The pyramid of glasses

Problem

Dmitri, the waiter at the wedding, stacks glasses into a pyramid: one on top (row 0), two below it and so on; row r has r + 1 glasses, numbered from the left starting at 0, and there are always rows to spare.

He pours punch glassfuls of punch on top (a whole number, 0 or more). Each glass holds 1, and anything over 1 spills half and half: glass pos in a row pours into glasses pos and pos + 1 of the row below. A glass that is not full spills nothing.

The couple will toast with glass pos of row row (0 <= pos <= row). Return how full it gets, as a decimal from 0 to 1: 0 if nothing reaches it and 1 if it ends up full, even if more falls into it.

With 4 glassfuls poured, the top glass keeps 1 and spills 3: each glass in row 1 gets 1.5, keeps 1 and spills 0.5. In row 2, the middle one gets 0.25 from each side and ends at 0.5, and the ones on the edges get 0.25 each. With row 2 and pos 1 you return 0.5.

Examples

• The example

  4, 2, 1 → 0.5

• A glass on the edge

  4, 2, 0 → 0.25

• Half and half

  2, 1, 0 → 0.5

• The top one is never more than full

  5, 0, 0 → 1

• No punch yet

  0, 0, 0 → 0

• A glass filled exactly spills nothing

  1, 1, 1 → 0

Besides these, the challenge has hidden tests that are revealed when you submit your solution.

You start with this

def fill_level(punch, row, pos):
    pass

function fillLevel(punch, row, pos) {
}