How to indicate intersection points on graph?

Question

I am using Insertion and Merge sort and trying to indicate the intersection point on the graph below. I found a possible solution on rosettacode, but a bit confusing for a newbie like me... Where should I look, do you guys know how to indicate it in Julia?

The output would is like

I am trying to show something like this

Answer 1

Your data has some noise, which means there might be more than one intersection point (all close). Assuming no noise, just two monotonically increasing functions, this should work:

    using Plots
    x = 1:5
    y1 = x .+ 5
    y2 = 3x 
    idx = argmin(abs.(y1-y2))
    plot(x, [y1, y2], label=["y1", "y2"], markershape=:circle)
    scatter!([x[idx]], [y1[idx]], label="intersection", markershape=:circle, markersize=10)

Note that this method gives you 1/4 possible points closest to the intersection. The intersection itself is not defined for functions only defined from discrete points. By changing the order of y1 and y2 in the code above you can get all 4 points. For fine enough discretization using one of those 4 points might be good enough for your needs.

A better approximation would be to use those 4 points to fit 2 lines, for y1 and y2, and find the intersection of those two lines analytically (e.g. with the equations y1=m1*x+b1, ...). But I leave this to you ;)