Sunday Times Teaser 3051- Shipping Forecast

by BRG on March 14, 2021

by Colin Vout

Published Sunday March 14 2021 (link)

Here is the shipping forecast for the regions surrounding our island.

First, the coastal regions.

\[\begin{array}{|l|c|c|c|c|c|}\hline \mathbf{Region} & \mathbf{Direction} & \mathbf{Strength} & \mathbf{Sea\;State} & \mathbf{Weather}& \mathbf{Visibility} \\
\hline \mathbf{Hegroom} & E & 6 & rough & drizzle & moderate \\
\hline \mathbf{Forkpoynt} & E & 7 & rough & rain & good \\
\hline \mathbf{Angler} & NE & 7 & rough & drizzle & moderate \\
\hline \mathbf{Dace} & NE & 7 & smooth & drizzle & moderate \\
\hline \end{array}\]

Now, the offshore regions.

\[\begin{array}{|l|c|c|c|c|c|}\hline \mathbf{Region} & \mathbf{Direction} & \mathbf{Strength} & \mathbf{Sea\;State} & \mathbf{Weather}& \mathbf{Visibility} \\
\hline \mathbf{Back} & E & gale\;8 & rough & rain & moderate \\
\hline \mathbf{Greigh} & E & 7 & smooth & drizzle & poor \\
\hline \mathbf{Intarsia} & SE & 7 & rough & drizzle & moderate \\
\hline \mathbf{Catter} & E & gale\;8 & high & drizzle & moderate \\
\hline \mathbf{Eighties} & E & 7 & rough & fair & good \\
\hline \end{array}\]

In this forecast, no element jumps from one extreme to another between adjacent regions. The extremes are:

\[\begin{array}{|l|c|c|}
\hline Wind\;Direction & SE & NE \\
\hline Wind\;Strength & 6 & gale\; 8 \\
\hline Sea State & smooth & high \\
\hline Weather & fair & rain \\
\hline Visibility & good & poor \\
\hline \end{array}\]

Each region adjoins four others (meeting at just one point doesn’t count).

Which of the regions does Angler touch?

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Brian Gladman permalink


from itertools import permutations

# adjacency maps for coastal regions 0..3 and offshore regions 4..8

adj = ( (1, 3, 4, 7), (0, 2, 4, 5), (1, 3, 5, 6), (2, 0, 6, 7),
        (0, 1, 5, 8), (1, 2, 4, 8), (2, 3, 7, 8), (3, 0, 8, 6),
        (4, 5, 6, 7)      # credit: John Crabtree
)

# adj = ( (1, 3, 6, 8), (0, 2, 4, 6), (1, 3, 4, 5), (0, 2, 5, 8),
#         (1, 2, 6, 7), (2, 3, 7, 8), (0, 1, 4, 7), (4, 5, 6, 8),
#         (0, 3, 5, 7) )  # credit: Jim Randell

# map names to the weather forecasts (low, mid high) ==> (0, 1, 2)
n2wf = {
  'A' : (2, 1, 1, 1, 1), 'B' : (1, 2, 1, 2, 1),
  'C' : (1, 2, 2, 1, 1), 'D' : (2, 1, 0, 1, 1),
  'E' : (1, 1, 1, 0, 0), 'F' : (1, 1, 1, 2, 0),
  'G' : (1, 1, 0, 1, 2), 'H' : (1, 0, 1, 1, 1),
  'I' : (0, 1, 1, 1, 1),
}

# check a map to ensure that adjacent regions don't have opposite 
# extremes for any of the weather items in their reports
def check(m):
  # consider each region that has been assigned a name
  for i, n in m.items():
    # consider report items that contain an extreme 
    for j, w in enumerate(n2wf[n]):
      if w in {0, 2}:
        # consider the adjacent regions ...
        for k in adj[i]:
          # ... if they have been assigned a name
          if k in m.keys():
            ww = n2wf[m[k]][j]
            # the mapping fails if any adjacent regions have
            # the opposite exterme of the weather item
            if w + ww == 2:
              return False
  return True

# map off-shore regions 4..8 to off-shore names
for p in permutations("BCEGI"):
  r2no = dict(zip((4, 5, 6, 7, 8), p))
  # check that the mapping is valid
  if check(r2no):
    # map coastal regions 0..3 to coastal names
    for q in permutations("ADFH"):
      # complete the map and check its validity
      r2nc = r2no.copy()
      r2nc.update(zip((0, 1, 2, 3), q))
      if check(r2nc): 

        # output the regions adjacent to A and the map from regions to names
        an2r = tuple(ar for ar, nm in r2nc.items() if nm == 'A')[0]
        nadj = ''.join(sorted(r2nc[x] for x in adj[an2r]))
        r2ns = ', '.join(f"{ar} -> {r2nc[ar]}" for ar in sorted(r2nc.keys()))
        print(f"{nadj} ({r2ns})")

from itertools import permutations

# adjacency maps for coastal regions 0..3 and offshore regions 4..8

adj = ( (1, 3, 4, 7), (0, 2, 4, 5), (1, 3, 5, 6), (2, 0, 6, 7),

(0, 1, 5, 8), (1, 2, 4, 8), (2, 3, 7, 8), (3, 0, 8, 6),

(4, 5, 6, 7) # credit: John Crabtree

)

# adj = ( (1, 3, 6, 8), (0, 2, 4, 6), (1, 3, 4, 5), (0, 2, 5, 8),

# (1, 2, 6, 7), (2, 3, 7, 8), (0, 1, 4, 7), (4, 5, 6, 8),

# (0, 3, 5, 7) ) # credit: Jim Randell

# map names to the weather forecasts (low, mid high) ==> (0, 1, 2)

n2wf = {

'A' : (2, 1, 1, 1, 1), 'B' : (1, 2, 1, 2, 1),

'C' : (1, 2, 2, 1, 1), 'D' : (2, 1, 0, 1, 1),

'E' : (1, 1, 1, 0, 0), 'F' : (1, 1, 1, 2, 0),

'G' : (1, 1, 0, 1, 2), 'H' : (1, 0, 1, 1, 1),

'I' : (0, 1, 1, 1, 1),

}

# check a map to ensure that adjacent regions don't have opposite

# extremes for any of the weather items in their reports

def check(m):

# consider each region that has been assigned a name

for i, n in m.items():

# consider report items that contain an extreme

for j, w in enumerate(n2wf[n]):

if w in {0, 2}:

# consider the adjacent regions ...

for k in adj[i]:

# ... if they have been assigned a name

if k in m.keys():

ww = n2wf[m[k]][j]

# the mapping fails if any adjacent regions have

# the opposite exterme of the weather item

if w + ww == 2:

return False

return True

# map off-shore regions 4..8 to off-shore names

for p in permutations("BCEGI"):

r2no = dict(zip((4, 5, 6, 7, 8), p))

# check that the mapping is valid

if check(r2no):

# map coastal regions 0..3 to coastal names

for q in permutations("ADFH"):

# complete the map and check its validity

r2nc = r2no.copy()

r2nc.update(zip((0, 1, 2, 3), q))

if check(r2nc):

# output the regions adjacent to A and the map from regions to names

an2r = tuple(ar for ar, nm in r2nc.items() if nm == 'A')[0]

nadj = ''.join(sorted(r2nc[x] for x in adj[an2r]))

r2ns = ', '.join(f"{ar} -> {r2nc[ar]}" for ar in sorted(r2nc.keys()))

print(f"{nadj} ({r2ns})")

Jim Randell permalink

@Brian: I tried to reconstruct the map you are using from the adjacency matrix you give, but it doesn’t seem to give a valid layout. For example, 6 is in adj[5], but 5 is not in adj[6].

Reply
- Brian Gladman permalink
  
  @Jim Yes, there is an error in the map, item 5 (1,2, 6,8) should be
  (1,2,4,8). I will correct it later.
  
  Reply
  - Jim Randell permalink
    
    @Brian: OK. That makes it equivalent to my map then.
    
    Reply
    - Brian Gladman permalink
      
      @Jim. It now gets four solutions so I assume so.

Sunday Times Teaser 3051- Shipping Forecast

by Colin Vout

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