Reverse of a number taking care of boundary conditions - java

I'm trying to write a simple method in Java that return the reverse of a number (in the mathematical way, not string-wise). I want to take care of boundary conditions since a number whose reverse is out of int range would give me a wrong answer. Even to throw exceptions, I'm not getting clearcut logic. I've tries this code.
private static int reverseNumber(int number) {
int remainder = 0, sum = 0; // One could use comma separated declaration for primitives and
// immutable objects, but not for Classes or mutable objects because
// then, they will allrefer to the same element.
boolean isNegative = number < 0 ? true : false;
if (isNegative)
number = Math.abs(number); // doesn't work for Int.MIN_VALUE
// http://stackoverflow.com/questions/5444611/math-abs-returns-wrong-value-for-integer-min-value
System.out.println(number);
while (number > 0) {
remainder = number % 10;
sum = sum * 10 + remainder;
/* Never works, because int won't throw error for outside int limit, it just wraps around */
if (sum > Integer.MAX_VALUE || sum < Integer.MIN_VALUE) {
throw new RuntimeException("Over or under the limit");
}
/* end */
/* This doesn't work always either.
* For eg. let's take a hypothetical 5 bit machine.
* If we want to reverse 19, 91 will be the sum and it is (in a 5 bit machine), 27, valid again!
*/
if (sum < 0) {
throw new RuntimeException("Over or under the limit");
}
number /= 10;
}
return isNegative ? -sum : sum;
}

Your approach of dividing by 10, transfering the reminder to the current result * 10 is the way to go.
The only thing you are doing wrong is the check for the "boundary violation", because
sum > Integer.MAX_VALUE || sum < Integer.MIN_VALUE
can ofc. NEVER be true - Otherwhise MIN and MAX wouldn't have any meaning.
So, think mathematical :-)
sum = sum * 10 + remainder;
should not exceed Integer.MAX_VALUE, i.e.
(!)
Integer.MAX_VALUE >= sum * 10 + remainder;
or transformed:
(!)
(Integer.MAX_VALUE - remainder) / 10 >= sum
So, you can use the following check BEFORE multiplying by 10 and adding the remainder:
while (number > 0) {
remainder = number % 10;
if (!(sum <= ((Integer.MAX_VALUE -remainder) / 10))) {
//next *10 + remainder will exceed the boundaries of Integer.
throw new RuntimeException("Over or under the limit");
}
sum = sum * 10 + remainder;
number /= 10;
}
simplified (DeMorgan) the condition would be
if (sum > ((Integer.MAX_VALUE -remainder) / 10))
which makes perfect sence - because its exactly the reversed calculation of what your next step will be - and if sum is already GREATER than this calculation - you will exceed Integer.MAX_VALUE with the next step.
Untested, but that should pretty much solve it.

Related

The loop has no output?

The code below has no output when I run it, I think somehow it is infinite loop? How to fix it?
Write a method named getEvenDigitSum with one parameter of type int called number.
The method should return the sum of the even digits within the number.
If the number is negative, the method should return -1 to indicate an invalid value.
EXAMPLE INPUT/OUTPUT:
getEvenDigitSum(123456789); → should return 20 since 2 + 4 + 6 + 8 = 20
getEvenDigitSum(252); → should return 4 since 2 + 2 = 4
getEvenDigitSum(-22); → should return -1 since the number is negative
public class getEvenDigitSum {
public static int getEvenDigitSum(int number) {
int sum = 0;
int lastDigit=0;
if (number < 0) {
return -1;
}
while (number >0) {
lastDigit = number % 10;
if (number % 2 == 0)
{
sum += lastDigit;
number = number / 10;
}
}
return sum;
}
}
while (number >0) {
lastDigit = number % 10;
if (number % 2 == 0)
{
sum += lastDigit;
number = number / 10;
}
}
OK, and what happens if the number isn't even? You didn't make an else/else if statement after; if your number is odd, it stays the same, the loop is infinite, and hence your code does nothing.
Your condition only handles even digits, but think about what happens when you get a number that contains odd digit, like 1221 for example.
Try adding the missing else statement:
while (number >0) {
lastDigit = number % 10;
if (number % 2 == 0)
{
sum += lastDigit;
number = number / 10;
}
else {
// Deal with odd digit, leaving for you to implement
{
}
General tip: The best way to find errors in your code is to write tests and debug your code.
These are two skills every developer should poses and practice regularly

How to find this checksum using Java

To find this particular checksum, we need to sum the digits of the input and multiply by 2. Simple enough by finding the remainder using a loop.
If the result is less than 10, that is the number's checksum. If it is 10 or higher, we need to do it again until the result is less than 10.
If it gets caught in an infinite loop, such as with the input of 18, return -1.
This is what I have so far:
public int getChecksum(int input, int previous) {
int sum = 0;
while (input > 0) {
sum += input % 10;
input /= 10;
}
if (sum * 2 < 10) {
return sum * 2;
} else if (sum * 2 >= 10 && previous != sum) {
previous = sum;
return getChecksum(sum * 2, previous);
} else if (previous == sum) {
return -1;
}
return sum * 2;
}
I really wanted to know if there was a way to do this without doing it recursively as I am doing here.
A rather simple recursive algorithm like this can also be implemented iteratively. Usually you would go about this turning the recursive call into a loop with the recursive termination condition as the loop termination condition.

Sum even index places in Java

I tried to write a method (for kicks) that would sum up the digits at even places using Java recursion.
For example, the number 23495 would return 3+9 = 12.
I am unsuccessful and would appreciate hints or what I'm doing wrong.
int sumEven = 0;
int sumOdd = 0;
int i = 1;
if (n == 0)
return sumEven;
if (n != 0) {
if (i % 2 == 0)
{
i++;
sumEven += n % 10;
}
else
{
i++;
sumOdd += n % 10;
}
}
return sumEven + getEven (n/=10);
The problem is you're trying to do too much - take a look at my comment on the Q
A recursive method needs an input that contains everything it needs to work with, a return value, and an execution path where it calls itself until something happens that means it doesn't need to call itself any more - without this bit it will recourse until it overflows the stack
int sumEveryOtherDigit(int input){
if(input >= 100)
return input%10 + sumEveryOtherDigit(input/100);
else
return input%10;
}
This takes the input , and if there is any point to running again (if the input is at least 100) takes the rightmost digit plus running itself again with a smaller number
Eventually the number gets so small that there isn't any point running itself again so it just returns without running itself again and that is how the recursion stops
Now from your comment on another answer it seems you want to determine even and odd as working from the left so we need to either start with the number (1630) or the number divided by ten (23495 -> 2349) - basically to start the recursion going we always want to pass in a number with an even number of digits
int num = 23495;
int numOfDigits = (int)Math.log10(num)+ 1;
if(numOfDigits%2==0)
result = sumEveryOtherDigit(num);
else
result = sumEveryOtherDigit(num/10);
You should iterate over the digits of the input number, and then sum the remainder mod 10 only for even position digits:
int input = 23495;
input /= 10;
int sum = 0;
while (input > 0) {
sum += input % 10; // add last even digit
input /= 100; // advance by two digits, to the next even digit
}
System.out.println("sum of even digits of input is: " + sum);
This prints:
sum of even digits of input is: 12

Starting from 1 how far can I count, when I can use any digit a maximum of N times

My problem is as follows; for number N, I need to find out what is the largest value I can count to, when each digit can be used N times.
For example if N = 5, the largest value is 12, since at that point the digit 1 has been used 5 times.
My original approach was to simply iterate through all numbers and keep a tally of how many times each digit has been used so far. This is obviously very inefficient when N is large, so am looking for advice on what would be a smarter (and more efficient) way to achieve this.
public class Counter {
private static Hashtable<Integer, Integer> numbers;
public static void main(String[] args){
Counter c = new Counter();
c.run(9);
}
public Counter() {
numbers = new Hashtable<Integer, Integer>();
numbers.put(0, 0);
numbers.put(1, 0);
numbers.put(2, 0);
numbers.put(3, 0);
numbers.put(4, 0);
numbers.put(5, 0);
numbers.put(6, 0);
numbers.put(7, 0);
numbers.put(8, 0);
numbers.put(9, 0);
}
public static void run(int maxRepeat) {
int keeper = 0;
for(int maxFound = 0; maxFound <= maxRepeat; maxFound++) {
keeper++;
for (int i = 0; i < Integer.toString(keeper).length(); i++) {
int a = Integer.toString(keeper).charAt(i);
//here update the tally for appropriate digit and check if max repeats is reached
}
}
System.out.println(keeper);
}
}
For starters, rather than backing your Counter with a Hashtable, use an int[] instead. When you know exactly how many elements your map has to have, and especially when the keys are numbers, an array is perfect.
That being said, I think the most effective speedup is likely to come from better math, not better algorithms. With some experimentation (or it may be obvious), you'll notice that 1 is always the first digit to be used a given number of times. So given N, if you can find which number is the first to use the digit 1 N+1 times, you know your answer is the number right before that. This would let you solve the problem without actually having to count that high.
Now, let's look at how many 1's are used counting up to various numbers. Throughout this post I will use n to designate a number when we are trying to figure out how many 1's are used to count up to a number, whereas capital N designates how many 1's are used to count up to something.
One digit numbers
Starting with the single-digit numbers:
1: 1
2: 1
...
9: 1
Clearly the number of 1's required to count up to a one-digit number is... 1. Well, actually we forgot one:
0: 0
That will be important later. So we should say this: the number of 1's required to count up to a one-digit number X is X > 0 ? 1 : 0. Let's define a mathematical function f(n) that will represent "number of 1's required to count up to n". Then
f(X) = X > 0 ? 1 : 0
Two-digit numbers
For two-digit numbers, there are two types. For numbers of the form 1X,
10: 2
11: 4
12: 5
...
19: 12
You can think of it like this: counting up to 1X requires a number of 1's equal to
f(9) (from counting up to 9) plus
1 (from 10) plus
X (from the first digits of 11-1X inclusive, if X > 0) plus
however many 1's were required to count up to X
Or mathematically,
f(1X) = f(9) + 1 + X + f(X)
Then there are the two-digit numbers higher than 19:
21: 13
31: 14
...
91: 20
The number of 1's required to count to a two-digit number YX with Y > 1 is
f(19) (from counting up to 19) plus
f(9) * (Y - 2) (from the 1's in numbers 20 through (Y-1)9 inclusive - like if Y = 5, I mean the 1's in 20-49, which come from 21, 31, 41) plus
however many 1's were required to count up to X
Or mathematically, for Y > 1,
f(YX) = f(19) + f(9) * (Y - 2) + f(X)
= f(9) + 1 + 9 + f(9) + f(9) * (Y - 2) + f(X)
= 10 + f(9) * Y + f(X)
Three-digit numbers
Once you get into three-digit numbers, you can kind of extend the pattern. For any three-digit number of the form 1YX (and now Y can be anything), the total count of 1's from counting up to that number will be
f(99) (from counting up to 99) plus
1 (from 100) plus
10 * Y + X (from the first digits of 101-1YX inclusive) plus
however many 1's were required to count up to YX in two-digit numbers
so
f(1YX) = f(99) + 1 + YX + f(YX)
Note the parallel to f(1X). Continuing the logic to more digits, the pattern, for numbers which start with 1, is
f(1[m-digits]) = f(10^m - 1) + 1 + [m-digits] + f([m-digits])
with [m-digits] representing a sequence of digits of length m.
Now, for three-digit numbers ZYX that don't start with 1, i.e. Z > 1, the number of 1's required to count up to them is
f(199) (from counting up to 199) plus
f(99) * (Z - 2) (from the 1's in 200-(Z-1)99 inclusive) plus
however many 1's were required to count up to YX
so
f(ZYX) = f(199) + f(99) * (Z - 2) + f(YX)
= f(99) + 1 + 99 + f(99) + f(99) * (Z - 2) + f(YX)
= 100 + f(99) * Z + f(YX)
And the pattern for numbers that don't start with 1 now seems to be clear:
f(Z[m-digits]) = 10^m + f(10^m - 1) * Z + f([m-digits])
General case
We can combine the last result with the formula for numbers that do start with 1. You should be able to verify that the following formula is equivalent to the appropriate case given above for all digits Z 1-9, and that it does the right thing when Z == 0:
f(Z[m-digits]) = f(10^m - 1) * Z + f([m-digits])
+ (Z > 1) ? 10^m : Z * ([m-digits] + 1)
And for numbers of the form 10^m - 1, like 99, 999, etc. you can directly evaluate the function:
f(10^m - 1) = m * 10^(m-1)
because the digit 1 is going to be used 10^(m-1) times in each of the m digits - for example, when counting up to 999, there will be 100 1's used in the hundreds' place, 100 1's used in the tens' place, and 100 1's used in the ones' place. So this becomes
f(Z[m-digits]) = Z * m * 10^(m-1) + f([m-digits])
+ (Z > 1) ? 10^m : Z * ([m-digits] + 1)
You can tinker with the exact expression, but I think this is pretty close to as good as it gets, for this particular approach anyway. What you have here is a recursion relation that allows you to evaluate f(n), the number of 1's required to count up to n, by stripping off a leading digit at each step. Its time complexity is logarithmic in n.
Implementation
Implementing this function is straightforward given the last formula above. You can technically get away with one base case in the recursion: the empty string, i.e. define f("") to be 0. But it will save you a few calls to also handle single digits as well as numbers of the form 10^m - 1. Here's how I'd do it, omitting a bit of argument validation:
private static Pattern nines = Pattern.compile("9+");
/** Return 10^m for m=0,1,...,18 */
private long pow10(int m) {
// implement with either pow(10, m) or a switch statement
}
public long f(String n) {
int Z = Integer.parseInt(n.substring(0, 1));
int nlen = n.length();
if (nlen == 1) {
return Z > 0 ? 1 : 0;
}
if (nines.matcher(n).matches()) {
return nlen * pow10(nlen - 1);
}
String m_digits = n.substring(1);
int m = nlen - 1;
return Z * m * pow10(m - 1) + f_impl(m_digits)
+ (Z > 1 ? pow10(m) : Z * (Long.parseLong(m_digits) + 1));
}
Inverting
This algorithm solves the inverse of the the question you're asking: that is, it figures out how many times a digit is used counting up to n, whereas you want to know which n you can reach with a given number N of digits (i.e. 1's). So, as I mentioned back in the beginning, you're looking for the first n for which f(n+1) > N.
The most straightforward way to do this is to just start counting up from n = 0 and see when you exceed N.
public long howHigh(long N) {
long n = 0;
while (f(n+1) <= N) { n++; }
return n;
}
But of course that's no better (actually probably worse) than accumulating counts in an array. The whole point of having f is that you don't have to test every number; you can jump up by large intervals until you find an n such that f(n+1) > N, and then narrow down your search using the jumps. A reasonably simple method I'd recommend is exponential search to put an upper bound on the result, followed by a binary search to narrow it down:
public long howHigh(long N) {
long upper = 1;
while (f(upper + 1) <= N) {
upper *= 2;
}
long lower = upper / 2, mid = -1;
while (lower < upper) {
mid = (lower + upper) / 2;
if (f(mid + 1) > N) {
upper = mid;
}
else {
lower = mid + 1;
}
}
return lower;
}
Since the implementation of f from above is O(log(n)) and exponential+binary search is also O(log(n)), the final algorithm should be something like O(log^2(n)), and I think the relation between N and n is linear enough that you could consider it O(log^2(N)) too. If you search in log space and judiciously cache computed values of the function, it might be possible to bring it down to roughly O(log(N)). A variant that might provide a significant speedup is sticking in a round of interpolation search after determining the upper bound, but that's tricky to code properly. Fully optimizing the search algorithm is probably a matter for another question though.
This should be more efficient. Use integer array of size 10 to keep the count of digits.
public static int getMaxNumber(int N) {
int[] counts = new int[10];
int number = 0;
boolean limitReached = false;
while (!limitReached) {
number++;
char[] digits = Integer.toString(number).toCharArray();
for (char digit : digits) {
int count = counts[digit - '0'];
count++;
counts[digit - '0'] = count;
if (count >= N) {
limitReached = true;
}
}
}
return number;
}
UPDATE 1: As #Modus Tollens mentioned initial code has a bug. When N = 3 it returns 11, but there are four 1s between 1 and 11. The fix is to check if limit is breached count[i] > N on given number, previous number should be return. But if for some i count[i] == N for other j count[j] <= N, the actual number should be returned.
Please see corresponding code below:
public static int getMaxNumber(int N) {
int[] counts = new int[10];
int number = 0;
while (true) {
number++;
char[] digits = Integer.toString(number).toCharArray();
boolean limitReached = false;
for (char digit : digits) {
int count = counts[digit - '0'];
count++;
counts[digit - '0'] = count;
if (count == N) {
//we should break loop if some count[i] equals to N
limitReached = true;
} else if (count > N) {
//previous number should be returned immediately
//, if current number gives more unique digits than N
return number - 1;
}
}
if (limitReached) {
return number;
}
}
}
UPDATE 2: As #David Z and #Modus Tollens mentioned, in case if N=13, 30 should be returned, ie, algo stops when N is breached but not reached. If this is initial requirement, the code will be even simpler:
public static int getMaxNumber(int N) {
int[] counts = new int[10];
int number = 0;
while (true) {
number++;
char[] digits = Integer.toString(number).toCharArray();
for (char digit : digits) {
int count = counts[digit - '0'];
count++;
counts[digit - '0'] = count;
if (count > N) {
return number - 1;
}
}
}
}

I have a program that calculates the first 200 prime numbers, but I do not understand a formula in it

I need to write a code which should calculate the first 200 prime numbers, but I can't hand it in as long as I can't explain everything. I used a piece of code from the internet as reference (http://crab.rutgers.edu/~dhong/cs325/chapter3/PrimeNumber.java).
Whole code:
public class Opdracht3 {
public static void main(String[] args) {
int limiet = 200;
int counter = 1;
int testpriem = 3;
boolean isPriem;
while (counter <= limiet) {
isPriem = true;
for (int i = 2; i <= testpriem / 2; i++) {
if (testpriem % i == 0) {
isPriem = false;
break;
}
}
if (isPriem) {
System.out.println(counter + ": " + testpriem);
counter++;
}
testpriem++;
}
}
}
Below part of code verifies if the number is a composite. If testpriem is composite, then comes out of the loop and starts over. Otherwise, it continues and prints the prime number testpriem.
The problem is here:
for (int i = 2; i <= testpriem / 2; i++) {
if (testpriem % i == 0) {
isPriem = false;
break;
}
}
I tested what happens to i, and one way or another it recognizes the divisor needed to calculate the composite. (With 4 divisor is 2, with 9 divisor is 3, with 221 divisor is 13) But I am flabbergasted as of why.
Any ideas?.
the % or ("remainder") operator in Java divides one operand by another and returns the remainder as its result. And of course if integer x is evenly divisible by another integer y (meaning x/y = some integer z with a remainder of zero), then x can not be prime.
First remember every number able to divide by its half or less. Consider number 7 it is possible divided by 1,2,3 because after 3, if try to divide number by 4 means 4x2 = 8 that is greater than 7. so it is optimum way to find divisor in this way. One more thing every number divided by 1 and number itself. so if number number is divided by 1 or itself then it is called prime so i starts from 2.
now consider testpriem =7 so you will get loop like
for (int i = 2; i <= 7 / 2(i.e 3); i++)
{
if(7 % i == 0)
{
isPriem = false;
break;
}
so first time it checks 7%2=1 so condition false. again check for 7%3 = 1 again condition false. and now this condition full fills here i <= 7 / 2(i.e 3) so loop stopped and it result 7 number is prime
Well, if testpriem % i == 0, it means that i divides testpriem, which means that testpriem is not a prime a number and i, is its first divider. % is the modulo operation, which is the rest of the division.
https://en.wikipedia.org/wiki/Modulo_operation
The break stops the for loop and moves to the next position in the while loop. So it does not restart the for loop for the current tested number.
The break is used for efficiency reasons. You could remove it and the algorithm would still work correctly but slower.

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