Problem 44307. The glass half full

Created by HH

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Identical glasses are placed in a triangular tower structure, such that the top level (L = 1) comprises one glass, the next level down (L = 2) comprises three glasses, the next level down (L = 3) comprises six glasses, and so on.Follow the <a href = "https://imgur.com/a/j9ZZa">link</a> to see a diagram shows the first three levels. The glasses in each levels are represented by the blue circles, while the yellow circles represent the positions of the glasses in the next higher level.Water is poured into the top glass at a constant volumetric flow rate. When the glass is filled, the water starts spilling over and into the glasses below. Note that water only spills outward , meaning that at some point, some glasses will remain empty.Given the volume of a glass in liters, v, the volumetric flow rate in liters per second, u, and an integer, L, representing a level in the glass structure, return the total number of glasses in that level, g, the number of glasses in that level that will be filled with water, f, and the time, in seconds, it would take to fill all "fillable" glasses in that level, t, starting with no water in any of the levels.Example:Input: v = 0.25, u = 0.1, L = 2Output: g = 3, f = 3, t = 10

Identical glasses are placed in a triangular tower structure, such that the top level (L = 1) comprises one glass, the next level down (L = 2) comprises three glasses, the next level down (L = 3) comprises six glasses, and so on.

Follow the <https://imgur.com/a/j9ZZa link> to see a diagram shows the first three levels. The glasses in each levels are represented by the blue circles, while the yellow circles represent the positions of the glasses in the next higher level.

Water is poured into the top glass at a constant volumetric flow rate. When the glass is filled, the water starts spilling over and into the glasses below. Note that *water only spills outward* , meaning that at some point, some glasses will remain empty.

Given the volume of a glass in liters, v, the volumetric flow rate in liters per second, u, and an integer, L, representing a level in the glass structure, return the total number of glasses in that level, g, the number of glasses in that level that will be filled with water, f, and the time, in seconds, it would take to fill all "fillable" glasses in that level, t, starting with no water in any of the levels.

Example:

Input: v = 0.25, u = 0.1, L = 2

Output: g = 3, f = 3, t = 10

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Last Solution submitted on Jan 20, 2023

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Stefan Abendroth on 11 Jan 2023

Glad you aren't asking for the water pouring in the spaces!

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Solution 1656065

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2 Comments

Chris Breshike on 22 Oct 2018

could someone explain the different between g and f in this problem? don't all the glasses get filled in the bottom level?

HH on 23 Oct 2018

Chris, the problem states (in bold font) that "water only spills outward" and therefore not all glasses are necessarily filled.

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Problem 44307. The glass half full

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Problem 44307. The glass half full

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