From 63982f51a0fa110e69610de89f0ab79cad857c62 Mon Sep 17 00:00:00 2001
From: Correl Roush <correl@gmail.com>
Date: Mon, 12 Apr 2010 21:06:47 +0000
Subject: [PATCH] Problem 018

git-svn-id: file:///srv/svn/euler@44 e5f4c3ec-3c0c-11df-b522-21efaa4426b5
---
 e018.py           | 96 +++++++++++++++++++++++++++++++++++++++++++++++
 p018/test.txt     |  4 ++
 p018/triangle.txt | 15 ++++++++
 3 files changed, 115 insertions(+)
 create mode 100644 e018.py
 create mode 100644 p018/test.txt
 create mode 100644 p018/triangle.txt

diff --git a/e018.py b/e018.py
new file mode 100644
index 0000000..ef89a2a
--- /dev/null
+++ b/e018.py
@@ -0,0 +1,96 @@
+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
+
+if __name__ == '__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])
diff --git a/p018/test.txt b/p018/test.txt
new file mode 100644
index 0000000..65ff300
--- /dev/null
+++ b/p018/test.txt
@@ -0,0 +1,4 @@
+3
+7 4
+2 4 6
+8 5 9 3
diff --git a/p018/triangle.txt b/p018/triangle.txt
new file mode 100644
index 0000000..e236c2f
--- /dev/null
+++ b/p018/triangle.txt
@@ -0,0 +1,15 @@
+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