I came across this in the solution presented by Saurabh Kr Vats at this http://www.careercup.com/question?id=14990323
He says:
# Finally, the sequence could be "rho-shaped." In this
# case, the sequence looks something like this:
#
# x_0 -> x_1 -> ... x_k -> x_{k+1} ... -> x_{k+j}
# ^ |
# | |
# +-----------------------+
#
# That is, the sequence begins with a chain of elements that enters a cycle,
# then cycles around indefinitely. We'll denote the first element of the cycle
# that is reached in the sequence the "entry" of the cycle.
I searched online and reached cycle detection. I could see the rho shaped being formed when we reach the start/end of a cycle and try to go to an element which is not adjacent to it. I did not however understand the representation of the sequence or its usage.
It would be great if someone could explain it with an example.
It means literally in the shape of the Greek letter rho, which is "ρ". The idea is that if you map the values out as a graph, the visual representation forms this shape. You could also think of it as "d" shaped or "p" shaped. But look carefully at the font and notice that the line or stem extends slightly past the loop, while it doesn't on a rho. Rho is a better description of the shape because the loop never exits; i.e., there shouldn't be any lines leading out of the loop. That and mathematicians love Greek letters.
You have some number of values which do not repeat; these form a line or the "stem" of the "letter". The values then enter a loop or cycle, forming a circle or the "loop" of the "letter".
For example, consider the repeating decimals 7/12 (0.5833333...) and 3227/55 (5.81441441444...). If you make your sequence the digits in the number, then you can graph these out to form a rho shape. Let's look at 3227/55.
You can graph it like so:
5 -> 8 -> 1
^ \
/ v
4 <- 4
You can see this forms a "ρ" shape.