I have a line graph with $8,000,000$ points. The X axis goes from $0$ to $7,999,999$ in increments of $1$ and the Y axis is either a $0$ or a $1$. There are no fractions on either axis.
Is there an efficient manner to convert these points into a single continuous function that describes my line?
What is the "time" it would take to create such a function given these 8,000,000 points? Is the time the same for any $8,000,000$ points?
Any tips on where to look/research are also appreciated.
There are many interpolation techniques that you could use. A very simple example would be to use linear splines i.e. connect each data point with a straight-line. This idea can be extended to quadratic, cubic splines.
You could also generate a polynomial of degree $8\times10^6-1$ using Legrange interpolation but I doubt you would want to go this route.
As to the time it would take, the answer is it depends. A more complicated method will take longer as it requires more computation.