My solution to 860

Author: jeremymanning

problems/860/jeremymanning.md

@@ -1,11 +1,56 @@
 # [Problem 860: Lemonade Change](https://leetcode.com/problems/lemonade-change/description/?envType=daily-question)
 
 ## Initial thoughts (stream-of-consciousness)
+- What a breath of fresh air after yesterday's problem.
+- This one seems very easy.  We could either solve this by using a list to track all of the bills in our collection, or (more efficiently) we could use a hash table to track the numbers of each possible type of bill.  There are only three, so we can initialize `register = {5: 0, 10: 0, 20: 0}`.
+- Then we just step through one bill at a time, updating `register` as needed.  The amount of change is just `bill[i] - 5`.
+- There are just a few options for how much change might be needed: 0, 5, or 15:
+    - No change is needed if someone pays with a $5 bill.  There's no need to check the register, but we update `register[5] += 1`.
+    - $5 in change is needed if someone pays with $10.  Update `register[10] += 1` and decrement `register[5] -= 1` (or return false if that dips `register[5]` below 0.
+    - $15 in change is needed if someone pays with a $20.  This requires one of the following:
+        - 1 $10 and 1 $5 bill if available
+        - 3 $5 bills otherwise
+        - We should always prefer giving change with larger bills, because this preserves our flexibility in later transactions
 
 ## Refining the problem, round 2 thoughts
+- No edge cases I can think of...let's implement it!
 
 ## Attempted solution(s)
 ```python
-class Solution:  # paste your code here!
-    ...
+class Solution:
+    def lemonadeChange(self, bills: List[int]) -> bool:
+        cost = 5
+        register = {5: 0, 10: 0, 20: 0}
+        
+        for payment in bills:
+            register[payment] += 1
+            change = payment - cost
+            if change == 0:
+                continue
+            elif change == 5:
+                if register[5] <= 0:
+                    return False
+                register[5] -= 1
+            elif change == 15:                
+                if register[10] > 0 and register[5] > 0:  # try making change with $10 and $5
+                    register[10] -= 1
+                    register[5] -= 1
+                elif register[5] >= 3:  # try making change with 3 $5 bills
+                    register[5] -= 3
+                else:  # correct change is not available
+                    return False
+        
+        return True
 ```
+- Given test cases pass
+- Let's make up some new test cases:
+    - `bills = [10, 5, 10, 5, 10, 20, 5, 5, 10, 5, 5, 5, 20, 20, 20, 10, 10, 10, 10, 5, 10, 10, 10, 10, 20, 5, 20, 10, 10, 10, 20, 10, 10, 5, 5, 20, 20, 5, 5, 10, 10, 5, 5, 5, 5, 10, 10, 20, 5, 5, 10, 20, 20, 5, 20, 5, 20, 10, 5, 20, 20, 5, 5, 5, 10, 5, 20, 10, 10, 10, 5, 10, 5, 5, 10, 20, 10, 10, 20, 10, 20, 20, 20, 10, 20, 5, 20, 5, 10, 10, 20, 5, 5, 20, 20, 5, 5, 10, 20, 20]`: pass
+    - `bills = [5, 10, 5, 10, 5, 10, 20, 5, 5, 10, 5, 5, 5, 20, 20, 20, 10, 10, 10, 10, 5, 10, 10, 10, 10, 20, 5, 20, 10, 10, 10, 20, 10, 10, 5, 5, 20, 20, 5, 5, 10, 10, 5, 5, 5, 5, 10, 10, 20, 5, 5, 10, 20, 20, 5, 20, 5, 20, 10, 5, 20, 20, 5, 5, 5, 10, 5, 20, 10, 10, 10, 5, 10, 5, 5, 10, 20, 10, 10, 20, 10, 20, 20, 20, 10, 20, 5, 20, 5, 10, 10, 20, 5, 5, 20, 20, 5, 5, 10, 20, 20]`: pass
+    - `bills = [5, 5, 10, 20, 20, 10, 10, 20, 20, 5, 5, 10, 20, 10, 20, 5, 10, 10, 20, 5]`: pass
+    - `bills = [5, 5, 5, 5, 10, 20, 5, 5, 5, 5, 10, 5, 10, 10, 10, 20, 5]`: pass
+- Ok...seems like it's working; let's submit...
+
+![Screenshot 2024-08-14 at 11 55 03 PM](https://github.com/user-attachments/assets/1001e9e4-6917-4727-ab28-5523c342a859)
+
+Solved!
+