Given a bitstring generate all bitstring with n flipped bits
$begingroup$
For an algorithm I need to be able to iterate over all bit strings where $k$ bits are flipped given a bit string with length $n$ and $n geq k$. For instance let's say I have the bit string $1001$ and I want to have all bit strings with $2$ bits flipped. That should result in the following bit strings:
1010
1100
1110
0000
0011
0101
So given a bit string of length $n$ and where $k$ bits will be flipped the result will be $binom{n}{k}$ bit strings. Is there an efficient way to generate all of them? The bit strings I have as input are just unsigned integers so I can use bit twiddling!
algorithms combinatorics bit-manipulation
asked Dec 27 '18 at 12:00
John SmithJohn Smith
1184
$endgroup$
add a comment |
$begingroup$
For an algorithm I need to be able to iterate over all bit strings where $k$ bits are flipped given a bit string with length $n$ and $n geq k$. For instance let's say I have the bit string $1001$ and I want to have all bit strings with $2$ bits flipped. That should result in the following bit strings:
1010
1100
1110
0000
0011
0101
So given a bit string of length $n$ and where $k$ bits will be flipped the result will be $binom{n}{k}$ bit strings. Is there an efficient way to generate all of them? The bit strings I have as input are just unsigned integers so I can use bit twiddling!
algorithms combinatorics bit-manipulation
asked Dec 27 '18 at 12:00
John SmithJohn Smith
1184
$endgroup$
add a comment |
$begingroup$
For an algorithm I need to be able to iterate over all bit strings where $k$ bits are flipped given a bit string with length $n$ and $n geq k$. For instance let's say I have the bit string $1001$ and I want to have all bit strings with $2$ bits flipped. That should result in the following bit strings:
1010
1100
1110
0000
0011
0101
So given a bit string of length $n$ and where $k$ bits will be flipped the result will be $binom{n}{k}$ bit strings. Is there an efficient way to generate all of them? The bit strings I have as input are just unsigned integers so I can use bit twiddling!
algorithms combinatorics bit-manipulation
asked Dec 27 '18 at 12:00
John SmithJohn Smith
1184
$endgroup$
For an algorithm I need to be able to iterate over all bit strings where $k$ bits are flipped given a bit string with length $n$ and $n geq k$. For instance let's say I have the bit string $1001$ and I want to have all bit strings with $2$ bits flipped. That should result in the following bit strings:
1010
1100
1110
0000
0011
0101
So given a bit string of length $n$ and where $k$ bits will be flipped the result will be $binom{n}{k}$ bit strings. Is there an efficient way to generate all of them? The bit strings I have as input are just unsigned integers so I can use bit twiddling!
algorithms combinatorics bit-manipulation
algorithms combinatorics bit-manipulation
asked Dec 27 '18 at 12:00
John SmithJohn Smith
1184
asked Dec 27 '18 at 12:00
John SmithJohn Smith
1184
asked Dec 27 '18 at 12:00
John SmithJohn Smith
1184
asked Dec 27 '18 at 12:00
John SmithJohn Smith
1184
asked Dec 27 '18 at 12:00
John SmithJohn Smith
1184
1184
add a comment |
add a comment |
1 Answer
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Let your initial bit string be x.
For all numbers b with k bits set (i.e. where k bits are 1), output x xor b.
Finding all numbers with k bits set is described elsewhere, for example here
answered Dec 27 '18 at 12:38
Albert HendriksAlbert Hendriks
1,391529
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$begingroup$
Let your initial bit string be x.
For all numbers b with k bits set (i.e. where k bits are 1), output x xor b.
Finding all numbers with k bits set is described elsewhere, for example here
answered Dec 27 '18 at 12:38
Albert HendriksAlbert Hendriks
1,391529
$endgroup$
add a comment |
$begingroup$
Let your initial bit string be x.
For all numbers b with k bits set (i.e. where k bits are 1), output x xor b.
Finding all numbers with k bits set is described elsewhere, for example here
answered Dec 27 '18 at 12:38
Albert HendriksAlbert Hendriks
1,391529
$endgroup$
add a comment |
$begingroup$
Let your initial bit string be x.
For all numbers b with k bits set (i.e. where k bits are 1), output x xor b.
Finding all numbers with k bits set is described elsewhere, for example here
answered Dec 27 '18 at 12:38
Albert HendriksAlbert Hendriks
1,391529
$endgroup$
Let your initial bit string be x.
For all numbers b with k bits set (i.e. where k bits are 1), output x xor b.
Finding all numbers with k bits set is described elsewhere, for example here
answered Dec 27 '18 at 12:38
Albert HendriksAlbert Hendriks
1,391529
answered Dec 27 '18 at 12:38
Albert HendriksAlbert Hendriks
1,391529
answered Dec 27 '18 at 12:38
Albert HendriksAlbert Hendriks
1,391529
answered Dec 27 '18 at 12:38
Albert HendriksAlbert Hendriks
1,391529
1,391529
add a comment |
add a comment |
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