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I have a recursive function, and I’m trying to figure out it’s complexity.
denote P(n) – the runtime of the function (when given the parameter n).
I know that : P(n)=n+(n-1)*P(n-1) [p(1)=1]
How can I express P(n) without using P(…) ?
That would be O(nn). Notice that if you start expanding the expression, you’ll get an element with power of n increased by 1 on each iteration. This will be the dominant element so others can be dropped for the O() calculation. For a more formal solution see the link provided by @Max.