Posts Tagged ‘aggregator’

Problem 18, Problem 67

Wednesday, February 11th, 2009

By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.

3
7 5
2 4 6
8 5 9 3

That is, 3 + 7 + 4 + 9 = 23.

Find the maximum total from top to bottom of the triangle below:

75
95 64
17 47 82
18 35 87 10
20 04 82 47 65
19 01 23 75 03 34
88 02 77 73 07 63 67
99 65 04 28 06 16 70 92
41 41 26 56 83 40 80 70 33
41 48 72 33 47 32 37 16 94 29
53 71 44 65 25 43 91 52 97 51 14
70 11 33 28 77 73 17 78 39 68 17 57
91 71 52 38 17 14 91 43 58 50 27 29 48
63 66 04 68 89 53 67 30 73 16 69 87 40 31
04 62 98 27 23 09 70 98 73 93 38 53 60 04 23

NOTE: As there are only 16384 routes, it is possible to solve this problem by trying every route. However, Problem 67, is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method! ;o)

Using the functional programming concept of an aggregator (with reduce and a custom aggregating function):

?View Code PYTHON
triangle = \
"""75
95 64
17 47 82
18 35 87 10
20 04 82 47 65
19 01 23 75 03 34
88 02 77 73 07 63 67
99 65 04 28 06 16 70 92
41 41 26 56 83 40 80 70 33
41 48 72 33 47 32 37 16 94 29
53 71 44 65 25 43 91 52 97 51 14
70 11 33 28 77 73 17 78 39 68 17 57
91 71 52 38 17 14 91 43 58 50 27 29 48
63 66 04 68 89 53 67 30 73 16 69 87 40 31
04 62 98 27 23 09 70 98 73 93 38 53 60 04 23"""
 
def get_row_maximal_sums(prow,row):
  """
  Given the previous and current rows, find the sum of
  the maximal path leading to each node of the current row.
  """
  sums = [0]*len(row)
  for index, item in enumerate(row):
    try:
      left_pred = prow[index-1]
    except IndexError:
      # node has no left predecessor
      left_pred = 0
    try:
      right_pred = prow[index]
    except IndexError:
      # node has no right predecessor
      right_pred = 0
    sums[index] = item + max(left_pred,right_pred)
  return sums
 
# process triangle into list of row lists
t = triangle.split("\n")
for i,row in enumerate(t):
  t[i] = map(int,row.split(" "))
 
# problem 18
>>> max(reduce(get_row_maximal_sums,t))
1074
 
# problem 67
>>> max(reduce(get_row_maximal_sums,t))
7273

Tags: , , , , , ,
Posted in triangle | No Comments »