Rainfall problem: 

About a year ago when I was applying to jobs for the first time, I had an
interview at a company and they posed the following problem to me, which I
proceeded to bomb.

A year later I went back and came up with a solution, I think this is a good
indicator of my progress in the past year. After some help from
codereview.stackexchange.com/questions/38500/rainfall-problem I am really
happy with the soltuion.

Problem Statement

A group of farmers has some elevation data, and we’re going to help them
understand how rainfall flows over their farmland. We’ll represent the land as
a two-dimensional array of altitudes and use the following model, based on the
idea that water flows downhill:

If a cell’s four neighboring cells all have higher altitudes, we call this
cell a sink; water collects in sinks. Otherwise, water will flow to the
neighboring cell with the lowest altitude. If a cell is not a sink, you may
assume it has a unique lowest neighbor and that this neighbor will be lower
than the cell.

Cells that drain into the same sink – directly or indirectly – are said to be
part of the same basin.

Your challenge is to partition the map into basins. In particular, given a map
of elevations, your code should partition the map into basins and output the
sizes of the basins, in descending order.

Assume the elevation maps are square. Input will begin with a line with one
integer, S, the height (and width) of the map. The next S lines will each
contain a row of the map, each with S integers – the elevations of the S cells
in the row. Some farmers have small land plots such as the examples below,
while some have larger plots. However, in no case will a farmer have a plot of
land larger than S = 5000.

Your code should output a space-separated list of the basin sizes, in
descending order. (Trailing spaces are ignored.)

A few examples are below:

-----------------------------------------
Input:                 Output: 
 3                      7 2
 1 5 2 
 2 4 7 
 3 6 9 

The basins, labeled with A’s and B’s, are: 
 A A B 
 A A B 
 A A A 
-----------------------------------------
Input:                  Output: 
 1                       1
 10 

There is only one basin in this case. 
The basin, labeled with A’s is: 
 A
-----------------------------------------
Input:                  Output:            
 5                       11 7 7
 1 0 2 5 8 
 2 3 4 7 9 
 3 5 7 8 9 
 1 2 5 4 3 
 3 3 5 2 1 

The basins, labeled with A’s, B’s, and C’s, are: 
 A A A A A 
 A A A A A 
B B A C C 
 B B B C C 
 B B C C C 
-----------------------------------------
Input:                  Output: 
 4                       7 5 4
 0 2 1 3                
 2 1 0 4 
 3 3 3 3 
 5 5 2 1 

The basins, labeled with A’s, B’s, and C’s, are: 
 A A B B 
 A B B B 
 A B B C 
 A C C C
-----------------------------------------