in reply to Re^3: Speeding permutation counting
in thread Speeding permutation counting

Oh. I see what you mean.

Eg. If of 1000 strings, 500 have a 1 in bit 0, then you know that in the 500500 2-way compares, you would get '00' & '11' 1/4 of the time each and '01' or '10' 1/2 of the time.

But I don't see a way of determining how many '10's relative to the '01's?

And no way to determine which pairs of strings render which values for any given bit, nor a count of the four possible values for any given pair of strings?

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.
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Re^5: Speeding permutation counting
by Limbic~Region (Chancellor) on Jul 20, 2007 at 00:08 UTC
    BrowserUk,
    I am likely misunderstanding the problem. For the sake of simplicity, I am using strings of 1 character. Do I have the correct output for the provided input? 
    string 1: 0
string 2: 1
string 3: 0
string 4: 1
string 5: 0

1 & 2 -> 01 10
1 & 3 -> 00 00
1 & 4 -> 01 10
1 & 5 -> 00 00
2 & 3 -> 10 01
2 & 4 -> 11 11
2 & 5 -> 10 01
3 & 4 -> 01 10
3 & 5 -> 00 00
4 & 5 -> 10 01

Totals

01 = 6
10 = 6
11 = 2
00 = 6

    [download]
    If that is correct, then I think my math approach will work.

    Cheers - L~R

[reply]
[d/l]

      What the OP is calculating is the number of bit pairing (4 values) for each combination of 2 strings.

      Eg: Assuming 32-bit strings, typical values might be: 

      strings: '00'   '01'    '10'    '11'
1 & 2     10      5      12      15
1 & 3      2     17       7       6
1 & 4    
1 & 5 
2 & 3 ....

      [download]

      So the OP wants 4 numbers per pairing of strings, regardless of the number of bits.

      What you would be calculating is 4 numbers per bit position, regardless of the number of strings.

      Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
      "Science is about questioning the status quo. Questioning authority".
      In the absence of evidence, opinion is indistinguishable from prejudice.
[reply]
[d/l]
        BrowserUk,
        See, I told you I was misunderstanding the problem ;-)

        Cheers - L~R

[reply]

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