Combination under constrained situation with a condition

asked 2020-07-05 13:36:40 -0500

sriram gravatar image

updated 2020-07-11 20:55:24 -0500

slelievre gravatar image

Step 1: I want to take a number n as input from user

Step 2: We form the set S consisting of elements from 0 to n*(2^{n-1})

Step 3: Now I pick each possible two-element subsets of S and store it in P.

Step 4: Now I need to pick n*(2^{n-1}) two-element subsets from P such that each number that occurs in that set occurs exactly n times neither less nor more and put them all in a list.

Example

n = 2
n*(2^{n-1}) = 2*(2^{2-1}) = 4
S = {0,1,2,3,4}
p = {(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)}

Step 4 One element which satisfies condition of step 4; HERE n = 2.

{(0,1),(1,2),(2,3),(0,3)} which has 2*(2^{n-1}) = 2*(2^{2-1}) = 4 elements.

Now see in the above set

  • 0 occurred n=2 times only in (0,1) and (0,3) only
  • 1 occurred n=2 times only in (0,1) and (1,2) only
  • 2 occurred n=2 times only in (1,2) and (2,3) only
  • 3 occurred n=2 times only in (2,3) and (0,3) only

Similarly we may get for {(0,1),(1,4),(4,2),(2,0)} we can easily verify like above.

Now based on n the number of elements size etc will vary.

Kindly help if possible any one.

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