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Check whether an specific index has been already used - Bitwise?

I wanna say that I appreciate every contribution on the following problem;
I am currently programming an array shuffler that is shuffling the elements of an array to different randomized positions without changing the instance, so there is no need for revaluating the array field with the returning created array instance (the invocation of that shuffling). I want to create an alternative to other already existing shuffle algorithms like the Fisher-Yates shuffle algorithm, as an experiment. So I tried several operations but I think I am stuck. I could create an array that stores already used indicies and create a random index that has not been used yet (during the iteration of every element within the array that I want to shuffle). But I want to make this way more cleaner. As the bitwise operations could help me, but just with 2^x hexadecimals.
Here is an example on what I want to achieve and what I've already tried, but simplified:
//Integer that holds information on what indices are being used
int used = 0;
//Some indices being used
used |= 3;
used |= 4;
used |= 6;
//Check whether the 2, 4 are used
boolean isUsed2 = (used & 2) != 0; //=> false as 2 is not used?
boolean isUsed4 = (used & 4) != 0; //=> true as 4 is used?
So basically what I do not understand is how I can create an integer, that contains information on what specific values have been used and which have not. So to determine if the index 2 or 0 or 8 have been used yet.
Hope my english was understandable.
Sincerly

You have to right-shift your bitMask by index and bitwise and it with 0x1.
public boolean getBitState(int bitIndex, int bitMask) {
return (bitMask >> bitIndex & 0x1) == 0x1;
}
true = 1, false = 0
Setting a bit...
// returns new bitmask value
public int setBitState(int bitIndex, boolean value, int bitMask) {
if (value) {
return bitMask |= (0x1 << bitIndex);
} else {
return bitMask &= ~(0x1 << bitIndex);
}
}

Using a for loop and charAt(); to print letters of a string in alternating cases

import java.util.*;
public class BugFixes
{
public static void main(String[] args)
{
Scanner in = new Scanner(System.in);
altCaps("Computer Science");
}
static void altCaps(String hi)
{
String hi2 = hi;
int locate = 0;
for(int i = 0; i < hi2.length();i++)
{
if((Character.isLetter(hi2.charAt(locate))))
{
if(hi2.charAt(locate) % 2 == 0)
{
System.out.print(hi2.toLowerCase().charAt(locate));
locate++;
}
else if(hi2.charAt(locate) % 2 == 1)
{
System.out.print(hi2.toUpperCase().charAt(locate));
locate++;
}
}
else if(hi2.charAt(locate) == ' ')
{
System.out.print(" ");
locate++;
}
}
}
}
This is one of the problems that I have on my current lab. I was able to fix a few other mistakes but I can't seem to find this one.
My question is why it is outputting "COMpUtER SCIEnCE"? I don't understand what is happening here and I've been looking through it for an hour now. My goal is to output "CoMpUtEr ScIeNcE"
I thought the (hi2.charAt(locate) % 2 == 0) and vice versa would alternate between the even and odd locations in the string, but I believe I have made a mistake somewhere. I just can't find it.
Using BlueJ V3.1.7
1 year high school Computer Science Experience and currently enrolled in AP Computer Science
Any Tips?

not really. So hi2.charAt(locate) % 2 == 0 is actually checking if the integer value of the character is odd or even, but you want to actually check if the index is odd or even if I get you right. In other words:
hi2.charAt(2) % 2 == 0
Is check if m is odd or even. However, I think you want to check if 2 (the index) is odd or even. I guess from here it's easy to assume that you need to change:
if(hi2.charAt(locate) % 2 == 0)
//...
else if(hi2.charAt(locate) % 2 == 1)
//...
to
if(locate % 2 == 0)
//...
else if(locate % 2 == 1)
//...
This won't give you exactly the output you want, but it's just a matter of inverting the if conditions or the body as you wish. Also, there's no other cases for the operation % 2, meaning you'd only get either an odd or even index, so you could simplify the code by just doing:
if(locate % 2 == 0)
//...
else
//...
Which reads better. Hope this helps!

I would strongly advise refactoring your code to reduce repetative calls, and make inspection of values possible (rather than comparison of function evaluation).
For example:
char currentCharacter = hi2.charAt(locate);
would replace four instances of the function call, and allow you to inspect what the actual value is (rather than what you expect the value to be). This would likely make your error more evident.
Assuming the following values:
hi2 = "Computer Science";
locate = 0;
then it may be worth stepping through the evaluation.
0. hi2.charAt(locate) % 2 == 0
1. "Computer Science".charAt(0) % 2 == 0
2. 'C' % 2 == 0
3. 67 % 2 == 0
4. 1 == 0
5. false
The fundamental problem is that by never assigning your value to a variable, you never take the time to understand what is in it. By assigning it to the variable, you are able to inspect the value using a debugger.
By inspecting the values, we can see that you probably want the mod of 0, not 'C', therefore you probably wanted
0. locate % 2 == 0
1. 0 % 2 == 0
2. 0 == 0
3. true
Bonus
Refactoring your code to reduce repetition, would also highlight other errors. For example, try the following:
assert "CoMpUtEr sCiEnCe".equals(BugFixes.altcaps("Computer Science"));
assert "CoMpUtEr-sCiEnCe 201".equals(BugFixes.altcaps("Computer-Science 201"));
KISS: removal of needless logic would reduce the chance of things going wrong.

For starters, you don't need to reassign the string, or the locate variable, or check if a character is already a character. Just use the iteration integer, if you need it, and the parameter.
Secondly, you're modding the character, not the position.
Anyways, a simple boolean toggle would be easier to understand than modding.
void altCaps(String hi) {
boolean caps = true;
for (char ch : hi.toCharArray()) {
if (ch == ' ') {
System.out.print(ch);
}
else if (Character.isLetter(ch)) {
if (caps) System.out.print(Character.toUpperCase(ch));
else System.out.print(Character.toLowerCase(ch));
caps = !caps; // switch between upper and lower every character
}

check number present in a sequences

I am writing a program which I found on a coding competition website, I have sort of figured out how to solve the problem but, I am stuck on a math part of it, I am completely diluting the problem and showing what I need.
first I need to check if a number is part of a sequence, my sequence is 2*a+1 where a is the previous element in the sequence or 2^n-1 to get nth item in the sequence. so it is 1,3,7,15,31,63...
I don't really want to create the whole sequence and check if a number is present, but I am not sure what a quicker method to do this would be.
Second if I am given a number lets say 25, I want to figure out the next highest number in my sequence to this number. So for 25 it would be 31 and for 47 it would be 63, for 8 it would be 13.
How can i do these things without creating the whole sequence.
I have seen similar questions here with different sequences but I am still not sure how to solve this

Start by finding the explicit formula for any term in your sequence. I'm too lazy to write out a proof, so just add 1 to each term in your sequence:
1 + 1 = 2
3 + 1 = 4
7 + 1 = 8
15 + 1 = 16
31 + 1 = 32
63 + 1 = 64
...
You can clearly see that a_n = 2^n - 1.
To check if a particular number is in your sequence, assume that it is:
x = 2^n - 1
x + 1 = 2^n
From Wikipedia:
The binary representation of integers makes it possible to apply a
very fast test to determine whether a given positive integer x is a
power of two:
positive x is a power of two ⇔ (x & (x − 1)) equals to zero.
So to check, just do:
bool in_sequence(int n) {
return ((n + 1) & n) == 0;
}

As #Blender already pointed out your sequence is essentially 2^n - 1, you can use this trick if you use integer format to store it:
boolean inSequence(int value) {
for (int i = 0x7FFF; i != 0; i >>>= 1) {
if (value == i) {
return true;
}
}
return false;
}
Note that for every elements in your sequence, its binary representation will be lots of 0s and then lots of 1s.
For example, 7 in binary is 0000000000000000000000000000111 and 63 in binary is 0000000000000000000000000111111.
This solution starts from 01111111111111111111111111111111 and use an unsigned bitshift, then compare if it is equal to your value.
Nice and simple.

How to find the next higher number :
For example, we get 19 ( 10011 ) , should return 31 (11111)
int findNext(int n){
if(n == 0) return 1;
int ret = 2; // start from 10
while( (n>>1) > 0){ // end with 100000
ret<<1;
}
return ret-1;
}

How to find the closest value of 2^N to a given input?

I somehow have to keep my program running until the output of the exponent function exceeds the input value, and then compare that to the previous output of the exponent function. How would I do something like that, even if in just pseudocode?

Find logarithm to base 2 from given number => x := log (2, input)
Round the value acquired in step 1 both up and down => y := round(x), z := round(x) + 1
Find 2^y, 2^z, compare them both with input and choose the one that suits better

Depending on which language you're using, you can do this easily using bitwise operations. You want either the value with a single 1 bit set greater than the highest one bit set in the input value, or the value with the highest one bit set in the input value.
If you do set all of the bits below the highest set bit to 1, then add one you end up with the next greater power of two. You can right shift this to get the next lower power of two and choose the closer of the two.
unsigned closest_power_of_two(unsigned value)
{
unsigned above = (value - 1); // handle case where input is a power of two
above |= above >> 1; // set all of the bits below the highest bit
above |= above >> 2;
above |= above >> 4;
above |= above >> 8;
above |= above >> 16;
++above; // add one, carrying all the way through
// leaving only one bit set.
unsigned below = above >> 1; // find the next lower power of two.
return (above - value) < (value - below) ? above : below;
}
See Bit Twiddling Hacks for other similar tricks.

Apart from the looping there's also one solution that may be faster depending on how the compiler maps the nlz instruction:
public int nextPowerOfTwo(int val) {
return 1 << (32 - Integer.numberOfLeadingZeros(val - 1));
}
No explicit looping and certainly more efficient than the solutions using Math.pow. Hard to say more without looking what code the compiler generates for numberOfLeadingZeros.
With that we can then easily get the lower power of 2 and then compare which one is nearer - the last part has to be done for each solution it seems to me.

set x to 1.
while x < target, set x = 2 * x
then just return x or x / 2, whichever is closer to the target.

public static int neareastPower2(int in) {
if (in <= 1) {
return 1;
}
int result = 2;
while (in > 3) {
in = in >> 1;
result = result << 1;
}
if (in == 3) {
return result << 1;
} else {
return result;
}
}

I will use 5 as input for an easy example instead of 50.
Convert the input to bits/bytes, in this case 101
Since you are looking for powers of two, your answer will all be of the form 10000...00 (a one with a certain amount of zeros). You take the input value (3 bits) and calculate the integer value of 100 (3 bits) and 1000 (4 bits). The integer 100 will be smaller then the input, the integer 1000 will be larger.
You calculate the difference between the input and the two possible values and use the smallest one. In this case 100 = 4 (difference of 1) while 1000 = 8 (difference of 3), so the searched answer is 4

public static int neareastPower2(int in) {
return (int) Math.pow(2, Math.round(Math.log(in) / Math.log(2)));
}

Here's the pseudo code for a function that takes the input number and returns your answer.
int findit( int x) {
int a = int(log(x)/log(2));
if(x >= 2^a + 2^(a-1))
return 2^(a+1)
else
return 2^a
}

Here's a bitwise solution--it will return the lessor of 2^N and 2^(N+1) in case of a tie. This should be very fast compare to invoking the log() function
let mask = (~0 >> 1) + 1
while ( mask > value )
mask >> 1
return ( mask & value == 0 ) ? mask : mask << 1

Circular increment: Which is "better"?

When you have a circular buffer represented as an array, and you need the index to wraparound (i.e., when you reach the highest possible index and increment it), is it "better" to:
return (++i == buffer.length) ? 0: i;
Or
return ++i % buffer.length;
Has using the modulo operator any drawbacks? Is it less readable than the first solution?
EDIT:
Of course it should be ++i instead of i++, changed that.
EDIT 2:
One interesting note: I found the first line of code in ArrayBlockingQueue's implementation by Doug Lea.

Update: OP has admitted in a comment that it should have been pre-increment instead. Most of the other answers missed this. There lies proof that the increment in this scenario leads to horrible readability: there's a bug, and most people couldn't see it.
The most readable version is the following:
return (i == buffer.length-1) ? 0 : i+1;
Using ++ adds unnecessary side effect to the check (not to mention that I strongly feel that you should've used pre-increment instead)
What's the problem with the original code? Let's have a look, shall we?
return (i++ == N) ? 0 : i; // OP's original, slightly rewritten
So we know that:
i is post-incremented, so when i == N-1 before the return statement, this will return N instead of wrapping to 0 immediately
Is this intended? Most of the time, the intent is to use N as an exclusive upper bound
The variable name i suggests a local variable by naming convention, but is it really?
Need to double check if it's a field, due to side-effect
In comparison:
return (i == N-1) ? 0 : i+1; // proposed alternative
Here we know that:
i is not modified, doesn't matter if it's local variable or field
When i == N-1, the returned value is 0, which is more typical scenario
The % approach
Alternatively, you can also use the % version as follows:
return (i+1) % N;
What's the problem with %? Well, the problem is that even though most people think it's the modulo operator, it's NOT! It's the remainder operator (JLS 15.17.3). A lot of people often get this confused. Here's a classic example:
boolean isOdd(int n) {
return (n % 2) == 1; // does this work???
}
That code is broken!!! It returns false for all negative values! The problem is that -1 % 2 == -1, although mathematically -1 = 1 (mod 2).
% can be tricky, and that's why I recommend the ternary operator version instead. The most important part, though, is to remove the side-effect of the increment.
See also
Wikipedia: modulo operation

Don't ask me to choose between two options which both contain postincrement (*) mixed with expression evaluation. I'll say "none".
(*) Update: It was later fixed to preincrement.

Wouldn't the i++ % buffer.length version have the drawback that it keeps incrementing i, which could lead to it hitting some sort of max_int/max_long/max_whatever limit?
Also, I would split this into
i = (i++ == buffer.length) ? 0 : i;
return i;
since otherwise you'd most likely have a bug.

The first one will give you an ArrayIndexOutOfBoundsException because i is never actually reset to 0.
The second one will (probably) give you an overflow error (or related undesirable effect) when i == Integer.MAX_VALUE (which might not actually happen in your case, but isn't good practice, IMHO).
So I'd say the second one is "more correct", but I would use something like:
i = (i+1) % buffer.length;
return i;
Which I think has neither of the two problems.
I went ahead and tested everyone's code, and was sad to find that only one of the previous posts (at the time of this post's writing) works. (Which one? Try them all to find out! You might be surprised!)
public class asdf {
static int i=0;
static int[] buffer = {0,1,2};
public static final void main(String args[]){
for(int j=0; j<5; j++){
System.out.println(buffer[getIndex()]);
}
}
public static int getIndex(){
// return (++i == buffer.length) ? 0: i;
// return ++i % buffer.length;
// i = (i++ == buffer.length) ? 0 : i;
// return i;
// i++;
// if (i >= buffer.length)
// {
// i = 0;
// }
// return i;
// return (i+1 == buffer.length) ? 0 : i+1;
i = (i+1) % buffer.length;
return i;
}
}
Expected output is:
1
2
0
1
2
Apologies in advance if there's a coding error on my part and I accidentally insult someone! x.x
PS: +1 for the previous comment about not using post-increment with equality checks (I can't actually upmod posts yet =/ )

I prefer the condition approach even if we use unsigned type, modulo operation has drawbacks. Using modulo has a bad side effect when the number tested rolls back to zero
Example:
255 % 7 == 3
So if you use byte (unsigned char) for example, when the number roll after 255 (i.e. zero), it will not result to 4. Should result to 4 (when 256 % 7), so it rotates correctly. So just use testing(if and ternary operator) constructs for correctness
If for achieving performance, and if the number is multiple of 2 (i.e. 2, 4, 8, 16, 32, 64, ...), use & operator.
So if the buffer length is 16, use:
n & 15
If buffer length is 64, use 63:
n & 63
Those rotate correctly even if the number goes back to zero. By the way, if the number is multiple of 2, even the modulo/remainder approach would also fit the bill, i.e. it will rotate correctly. But I can hazard a guess that & operation is faster than % operation.

I think the second solution has the clear advantage that it works, whereas the first does not. The first solution will always return zero when i becomes bigger than buffer.length because i is never reset.
The modulo operator has no drawbacks.

Surely it would be more readable to use an if:
i++;
if (i >= buffer.length)
{
i = 0;
}
return i;
Depends a bit if buffer.length ever changes.

This is very subjective and depends on what your colleagues are used to see. I would personally prefer the first option, as it expresses explicitly what the code does, i.e. if the buffer length is reached, reset to 0. You don't have to perform any mathematical thinking or even know what the modulo does (of course you should! :)

Personally, I prefer the modulo approach. When I see modulo, I immediately think of range limiting and looping but when I see the ternary operator, I always want to think more carefully about it simply because there are more terms to look at. Readability is subjective though, as you already pointed out in your tagging, and I suspect that most people will disagree with my opinion.
However, performance is not subjective. Modulo implies a divison operation which is often slower than a comparison against zero. Obviously, this is more difficult to determine in Java since we're not compiling to native code until the jitter kicks in.
My advice would be write which ever you feel is most appropriate (so long as it works!) and get a colleague (assuming you have one) to asses it. If they disagree, ask another colleague - then go with the majority vote. #codingbydemocracy

It is also worth noting, that if our buffer has length of power of 2 then very efficient bit manipulation will work:
idx = (idx + 1) & (length - 1)

You can use also bit manipulation:
idx = idx & ((idx-length)>>31)
But it's not faster than the if-variant on my machine.
Here is some code to compare running time in C#:
Stopwatch sw = new Stopwatch();
long cnt = 0;
int k = 0;
int modulo = 10;
sw.Start();
k = 0;
cnt = 0;
for ( int j=0 ; j<100000000 ; j++ ) {
k = (k+1) % modulo;
cnt += k;
}
sw.Stop();
Console.WriteLine( "modulo cnt=" + cnt.ToString() + " " + sw.Elapsed.ToString() );
sw.Reset();
sw.Start();
k = 0;
cnt = 0;
for (int j = 0; j < 100000000; j++) {
if ( ++k == modulo )
k = 0;
cnt += k;
}
sw.Stop();
Console.WriteLine( "if cnt=" + cnt.ToString() + " " + sw.Elapsed.ToString() );
sw.Reset();
sw.Start();
k = 0;
cnt = 0;
for (int j = 0; j < 100000000; j++) {
++k;
k = k&((k-modulo)>>31);
cnt += k;
}
sw.Stop();
Console.WriteLine( "bit cnt=" + cnt.ToString() + " " + sw.Elapsed.ToString() );
The Output:
modulo cnt=450000000 00:00:00.6406035
if cnt=450000000 00:00:00.2058015
bit cnt=450000000 00:00:00.2182448

I prefer the modulo operator for the simple reason it is shorter. And any program should be able to dream in modulo since it is almost as common as a plus operator.