Solve problem 145

python/e091.py

@@ -1,32 +1,55 @@
+from collections import namedtuple
 
+Point = namedtuple("P", ["x", "y"])
+Vector = namedtuple("V", ["x", "y"])
+
+def generate_triangles(n):
+    all_points = [Point(x, y)
+        for x in range(0, n + 1)
+        for y in range(0, n + 1)
+    ]
+    all_points = all_points[1:]  # remove (0, 0)
+    all_pairs = []
+
+    for i in range(len(all_points)):
+        for j in range(i + 1, len(all_points)):
+            p = (all_points[i], all_points[j])
+            yield p
+
+
+def vector(p1, p2):
+    return Vector(p2.x - p1.x, p2.y - p1.y)
+
+
+def dot_product(v1, v2):
+    return v1.x * v2.x + v1.y * v2.y
+
+
+def has_right_angle(p, q):
+    o = Point(0, 0)
+    oq = vector(o, q)
+    op = vector(o, p)
+    qp = vector(q, p)
+
+    if dot_product(oq, op) == 0:
+        return True
+    elif dot_product(oq, qp) == 0:
+        return True
+    elif dot_product(op, qp) == 0:
+        return True
+    return False
 
 def euler_091():
-    n = 2
-    qs = [(x, y)
-          for x in range(n + 1)
-          for y in range(n + 1)]
-
-    def count_possible_right_triangles(q):
-        o = (0, 0)
-        if o == q:
-            return 0
-
-        ps = [(x, y)
-              for x in range(n + 1)
-              for y in range(q[0], n + 1)]
-        for p in ps:
-            if q == p:
-                continue
-            print(o, q, p)
-
-        return 0
-
-    s = sum(map(count_possible_right_triangles, qs))
-    return s
-
+    count = 0
+    ts = generate_triangles(50)
+    for t in ts:
+        if has_right_angle(*t):
+            count += 1
+    return count
 
 
 if __name__ == "__main__":
     solution = euler_091()
     print("e091.py: " + str(solution))
-    assert(solution == 0)
+    assert(solution == 14234)
+

python/e145.py

@@ -0,0 +1,29 @@
+
+def reversible(n):
+    n_rev_str = str(n)[::-1]
+    if n_rev_str.startswith("0"):
+        return False
+    n_rev = int(n_rev_str)
+    ds = str(n + n_rev)
+    for d in ds:
+        if int(d) % 2 == 0:
+            return False
+    return True
+
+
+def euler_145():
+    # pure bruteforce, took about four minutes wity pypy
+    count = 0
+    counted = set()
+    for i in range(10**9):
+        if not i in counted and reversible(i):
+            count += 1
+            counted.add(i)
+    return count
+
+
+if __name__ == "__main__":
+    solution = euler_145()
+    print("e145.py: " + str(solution))
+    assert(solution == 608720)
+