Given a bitstring generate all bitstring with n flipped bits












1














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







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    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







    share|cite|improve this question

























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      1








      1







      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







      share|cite|improve this question













      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






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      asked 2 days ago









      John Smith

      1133




      1133






















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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






          share|cite|improve this answer





















          • Cool stuff! Thank you.
            – John Smith
            2 days ago











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          1 Answer
          1






          active

          oldest

          votes








          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          2














          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






          share|cite|improve this answer





















          • Cool stuff! Thank you.
            – John Smith
            2 days ago
















          2














          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






          share|cite|improve this answer





















          • Cool stuff! Thank you.
            – John Smith
            2 days ago














          2












          2








          2






          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






          share|cite|improve this answer












          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







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 2 days ago









          Albert Hendriks

          1,371429




          1,371429












          • Cool stuff! Thank you.
            – John Smith
            2 days ago


















          • Cool stuff! Thank you.
            – John Smith
            2 days ago
















          Cool stuff! Thank you.
          – John Smith
          2 days ago




          Cool stuff! Thank you.
          – John Smith
          2 days ago


















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