staircase with caching

Author: AnushreeBagchi

staircase.py

@@ -0,0 +1,45 @@
+def staircase(num):
+    if num<=0:
+        return 
+    if num ==1:
+        return 1
+    elif num == 2:
+        return 2
+    elif num == 3:
+        return 4
+    return staircase(num-1)+staircase(num-2)+staircase(num-3)
+
+# caching the output to get faster implementation of the function
+def staircase_with_hashmap(num):
+    num_dict = dict({})
+    return staircase_faster(num,num_dict)
+
+def staircase_faster(num,num_dict ):
+    if num<=0:
+        return 
+    if num ==1:
+        output = 1
+    elif num == 2:
+        output = 2
+    elif num == 3:
+        output = 4
+    else:
+        if (num-1) in num_dict:
+            n1 = num_dict[num-1]
+        else:
+            n1 = staircase(num-1)
+        if (num-2) in num_dict:
+            n2 = num_dict[num-2]
+        else:
+            n2 = staircase(num-2)
+        if (num-3) in num_dict:
+            n3 = num_dict[num-3]
+        else:
+            n3 = staircase(num-3)
+        output = n1+n2+n3
+    num_dict[num] = output
+    return output
+    
+
+
+print(staircase_with_hashmap(3))