;
}
return count;
}
and JUnit test:
assertEquals(3, Hello.persistence(39));
assertEquals(0, Hello.persistence(4));
assertEquals(2, Hello.persistence(25));
assertEquals(4, Hello.persistence(999));
the tests fails for 25 and 999, but if I try to call Hello.persistence(25) and Hello.persistence(999) in main method I got the needed values.
Please, explain how this is possible?

You should be looking at your outcomes and asking "Why am I not getting what I think I should be getting?". Using a debugger you would find your counter isn't being reset before you call persistance from the outside. Hello.persistance(39) sets the counter to 3 and then Hello.persistance(4) returns a hard coded value of 0.
Create a new class for each of your test cases and you'll be fine.

You are not reverting the state of counter to 0 between invocations:
Hello.persistence(39);
//counter is now equal to 3, furter invocations will add "3" to the result

Prime Tester for speed

I was given a homework assignment in Java to create classes that find Prime number and etc (you will see in code better).
My code:
class Primes {
public static boolean IsPrime(long num) {
if (num%2==0){
return false;
}
for (int i=3; i*i<=num;i+=2) {
if (num%i==0) {
return false;
}
}
return true;
} // End boolen IsPrime
public static int[] primes(int min, int max){
int counter=0;
int arcount=0;
for (int i=min;i<max;i++){
if (IsPrime(i)){
counter++;
}
}
int [] arr= new int[counter];
for (int i=min;i<max;i++){
if (IsPrime(i)){
arr[arcount]=i;
arcount++;
}
}
return arr;
} // End Primes
public static String tostring (int [] arr){
String ans="";
for (int i=0; i<arr.length;i++){
ans= ans+arr[i]+ " ";
}
return ans;
}
public static int closestPrime(long num){
long e = 0 , d = 0 , f = num;
for (int i = 2; i <= num + 1 ; i++){
if ((num + 1) % i == 0){
if ((num + 1) % i == 0 && (num + 1) == i){
d = num + 1;
break;
}
num++;
i = 1;
}
}
num = f;
for (int i = 2; i < num; i++){
if ((num - 1) % i == 0){
if ((num - 1) % i == 0 && (num - 1) == i){
e = num - 1;
break;
}
num--;
i = 1;
}
}
num = f;
if (d - num < num - e) System.out.println("Closest Prime: "+d);
else System.out.println("Closest Prime: "+e);
return (int) num;
} // End closestPrime
}//end class
The goal of my code is to be faster (and correct). I'm having difficulties achieving this. Suggestions?
**New code:
class Primes {
public static boolean IsPrime(int num) {
if (num==1){
return false;
}
for (int i=2; i<Math.sqrt(num);i++) {
if (num%i==0) {
return false;
}
}
return true;
}
// End boolen IsPrime
public static int[] primes(int min, int max){
int size=0;
int [] arrtemp= new int[max-min];
for (int i=min;i<max;i++){
if (IsPrime(i)){
arrtemp[size]=i;
size++;
}
}
int [] arr= new int[size];
for (int i=0;i<size;i++){
arr[i]=arrtemp[i];
}
return arr;
}
public static String tostring (int [] arr){
String ans="";
for (int i=0; i<arr.length;i++){
ans= ans+arr[i]+ " ";
}
return ans;
}
public static int closestPrime(int num) {
int count=1;
for (int i=num;;i++){
int plus=num+count, minus=num-count;
if (IsPrime(minus)){
return minus;
}
if (IsPrime(plus)) {
return plus;
}
count=count+1;
}
} // End closestPrime
}//end class
I did try to make it a bit better. what do you think, it can be improved more? (the speed test is still high...)

In your primes function you:
Check if the current number is divisible by two
Check to see if it's prime
Create an array to put your output in.
Check every number in the range again for primality before putting it in your array.
The problem is in the last step. By double-checking whether each number is prime, you're duplicating your most expensive operations.
You could use a dynamic data structure and add prime numbers to it as you find them. That way you only need to check once.
Alternatively, you could create a boolean array which is the size of your input range. Then as you find primes, set the corresponding array value to true.
UPDATE:
There are still a number of improvements you can make, but some will require more work than others to implement. Look at the specifics of your test and see what fits your needs.
Low-hanging fruit:
Use an ArrayList to collect primes as you find them in primes, as opposed to looping over the values twice.
In closestPrime, you're checking every single value on either side of num: half of these are even, thus not prime. You could adapt your code to check only odd numbers for primality.
Trickier to implement:
Try a more advanced algorithm for IsPrime: check out the Sieve of Eratosthenes
Above all, you should spend some time figuring out exactly where the bottlenecks are in your code. Oftentimes performance problems are caused by code we thought was perfectly fine. You might consider looking into the code-profiling options available in your development environment.

You make quite a few calls to isPrime(), each of which is very expensive. Your first step should be to minimize the number of times you do that, since the result doesn't change for any given number, there's no point calling more than once. You can do this with memoization by storing the values once they're computed:
ArrayList<Integer> memoList = new ArrayList<Integer>();
for(int i = 0; i < max; i++) {
if(isPrime(i)) {
memoList.add(i);
}
}
Now memoList holds all the primes you need, up to max, and you can loop over them rapidly without needing to recompute them every time.
Secondly, you can improve your isPrime() method. Your solution loops over every odd number from 3 to sqrt(n), but why not just loop over the primes, now that we know them?
public static boolean IsPrime(long num) {
for(int p : memoList) {
if(num % p == 0) {
return false;
}
}
return true;
}
These changes should dramatically improve how quickly your code runs, but there has been a lot of research into even more efficient ways of calculating primes. The Wikipedia page on Prime Numbers has some very good information on further tactics (prime sieves, in particular) you can experiment with.
Remember that as this is homework you should be sure to cite this page when you turn it in. You're welcome to use and expand upon this code, but not citing this question and any other resources you use is plagiarism.

I see a couple problems with your answer. First, 2 is a prime number. Your first conditional in IsPrime breaks this. Second, in your primes method, you are cycling through all number from min to max. You can safely ignore all negative numbers and all even numbers (as you do in IsPrime). It would make more sense to combine these two methods and save all the extra cycles.