0018-triangle-path.py

"""
Problem 18

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 4
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 t
riangle containing one-hundred rows; it cannot be solved by brute force, and
requires a clever method! ;o)
"""
import copy
data = """\
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 traditional():
    # Initialization of data
    global data
    data = data.splitlines()
    data = [x.split() for x in data]

    # Converting string to int
    for i in range(len(data)):
        data[i] = map(int, data[i])

    # Creating a answer matrix
    ans = copy.deepcopy(data)
    
    for i in range(len(data)-1):
        # Updating current matrix with answer matrix
        data = copy.deepcopy(ans)
        for j in range(len(data[i])):
            # Computing the left child
            temp = data[i][j] + data[i+1][j]
            ans[i+1][j] = max(ans[i+1][j], temp)

            # Computing the right child
            temp = data[i][j] + data[i+1][j+1]
            ans[i+1][j+1] = max(ans[i+1][j+1], temp)

    return max(ans[-1])

print "Answer:", traditional()