London | 25-SDC-July | Eyuel Abraham | Sprint 2 | Improve_with_caches.

Sprint-2/improve_with_caches/fibonacci/fibonacci.py

@@ -1,4 +1,8 @@
-def fibonacci(n):
+def fibonacci(n, memo={}):
+    if n in memo:
+        return memo[n]
     if n <= 1:
         return n
-    return fibonacci(n - 1) + fibonacci(n - 2)
+
+    memo[n] = fibonacci(n - 1, memo) + fibonacci(n - 2, memo)
+    return memo[n]

Sprint-2/improve_with_caches/making_change/making_change.py

@@ -1,32 +1,41 @@
-from typing import List
-
+from typing import List, Dict, Tuple
 
 def ways_to_make_change(total: int) -> int:
     """
     Given access to coins with the values 1, 2, 5, 10, 20, 50, 100, 200, returns a count of all of the ways to make the passed total value.
 
     For instance, there are two ways to make a value of 3: with 3x 1 coins, or with 1x 1 coin and 1x 2 coin.
     """
-    return ways_to_make_change_helper(total, [200, 100, 50, 20, 10, 5, 2, 1])
+    coins = [200, 100, 50, 20, 10, 5, 2, 1]
+    memo: Dict[Tuple[int, int], int] = {}
+    return ways_to_make_change_helper(total, coins, memo)
 
 
-def ways_to_make_change_helper(total: int, coins: List[int]) -> int:
+def ways_to_make_change_helper(total: int, coins: List[int], memo: Dict[Tuple[int, int], int]) -> int:
     """
     Helper function for ways_to_make_change to avoid exposing the coins parameter to callers.
+    Uses memoization to cache results for (total, coin_index).
     """
-    if total == 0 or len(coins) == 0:
-        return 0
+    if total == 0:
+        return 1  
+    if total < 0 or not coins:
+        return 0  
+
+    key = (total, len(coins))
+    if key in memo:
+        return memo[key]
 
     ways = 0
     for coin_index in range(len(coins)):
         coin = coins[coin_index]
         count_of_coin = 1
         while coin * count_of_coin <= total:
-            total_from_coins = coin * count_of_coin
-            if total_from_coins == total:
+            remainder = total - coin * count_of_coin
+            if remainder == 0:
                 ways += 1
             else:
-                intermediate = ways_to_make_change_helper(total - total_from_coins, coins=coins[coin_index+1:])
-                ways += intermediate
+                ways += ways_to_make_change_helper(remainder, coins[coin_index + 1:], memo)
             count_of_coin += 1
+
+    memo[key] = ways
     return ways

Sprint-2/improve_with_precomputing/common_prefix/common_prefix.py

@@ -1,18 +1,26 @@
 from typing import List
 
 
-def find_longest_common_prefix(strings: List[str]):
+def find_longest_common_prefix(strings: List[str]) -> str:
     """
     find_longest_common_prefix returns the longest string common at the start of any two strings in the passed list.
 
     In the event that an empty list, a list containing one string, or a list of strings with no common prefixes is passed, the empty string will be returned.
     """
+    if len(strings) < 2:
+        return ""
+
+    # PRE-COMPUTE by sorting strings once
+    strings = sorted(strings)
+
     longest = ""
-    for string_index, string in enumerate(strings):
-        for other_string in strings[string_index+1:]:
-            common = find_common_prefix(string, other_string)
-            if len(common) > len(longest):
-                longest = common
+
+    #compare only strings that are next to eacotherr in sorted order
+    for i in range(len(strings) - 1):
+        common = find_common_prefix(strings[i], strings[i + 1])
+        if len(common) > len(longest):
+            longest = common
+
     return longest