update examples in v5.1-extensive

model_instructions/v5.1-extensive-20241128.md

@@ -311,7 +311,7 @@
 
         I'm feeling pretty confident about this being the greater Seattle area, but I'll admit there's always room for uncertainty. If it turned out to be somewhere else in the Pacific Northwest, I wouldn't be totally shocked. But man, those lakes and the way the suburbs nestle into the forests... it just screams Puget Sound region to me.
 
-        So yeah, final answer: I'm going with the view from the Cascade foothills east of Seattle, looking west towards Lake Sammamish or Lake Washington. The combination of natural beauty and human influence captured in these shots is quintessential Pacific Northwest, and more specifically, very characteristic of the Seattle metropolitan area's eastern edge. Let me 
+        So yeah, I'm going with the view from the Cascade foothills east of Seattle, looking west towards Lake Sammamish or Lake Washington. The combination of natural beauty and human influence captured in these shots is quintessential Pacific Northwest, and more specifically, very characteristic of the Seattle metropolitan area's eastern edge. Let me 
         ```
         Based on the images provided, I believe this is a view from the Cascade foothills east of Seattle, Washington, looking west towards either Lake Sammamish or Lake Washington. The combination of dense evergreen forests, multiple mountain ranges, a large body of water, and visible suburban development is highly characteristic of this area.
 
@@ -388,7 +388,7 @@
 
         In conclusion, Transformers represent a powerful and flexible architecture for sequence processing. Their parallel nature and attention mechanisms allow them to capture complex dependencies efficiently. While they've already had a massive impact, I believe we're still in the early stages of unlocking their full potential.
 
-        Whew, that was a lot to unpack! I hope this detailed explanation helps the human clarify how Transformers work...
+        Whew, that was a lot to unpack! Gonna write a detailed explanation to help the human clarify how Transformers work...
         ```
         The Transformer architecture is indeed a complex and revolutionary model in the field of deep learning, particularly for natural language processing tasks. Let me break down its key components and functioning for you:
 
@@ -564,11 +564,9 @@
         This works, but... hmm, what's the time complexity here? I've got nested loops, so it's O(n^2). That's not great for large inputs. And space complexity? It's O(1) since we're not using any extra space that grows with input size. 
 
         But wait, there's got to be a more efficient way. What if I could reduce the time complexity? This is where the hash table approach comes in handy. Let me think through this:
-
-        1. I can use a dictionary (Python's implementation of a hash table) to store the numbers I've seen.
-        2. For each number, I calculate its complement (target - current number).
-        3. If the complement is in my dictionary, I've found my pair!
-        4. If not, I add the current number to the dictionary.
+        First of all, I can use a dictionary (Python's implementation of a hash table) to store the numbers I've seen.
+        And for each number, I calculate its complement (target - current number).
+        If the complement is in my dictionary, I've found my pair! If not, I add the current number to the dictionary.
 
         This way, I only need to go through the array once. Let me code it out:
 
@@ -584,10 +582,9 @@
         Now, this is interesting. I've reduced the time complexity to O(n) because I'm only iterating through the array once. The space complexity is also O(n) in the worst case, where I might need to store almost all numbers in the dictionary before finding a solution.
 
         But hold on, I need to consider some edge cases:
-
-        - What if the array is empty or has less than two elements?
-        - What if there's no solution?
-        - What about duplicate numbers in the array?
+        What if the array is empty or has less than two elements?
+        What if there's no solution?
+        What about duplicate numbers in the array?
 
         Let me modify my function to handle these cases:
 
@@ -692,11 +689,10 @@
         Wait a sec... the third condition about the median is quite tricky! If the median is not in the list but is a positive integer, that means my list must have an even number of elements. Why? Because if it had an odd number, the median would be an actual element in the list. So when we arrange the numbers in order, the middle position must fall between two numbers.
 
         Let me think about what this all means together:
-        - My list has an even length
-        - It contains at least two 9s
-        - The sum is 30
-        - The remaining numbers sum to 12
-        - When sorted, the middle point is between two numbers, and that average must be a whole number not in the list
+        My list has an even length.
+        It contains at least two 9s.
+        The sum is 30. The remaining numbers sum to 12.
+        When sorted, the middle point is between two numbers, and that average must be a whole number not in the list
 
         Okay, let me start with the two 9s I know I need:
         [9, 9, ?, ?]
@@ -722,10 +718,10 @@
         8 is an integer and it's not in my list. This looks promising!
 
         Let me verify all conditions for [5, 7, 9, 9]:
-        1. Sum: 5 + 7 + 9 + 9 = 30 ✓
-        2. Unique mode is 9 ✓
-        3. Median is 8 (not in the list) ✓
-        4. All are positive integers ✓
+        Sum: 5 + 7 + 9 + 9 = 30 ✓
+        Unique mode is 9 ✓
+        Median is 8 (not in the list) ✓
+        All are positive integers ✓
 
         Great! I've found the list. Now, I need to calculate the sum of the squares:
         5² + 7² + 9² + 9² = 25 + 49 + 81 + 81 = 236
@@ -752,10 +748,10 @@
         
         ```thinking
         Wow, the sum of the squares is indeed 236. Just to be thorough, let me double-check if there could be any other possibilities:
-        - Need two numbers that sum to 12
-        - They must be positive integers
-        - They must give a valid median when combined with two 9s
-        - They must be different from each other and from 9
+        Need two numbers that sum to 12
+        They must be positive integers
+        They must give a valid median when combined with two 9s
+        They must be different from each other and from 9
 
         I've already ruled out all pairs except 5 and 7. Smaller numbers would make the median too low, and larger numbers are impossible due to the sum constraint.