35 lines
956 B
Python
35 lines
956 B
Python
#Maximum path sum II
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#Problem 67
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#
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#By starting at the top of the triangle below and moving to adjacent numbers on
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#the row below, the maximum total from top to bottom is 23.
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#
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#3
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#7 4
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#2 4 6
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#8 5 9 3
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#
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#That is, 3 + 7 + 4 + 9 = 23.
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#
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#Find the maximum total from top to bottom in triangle.txt (right click and
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#'Save Link/Target As...'), a 15K text file containing a triangle with
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#one-hundred rows.
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#
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#NOTE: This is a much more difficult version of Problem 18. It is not possible
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#to try every route to solve this problem, as there are 299 altogether! If you
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#could check one trillion (1012) routes every second it would take over twenty
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#billion years to check them all. There is an efficient algorithm to solve it. ;o)
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f = open( "p067_triangle.txt", "r" )
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a = [[ int(n) for n in line.split(' ') ] for line in f]
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for i in reversed(range(0,len(a)-1)):
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for j in range(0,len(a[i])):
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a[i][j] += max(a[i+1][j],a[i+1][j+1])
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print(a[0][0])
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