There is a staircase and some person say X
can take 1 step or 2 steps . So how many ways can he take in total to climb up the staircase where there are n
steps in total. Also what will be the minimum steps for him to climb up the staircase ? I think the number of minimum steps would be $\frac{n}{2}$ if $n$ is even and $\frac{n}{2}$ +$1$ if $n$ is odd but not sure about the total number of ways .
Total number of ways and minimum number of steps of going up the stair case?
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$\begingroup$
combinatorics
1 Answers
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Total number of ways to climb the staircase is given recursively as:
T(n) = T(n-1) + T(n-2) for n >= 3.
T(1) = 1
T(2) = 2
The minimum number of steps to climb is n/2 if n is even else [n/2] + 1 where [x] denotes greatest integer less than or equal to x.
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0Oh yeah silly me! – 2012-09-05