euler/e018.py

"""Find the maximum sum travelling from the top of the triangle to the base.

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 triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method! ;o)
"""

from e012 import triangle

class Vertex:
    """Holds information on each vertex in the triangle
    
    The weight represents the weight of any edge between an adjacent vertex and
    this one
    """
    def __init__(self, value):
        self.value = value
        self.weight = 100 - self.value
        self.min_distance = float('+inf')
        self.previous_vertex = None
        self.adjacent = []
    def add_adjacent(self, vertex):
        self.adjacent.append(vertex)
    def __cmp__(self, other):
        return cmp(self.min_distance, other.min_distance)
    def __repr__(self):
        return '{0} ({1})'.format(self.value, [a.value for a in self.adjacent])

class Triangle:
    def __init__(self, vertex_data):
        self.vertices = []
        i = 0
        row = 1
        for v in vertex_data:
            if (i >= triangle(row)):
                row = row + 1
            vertex = Vertex(v)
            if row > 1:
                # Find upwards adjacent vertices
                above_row = self.vertices[triangle(row - 2):triangle(row - 1)]
                total_this_row = triangle(row) - triangle(row - 1)
                pos = i - triangle(row - 1)  + 1
                start = int((pos / float(total_this_row)) * len(above_row)) - 1
                end = int(((pos + 1) / float(total_this_row)) * len(above_row))
                adjacent = above_row[start if start >= 0 else 0:end]
                for a in adjacent:
                    vertex.add_adjacent(a)
            self.vertices.append(vertex)
            i = i + 1
        self.rows = row
        if len(self.vertices) != triangle(self.rows):
            raise Exception('Invalid vertex set')
    def find_path(self):
        """Implementation of Dijkstra's algorithm"""
        
        # Reset vertice info
        for v in self.vertices:
            v.min_distance = float('+inf')
            v.previous_vertex = None
        orig = Vertex(100)
        orig.min_distance = 0
        adjacent = self.vertices[triangle(self.rows - 1):]
        for a in adjacent:
            orig.add_adjacent(a)
        Q = [orig] + [v for v in self.vertices]
        while len(Q) > 0:
            u = min(Q)
            if u.min_distance == float('+inf'):
                return False
            Q.remove(u)
            for v in u.adjacent:
                distance = u.min_distance + v.weight
                if distance < v.min_distance:
                    v.min_distance = distance
                    v.previous_vertex = u
        return True
    def get_path(self):
        """Returns the found path as a list of vertices, from the top of the
        triangle to the bottom
        """
        
        v = self.vertices[0]
        path = [v]
        for i in range(self.rows - 1):
            v = v.previous_vertex
            if not v:
                raise Exception('Missing or incomplete path!')
            path.append(v)
        return path

def main():
    vertex_data = []
    with open('p018/triangle.txt', 'r') as f:
        while True:
            line = f.readline()
            if not line:
                break
            vertex_data = vertex_data + [int(v) for v in line.split(' ')]
    t = Triangle(vertex_data)
    t.find_path()
    path = t.get_path()
    print 'Path', [v.value for v in path]
    print 'Sum', sum([v.value for v in path])

if __name__ == '__main__':
    main()