Problem 15

0015.py

@@ -0,0 +1,84 @@
+from functools import reduce
+
+target = [19,19]
+start = [0,0]
+
+side = 2
+
+count = 0
+# 2: 6
+# 3: 20
+# 4: 70
+# 5: 252
+# 6: 924
+
+def recurse(x, y):
+    global count
+    # print(x, y)
+
+    if (x == side and y == side):
+        count += 1
+        print('found', count)
+        return
+
+    if (x < side):
+        # print('increasing x')
+        recurse(x + 1, y)
+
+    if (y < side):
+        # print('increasing y')
+        recurse(x, y + 1)
+
+count = 0
+def smarter_recurse(index, bits):
+    # print(index, bits)
+    global count
+
+    if (index == 0):
+        if (bits == 0):
+            count += 1
+        return;
+
+    if (index - 1 >= bits):
+        smarter_recurse(index-1, bits);
+
+    if (bits > 0):
+        smarter_recurse(index - 1, bits-1)
+
+# side = 2
+
+# smarter_recurse(side * 2, side)
+
+def product(x, y):
+    return x * y
+
+# 10! / 5!^2
+def do_it(slots, bits):
+    numerator = reduce(product, list(range(slots + 1 - bits, slots + 1)))
+    denomerator = reduce(product, list(range(1, bits + 1)))
+
+    print(int(numerator / denomerator))
+
+
+# smarter_recurse(8, 4)
+
+# print(count)
+# do_it(40, 20)
+
+slots = 7
+bits = 3
+# smarter_recurse(slots, bits)
+
+# print(count)
+
+# do_it(slots, bits)
+# do_it(7, 0)
+do_it(7, 1)
+do_it(7, 2)
+do_it(7, 3)
+do_it(7, 4)
+do_it(7, 5)
+do_it(7, 6)
+
+
+