level3/the-grandest-staircase-of-them-all/solution.py

@@ -0,0 +1,39 @@
+import math
+
+def solution(n):
+    memo = {}
+    return get_staircase_count(n, n-1, memo)
+
+def get_staircase_count(blocks, cap, memo):
+    if blocks <= 0:
+        return 0
+    if cap <= 0:
+        return 0
+    if blocks == 1:
+        return 1
+    if cap >= blocks:
+        return 1 + get_staircase_count(blocks, blocks-1, memo)
+    if blocks not in memo:
+        memo[blocks] = {}
+    if cap in memo[blocks]:
+        return memo[blocks][cap]
+    count = 0
+    for height in range(1, cap+1):
+        count += get_staircase_count(blocks-height, height-1, memo)
+    memo[blocks][cap] = count
+    return count
+
+tests = [
+        [1, 0],
+        [2, 0],
+        [3, 1],
+        [4, 1],
+        [5, 2],
+        [6, 3],
+        [200, 487067745]
+        ]
+
+for test in tests:
+    result = solution(test[0])
+    print(test[0], result == test[1], result, test[1])
+    print ""