Posted by rg123 on Wed 29 Jul 17:01
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- # List representing the given puzzle:
- # Number of letters in each row from top to bottom...
- positions = [1,2,3,4,3,2,3,4,3,2,1]
- def get_num_paths(positions):
- # Start with a list consisting of a 1 for every letter in the
- # top row. These are totals paths so far at top row...
- totals = [1 for x in xrange(positions[0])]
- # Now for every other row...
- for i in range(1, len(positions)):
- L = len(totals)
- # If current row is wider than previous row by 1...
- if positions[i] == L + 1:
- new_totals = [totals[0]] # New leftmost total is previous
- # leftmost total.
- if L > 1:
- # Calculate new totals in the middle by adding together
- # previous adjacent totals and add them to the new list...
- new_totals.extend([sum(totals[x : x + 2])
- for x in xrange(L - 1)])
- new_totals.append(totals[-1]) # New rightmost total is previous
- # rightmost total.
- totals = new_totals
- # Else if current row is narrower than previous row by 1...
- elif positions[i] == L - 1:
- # All new totals can be handled in this case by adding together
- # previous adjacent totals...
- new_totals = [sum(totals[x : x + 2])
- for x in xrange(L - 1)]
- totals = new_totals
- # Else it isn't a puzzle this function solves...
- else:
- return "Invalid structure."
- return sum(totals) # Sum of final path totals is the result.
- print get_num_paths(positions)
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