Count cycles by iteration

Verifying solution...
Test 1 passed!
Test 2 passed!
Test 3 failed  [Hidden]
Test 4 passed! [Hidden]
Test 5 failed  [Hidden]
Test 6 failed  [Hidden]
Test 7 failed  [Hidden]
Test 8 failed  [Hidden]
Test 9 passed! [Hidden]
Test 10 failed  [Hidden]

level5/disorderly-escape/solution.py

@@ -1,11 +1,36 @@
 import math
+import numpy as np
 
 def solution(w, h, s):
     return str(sum([s**cycle for cycle in generate_cycles(w, h)])/(math.factorial(w)*math.factorial(h)))
 
 def generate_cycles(w, h):
-    yield 1
+    identity = np.arange(w*h).reshape((w, h))
+    for i in generate_permutation(list(range(w))):
+        for j in generate_permutation(list(range(h))):
+            yield count_cycle(identity[i][:, j])
 
+def generate_permutation(numbers):
+    if len(numbers) == 1:
+        yield numbers
+    else:
+        for i, n in enumerate(numbers):
+            for j in generate_permutation(numbers[:i] + numbers[i+1:]):
+                yield [n] + j
+
+def count_cycle(arr):
+    cycle = np.zeros(arr.shape, dtype=int)
+    w, h = arr.shape
+    cycle_id = 0
+    for i in range(w):
+        for j in range(h):
+            x, y = i, j
+            if cycle[x, y] == 0:
+                cycle_id += 1
+            while cycle[x, y] == 0:
+                cycle[x, y] = cycle_id
+                x, y = arr[x, y]/h, arr[x, y]%h
+    return cycle_id
 
 tests = [
         ([2, 3, 4], '430'),