Solve problem 336

python/e336.py

@@ -0,0 +1,67 @@
+from itertools import permutations
+from string import ascii_uppercase
+from functools import cache
+
+
+@cache
+def count(xst: tuple) -> int:
+    expected = 0
+    for i in range(len(xst)):
+        if xst[i] == expected:
+            expected += 1
+        else:
+            # Carriage i is not the correct one
+            break
+    else:
+        # Train is fully sorted
+        return 0
+
+    # Find out where Simple Simon would split next; there are two cases.
+    xs = list(xst)
+
+    # If the next expected carriage is at the end of the list, Simon can just
+    # reverse from where we currently are.
+    if xs[-1] == expected:
+        xs[i:] = xs[i:][::-1]
+        return 1 + count(tuple(xs))
+
+    for j in range(i + 1, len(xst)):
+        if xst[j] == expected:
+            xs[j:] = xs[j:][::-1]
+            return 1 + count(tuple(xs))
+
+    assert False, "should not get here"
+
+
+def get_maximix_arrangements(n: int) -> list:
+    x = [i for i in range(n)]
+    xs = permutations(x)
+    max_xs = []
+    max_xs_count = 0
+    for x in xs:
+        if x[0] == 0 or x[-1] == 0:
+            continue
+        c = count(x)
+        if c == max_xs_count:
+            max_xs.append(x)
+        elif c > max_xs_count:
+            max_xs = [x]
+            max_xs_count = c
+    return sorted(map(to_ascii, max_xs))
+
+
+def to_ascii(x) -> str:
+    return "".join([ascii_uppercase[d] for d in x])
+
+
+def euler_336():
+    xs = get_maximix_arrangements(6)
+    assert len(xs) == 24
+    assert xs[10 - 1] == "DFAECB"
+    return get_maximix_arrangements(11)[2011 - 1]
+
+
+if __name__ == "__main__":
+    solution = euler_336()
+    print(f"e336.py: {solution}")
+    assert solution == "CAGBIHEFJDK"