How does my professor come up with the recursive case in this algorithm analysis?

Question

My professor gave us the following explanation for the recursive algorithm for finding the permutations of a set of numbers:

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When he has (T(m+1), n-1)) where does that come from? Why is it m+1 and n-1? I'm really confused as to where that comes from.

By the way - tell your professor that that permutation generator is inefficient. You can get `T(m, n) = nT(m + 1, n - 1)` fairly easily (I've got a few variations of such a generator floating around here somewhere). — Bernhard Barker, Oct 15 '13 at 15:19

Ron Teller · Accepted Answer · 2013-10-15T15:18:52.117

3

As he said, m represents the current size of P and n represents the size of S, in each recursive call you remove a number from S and add it to P, thus the size of your current permutation is increased by 1 (m+1) and the number of available numbers to add to the permutation is decreased by 1 (n-1)

Note that it is multiplied by n as you perform this action for each number in S.

edited Oct 15 '13 at 15:18

answered Oct 15 '13 at 15:10

Ron Teller

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score 0 · Answer 2 · answered Oct 15 '13 at 15:09

Note that part that says:

Let m be the length of P and n be the size of S

And then in printperm(P, S), you're calling printperm((P,i), S-{i}).

So, when recursing, we will add one element to P, and remove on element from S.

Thus m will increase by one and n will decrease by one, thus we get T(m+1, n-1)

I hope that helps.

How does my professor come up with the recursive case in this algorithm analysis?

2 Answers2