Develop Reference

How would I add two int that are in the same array to each other and convert them into an int. In the Luhn Algorithm

I am trying to add two parts of an array together to go into an int value. I am using Luhn algorithm to figure out of a credit card is a valid credit card. We are only using 6 digit credit card's just to make sure no one enter's a real credit card number. The part I am confused on is when I go to split a number that is above 10 and add it together. Example if the algorithm was to give me 12 I would need to separate it into 1 and 2 and then add them together to equal 3. I believe I am splitting it currently in the code but when I go to add them together I get some number that makes no since. here is a section of the code with some notes about it.
I have printed out numbers in certain places to show myself what is going on in certain places. I have also added in some comments that say that either the number that is printed out is what is expected, and some comments for when there isn't something I expected
int[] cardNumber = new int[]{ 1,2,3,4,5,5};
int doubleVariablesum = 0;
int singleVariablesum = 0;
int totalSum = 0;
int cutOffVar = 0;
String temp2;
for (int i = cardNumber.length - 1; i >= 0;) {
int tempSum = 0;
int temp = cardNumber[i];
temp = temp * 2;
System.out.println("This is the temp at temp * 2: " + temp);
temp2 = Integer.toString(temp);
if (temp2.length() == 1) {
System.out.println("Temp2 char 0: "+ temp2.charAt(0));
// this prints out the correct number
// Example: if there number should be 4 it will print 4
tempSum = temp2.charAt(0);
System.out.println("This is tempSum == 1: " + tempSum);
// when this goes to add temp2.charAt(0) which should be 4 it prints out //something like 56
} else {
System.out.println("TEMP2 char 0 and char 1: " + temp2.charAt(0) + " " + temp2.charAt(1));
// this prints out the correct number successfully spited
tempSum = temp2.charAt(0) + temp2.charAt(1);
System.out.println("This is tempSum != 1: " + tempSum);
// but here it when I try to add them together it is giving me something
// like 97 which doesn't make since for the numbers I am giving it
}
doubleVariablesum = tempSum + doubleVariablesum;
System.out.println("This is the Double variable: " + doubleVariablesum);
System.out.println();
i = i - 2;
}

Since you are converting the number to a string to split the integer, and then trying to add them back together. You're essentially adding the two characters numerical values together which is giving you that odd number. You would need to convert it back to an integer, which you can do by using
Integer.parseInt(String.valueOf(temp2.charAt(0)))

When adding char symbols '0' and '1' their ASCII values are added - not numbers 0 and 1.
It is possible to use method Character::getNumericValue or just subtract '0' when converting digit symbol to int.
However, it is also possible to calculate sum of digits in a 2-digit number without any conversion to String and char manipulation like this:
int sum2digits = sum / 10 + sum % 10; // sum / 10 always returns 1 if sum is a total of 2 digits

Seems like charAt() type casts into integer value, but the ascii one. Hence for the characters '0' and '1', the numbers 48 and 49 are returned resulting in a sum of 97. To fix this, you could just assign temp2 to (temp / 10) + (temp % 10). Which actually splits a two digit integer and adds their sum.

You need to be aware of the following when dealing with char and String
Assigning the result of charAt(index) to an int will assign the ASCII value and not the actual integer value. To get the actual value you need to String.valueOf(temp2.charAt(0)).
The result of concatenating chars is the sum of the ASCII values.
eg if char c = '1'; System.out.println(c + c); will print "98" not "11".
However System.out.println("" + c + c); will print "11". Note the "" will force String concatenation.

Calculating how many times a number is added to itself until it reaches an arbitrary value?

Considering two variables:
"n" is any arbitrary value.
"i" is the number of times a value is increased in a sum before it reaches the value of "n".
So for instance if the value n = 344 is chosen, then i = 26 because:
26 + 25 + 24 + ... + 3 + 2 + 1 = 351
26 is how many times the variable "i" gets added together in a descending order before it either is equal to n = 344 or the first time it surpasses.
public class Trstuff{
public static void main (String [] arg) {
int n = 4;
int i = computeIndex(n);
System.out.print(i);
}
public static int computeIndex(int n) {
int i = 1;
int sum = 0;
for(i = 1; sum <= n; i++) {
sum = sum + i;
}
return i;
}
}
My goal is to choose any "n" value and then have the program return the variable "i" to me.
As my program stands, I thought it should be correct, but somehow it's not. Here is the example with n = 4.
The result should be that "i = 3" because:
1 + 2 = 3
1 + 2 + 3 = 6
So the ascending value of "i" in the loop is added 3 times before the loop supposedly should stop because of the expression "sum <= n" in the loop.
However, when I run the program it returns the value 4 instead. I simply cannot figure out what is wrong and why my program gives me 4 instead of the correct answer, 3?

Read the for loop as follows:
for every value of i while sum smaller or equal to n, add i to sum and increment i
The last part of the line and increment i is executed after the sum of sum + i, but before the next check which checks if sum is smaller or equal to n, with as result that i always is one larger than expected.
The solution could be to use a different exit (different solutions exist):
public static int computeIndex(int n) {
int i = 1;
int sum = 0;
while true {
sum = sum + i;
if sum<n {
i++;
} else break;
}
return i;
}

the sum of p consecutive integers starting at 1 is p*(p+1)/2
so basically you need to solve x^2+x-2*n = 0, with solution
x = 0.5*(sqrt(1+8n)-1)

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;
}
}
}
}

How to write a program that reverses a number a user inputs

The homework problem is the user enters a number. Then you have to write a program that reverses that order. So if the user enters 7364 you have to write a program that presents 4637 on the next line. I think I've figured out the solution but I'm not sure how to write it.
Since the last number is the first number in reverse order that means that if someone enters 7364 that means i want to get 4637. I have to write a program that multiplies 4 by 1000, 6 by 100, 3 by 10 and 7 by 1 then add those up to get 4637. I'm not not 100% sure how to do it. What's messing me up is how to multiply one number by 1000, the next by 100, the next by 10 and the next by 1 then add those up.
import acm.program.*;
public class ReverseNumber extends ConsoleProgram{
public void run(){
int n = readInt("please enter any positive number: ");
int total = 0;
while ( n > 0){
total = total + n % 10; <----?
n = n * 1000; <----?
}
println("the reverse order is" + total);
}
}

The easiest way to do it using library.
System.out.println(new StringBuilder(String.valueOf(i)).reverse());

Try this:
while( n != 0 )
{
reverse = reverse * 10;
reverse = reverse + n%10;
n = n/10;
}
Logic is to get a single digit in each iteration starting from unit place, until all digits are encountered.
n is the input no.
reverse is the variable where reverse of n is stored after while is finished.
% operator when used with 10, gives you the digit at unit place.
/ operator when used with 10, goves you all the digits except the digit at unit place.
When n = 7364 and reverse = 0
in 1st iteration, loop will look like:
while(7364 != 0) // true
{
reverse = 0 * 10; // reverse = 0
reverse = 0 + 7364%10 // reverse = 4
n = 7364/10 // n = 736
}
in 2nd iteration:
while(736 != 0) // true
{
reverse = 4 * 10; // reverse = 40
reverse = 40 + 736%10 // reverse = 46
n = 736/10 // n = 73
}
in 3rd iteration:
while(73 != 0) // true
{
reverse = 46 * 10; // reverse = 460
reverse = 460 + 73%10 // reverse = 463
n = 73/10 // n = 7
}
in 4th iteration:
while(7 != 0) // true
{
reverse = 463 * 10; // reverse = 4630
reverse = 4630 + 7%10 // reverse = 4637
n = 7/10 // n = 0
}
in 5th iteration:
while(0 != 0) // false and loop ends
{
...
}
and we have reverse = 4637.

Well, to reverse the number the simplest solution would be to convert it to a string get the first letter and append it at the end until you reach the last letter or number in this case. Also, you can do pretty much the same with the multiplication part. Get the numbers one by one as a string convert it back to int then multiply and add.
EDIT: if you cant do it using strings. here is a somewhat mathematical solution.
int num = 123456; // any number than you want to reverse
string revnum = ''; // the reversed number
int temp = 0;
do {
temp= (temp*10)+(num%10);
num = (int)(num/10);
}while(num>0){
revnum = revnum + temp;
}

This should work:
total = 0;
while (n > 0) {
total = total * 10 + n % 10;
n = n / 10;
}
println("the reverse order is " + total);
You don't have to know how many digits there are in the original number, you're iterating through all of them anyway. Here's what happens:
When you get a new digit (n % 10), you multiply the result by 10 and add it to it. This way, you offset the digits in the result.
Then you eliminate the last digit (the one you added in the step before) from the original number by doing n / 10.

Do you have to represent it with an int? A String seems more natural?
If you stick with the int, you need to keep track of the factor to multiply with: which means another variable that you multiply by 10 each iteration.

Convert the Int to String, then put it in a StringBuffer
then use .reverse()
I wouldn't want to add the codes because there are many samples for this.
Like this one.
After that, you could convert it again to String.

public class value{
public static void main(String[] args){
int n=Integer.parseInt(args[0]);
int t=0;
do{
t=n%10;
System.out.print(t);
n=n/10;
}while(n>0);
}
}

Algorithm to find all permutations of a given N with condition

I am designing a program to print all permutations of a given N such that the each digit should be greater than the next digit.
For Example
if N=3:
output should be 123,456,789,134,145,178,189 etc...
Initial Design:
Generate all possible permutations
Pass the generated permutation to a digit extraction function which checks for the condition
Print out the result
This is a very naive algorithm. But I do not know the implementation/initial design because of the dynamic size of N.

Since N will always be less than 10, i've used recursion
Call the function as f(3,0,0)
public static void f(int N,int digit,int num)
{
if(N > 0 )
{
for(int d = digit + 1; d < 11 - N; d++) // earlier d < 10, see comments
{
f(N-1,d,num * 10 + d);
}
}else {
System.out.println(num); //add it to a list or whatever
}
}
Output:
123
124
...
678
679
689
789

The most straightforward way to do this is with recursion. Suppose you've generated the first n digits and the last digit generated is i. You have N - n digits left to generate and they must start with i + 1 or higher. Since the last digit can be no more than 9, the next digit can be no more than 10 - (N - n). This gives the basic rule for recursion. Something like this (in Java) should work:
void generate(int N) {
int[] generated = new int[N];
generate(generated, 0);
}
void generate(int[] generated, int nGenerated) {
if (nGenerated == generated.length) {
// print the generated digits
for (int g : generated) {
System.out.print(g);
}
System.out.println();
return;
}
int max = 10 - (generated.length - nGenerated);
int min = nGenerated == 0 ? 1 : (generated[nGenerated - 1] + 1);
for (int i = min; i <= max; ++i) {
generated[nGenerated] = i;
generate(generated, nGenerated + 1);
}
}

Just generate them in lexicographic order:
123
124
125
...
134
135
...
145
...
234
235
...
245
...
345
This assumes you have digits at most 5. For larger bound B, just keep going. Some simple code to do this is:
nextW = w;
for (int i=n-1; i>=0; --i) {
// THE LARGEST THE iTH DIGIT CAN BE IS B-(n-i-1)
// OTHERWISE YOU CANNOT KEEP INCREASING AFTERWARDS
// WITHOUT USING A NUMBER LARGER THAN B
if w[i]<B-(n-i-1) {
// INCREMENT THE RIGHTMOST POSITION YOU CAN
nextW[i] = w[i]+1;
// MAKE THE SEQUENCE FROM THERE INCREASE BY 1
for (int j=i+1; j<N; ++j) {
nextW[j] = w[i]+j-i+1;
}
// VOILA
return nextW;
}
}
return NULL;
Start with w = [1,2,3,...,N]; (easy to make with a for loop), print w, call the function above with w as an input, print that, and continue. With N = 3 and B = 5, the answer will be the above list (without the ... lines).
If there is no bound B, then you're SOL because there are infinitely many.
In general, you are computing the Nth elementary symmetric function e_N.