A recurrence relation is given by
P(1) := 1 P(n+1) := exp(1) - (n+1)*P(n)
Write a function that, given an integer n, returns P(n). The n will be smaller than 100 in all test-suite problems and an absolute precision of 10*eps (~2e-15, i.e. almost machine precision) is required.
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Problem Comments
2 Comments
Franck Dernoncourt
on 31 Jan 2012
Maybe you should specify the required precision in the problem description.
Tomasz
on 31 Jan 2012
OK, I added a sentence, thanks.
Solution Comments
1 player likes this solution
1 Comment
Aurelien Queffurust
on 24 Jul 2012
different matlab fnction used to solve this problem
1 Comment
Aurelien Queffurust
on 24 Jul 2012
lol ! need a translator for this solution!
2 Comments
@bmtran
on 31 Jan 2012
This solution should provide minimal rounding error since it's done in an essentially symbolic domain and then evaluated at the very end, but it doesn't satisfy the test cases. *sigh*
Tomasz
on 31 Jan 2012
The sequence is strictly positive. (Not easy to see, but true). If your pn's get negative at some higher n, you still have the roundoff problem. It would be indeed avoided if the integer calculation within the loop was exact, but the numbers quickly become larger than the 48bit mantissa of a double.
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