Finding an index with certain conditions

Question

EDIT: I need to find out an index i which depends on certain conditions and I'm not able to implement it. I have a list (time points) $t_i$ and two constants $a,c$ the length of the list $t_i$ is $n$.

So now I want to find the index $1 \leq i < n$, which can be found according to $t_{n-i}+a<c<t_{n-(i+1)}$ where $t_0:=\infty$.

For example I know that i=5in this example, but I would like to have a function which tells me that:

c = 0.07875`
a = 0.01125`
ti = {0.056249999999999994`, 0.045`, 0.03375`, 0.0225`, 0.01125`, 0.`}
n=6

Do you have any tips how to implement it?

Answer 1

 Pick[#, ti[[n - (# - 1)]] + a < c < If[# == n, Infinity, ti[[n - (#)]]] & /@ #]&[Range[Length[ti]]]

or

 Select[Range[Length[ti]], ti[[n - (# - 1)]] + a < c < If[# == n, Infinity, ti[[n - (#)]]] &]   
 (* {6} *)

Answer 2

I'm really not sure I understand your question but maybe by pure luck I'll hit upon something that helps you.

c = 0.07875`
a = 0.01125`
ti = {0.056249999999999994`, 0.045`, 0.03375`, 0.0225`, 0.01125`, 0.`};

AppendTo[ti, ∞]

Position[
 # + a < c < #2 & @@@ Partition[ti, 2, 1],
 True
]

{{6}}

Answer 3

Can create a large surrogate for infinity and use a zero-order interpolation.

inf = 10.^10;

func = Interpolation[
   Transpose[{Prepend[data, inf], Range[Length[data], 0, -1]}]
   , InterpolationOrder -> 0];

Exampless:

c = 0.07875`;
a = 0.01125`;

func[.04]

(* Out[122]= 4. *)

func[a + c]

(* Out[123]= 6. *)

For large data sets this method will be generally faster than linear search approaches. For example, try it on

data2 = Accumulate[RandomReal[1, 10^6]];