completed 8.1

Author: sloloris

chapter-8-recursion-and-dynamic-programming/8.1-triple-step.py

@@ -0,0 +1,20 @@
+""" 8.1 Triple Step: A child is running up a staircase with n steps an can hop either 1 step, 2 steps, or 3 steps at a time. Implement a method to count how many possible ways the child can run up the stairs. """
+
+
+def count_ways(n):
+    if n < 0:
+        return 0
+    elif n == 0:
+        return 1
+    else:
+        return count_ways(n-1) + count_ways(n-2) + count_ways(n-3)
+
+
+def count_ways_memo(n, memo={}):
+    if n < 0:
+        return 0
+    elif n == 0:
+        return 1
+    else:
+        memo[n] = count_ways_memo(n-1, memo) + count_ways_memo(n-2, memo) + count_ways_memo(n-3, memo)
+        return memo[n]