Wed Sep 25 08:48:34 PDT 2024

_internal/targets.json

@@ -1 +1 @@
-[{"due": "9/25/24", "link": "hw/hw03/", "name": "HW 03: Higher-Order Functions", "piazza_name": "HW 03", "release": "9/18/24"}, {"due": "9/27/24", "link": "lab/lab04/", "name": "Lab 04: Recursion", "piazza_name": "Lab 04", "release": "9/23/24"}]
+[{"due": "9/25/24", "link": "hw/hw03/", "name": "HW 03: Higher-Order Functions", "piazza_name": "HW 03", "release": "9/18/24"}, {"due": "9/27/24", "link": "lab/lab04/", "name": "Lab 04: Recursion", "piazza_name": "Lab 04", "release": "9/23/24"}, {"due": "10/2/24", "link": "hw/hw04/", "name": "HW 04: Recursion", "piazza_name": "HW 04", "release": "9/25/24"}]

assets/slides/09.py

@@ -0,0 +1,98 @@
+# Tree Recursion 
+
+# ----------------------- #
+# Tracing factorial
+
+from ucb import trace
+
+@trace
+def fact(n):
+    """ computes the factorial of n (n!)
+    >>> fact(5) # 5! = 5 * 4 * 3 * 2 * 1
+    120
+    """
+    if n == 0 or n == 1:
+        return 1
+    else:
+        return n * fact(n-1)
+
+# ----------------------- #
+# Mutual Recursion
+# (Counting Unique Prime Factors Recursively)
+# https://pythontutor.com/render.html#code=def%20smallest_factor%28n%29%3A%0A%20%20%20%20if%20%28n%252%20%3D%3D%200%29%3A%0A%20%20%20%20%20%20%20%20return%202%0A%20%20%20%20k%20%3D%203%0A%20%20%20%20while%20%28k%20%3C%20n%29%3A%0A%20%20%20%20%20%20%20%20if%20%28n%25k%20%3D%3D%200%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20k%0A%20%20%20%20%20%20%20%20k%20%2B%3D%201%0A%20%20%20%20return%20n%0A%0A%0Adef%20unique_prime_factors%28n%29%3A%0A%20%20%20%20%22%22%22Return%20the%20number%20of%20unique%20prime%20factors%20of%20n.%0A%0A%20%20%20%20%3E%3E%3E%20unique_prime_factors%2851%29%20%20%23%203%20*%2017%0A%20%20%20%202%0A%20%20%20%20%3E%3E%3E%20unique_prime_factors%2827%29%20%20%20%23%203%20*%203%20*%203%0A%20%20%20%201%0A%20%20%20%20%3E%3E%3E%20unique_prime_factors%28120%29%20%23%202%20*%202%20*%202%20*%203%20*%205%0A%20%20%20%203%0A%20%20%20%20%22%22%22%0A%20%20%20%20k%20%3D%20smallest_factor%28n%29%0A%20%20%20%20def%20no_k%28n%29%3A%0A%20%20%20%20%20%20%20%20%22Return%20the%20number%20of%20unique%20prime%20factors%20of%20n%20other%20than%20k.%22%0A%20%20%20%20%20%20%20%20if%20n%20%3D%3D%201%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%200%0A%20%20%20%20%20%20%20%20elif%20n%20%25%20k%20!%3D%200%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20unique_prime_factors%28n%29%0A%20%20%20%20%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20return%20no_k%28n//k%29%0A%20%20%20%20return%201%2Bno_k%28n%29%0A%0Aunique_prime_factors%2860%29&cumulative=false&curInstr=0&heapPrimitives=nevernest&mode=display&origin=opt-frontend.js&py=3&rawInputLstJSON=%5B%5D&textReferences=false
+def smallest_factor(n):
+    if (n%2 == 0):
+        return 2
+    k = 3
+    while (k < n):
+        if (n%k == 0):
+            return k
+        k += 1
+    return n
+
+
+def unique_prime_factors(n):
+    """Return the number of unique prime factors of n.
+
+    >>> unique_prime_factors(51)  # 3 * 17
+    2
+    >>> unique_prime_factors(27)   # 3 * 3 * 3
+    1
+    >>> unique_prime_factors(120) # 2 * 2 * 2 * 3 * 5
+    3
+    """
+    k = smallest_factor(n)
+    def no_k(n):
+        "Return the number of unique prime factors of n other than k."
+        if n == 1:
+            return 0
+        elif n % k != 0:
+            return unique_prime_factors(n)
+        else:
+            return no_k(n//k)
+    return 1+no_k(n)
+
+unique_prime_factors(120)
+
+# ----------------------- #
+# Count Partitions
+# https://pythontutor.com/cp/composingprograms.html#code=def%20count_partitions%28n,%20m%29%3A%0A%20%20%20%20if%20n%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20return%201%0A%20%20%20%20elif%20n%20%3C%200%3A%0A%20%20%20%20%20%20%20%20return%200%0A%20%20%20%20elif%20m%20%3D%3D%200%3A%0A%20%20%20%20%20%20%20%20return%200%0A%20%20%20%20else%3A%0A%20%20%20%20%20%20%20%20with_m%20%3D%20count_partitions%28n-m,%20m%29%20%0A%20%20%20%20%20%20%20%20without_m%20%3D%20count_partitions%28n,%20m-1%29%0A%20%20%20%20%20%20%20%20return%20with_m%20%2B%20without_m%0A%20%20%20%20%20%20%20%20%0Aresult%20%3D%20count_partitions%285,%203%29%0A%0A%23%201%20%2B%201%20%2B%201%20%2B%201%20%2B%201%20%3D%205%0A%23%201%20%2B%201%20%2B%201%20%2B%202%20%2B%20%20%20%3D%205%0A%23%201%20%2B%202%20%2B%202%20%2B%20%20%20%20%20%20%20%3D%205%0A%23%201%20%2B%201%20%2B%203%20%2B%20%20%20%20%20%20%20%3D%205%0A%23%202%20%2B%203%20%2B%20%20%20%20%20%20%20%20%20%20%20%3D%205&cumulative=false&curInstr=0&mode=display&origin=composingprograms.js&py=3&rawInputLstJSON=%5B%5D
+
+def count_partitions(n, m):
+    if n == 0:
+        return 1
+    elif n < 0:
+        return 0
+    elif m == 0:
+        return 0
+    else:
+        with_m = count_partitions(n-m, m) 
+        without_m = count_partitions(n, m-1)
+        return with_m + without_m
+
+result = count_partitions(5, 3)
+
+# 1 + 1 + 1 + 1 + 1 = 5
+# 1 + 1 + 1 + 2 +   = 5
+# 1 + 2 + 2 +       = 5
+# 1 + 1 + 3 +       = 5
+# 2 + 3 +           = 5
+
+# ----------------------- #
+
+def count_park(n):
+    """Count the ways to park cars and motorcycles in n adjacent spots.
+    >>> count_park(1)  # '.' or '%'
+    2
+    >>> count_park(2)  # '..', '.%', '%.', '%%', or '<>'
+    5
+    >>> count_park(4)  # some examples: '<><>', '.%%.', '%<>%', '%.<>'
+    29
+    """
+    if n < 0:
+        return 0
+    elif n == 0:
+        return 1
+    else:
+        return count_park(n-2) + count_park(n-1) + count_park(n-1)
+

assets/slides/10.py

@@ -0,0 +1,110 @@
+
+# Lists practice
+
+digits = [1, 8, 2, 8]
+8 in digits
+[1, 8] in digits
+1 in digits and 8 in digits
+
+for x in digits:
+    continue
+    #print(100 * x)
+
+def f(x):
+    for y in [x, x + 1, x + 2]:
+        print('this is y:', y)
+        if y > 0:
+            return y
+    return 1000
+
+def print_negatives(s):
+    for d in s:
+        d = -d
+        print(d)
+    print(s)
+    s = [2, 3, 4]
+    return s
+
+# Range practice
+
+def range_practice():
+    range(4)
+    list(range(4))
+    range(-2, 2)
+    list(range(-2, 2))
+    range(2, 100000000)  # 9 zeroes slows things down a lot
+    list(range(2, 100000000))
+    len(range(2, range(0, 23)[9]))
+
+def fib(n):
+    """Return the nth fibonnaci number.
+
+    >>> fib(0)
+    0
+    >>> fib(2)
+    1
+    >>> fib(10)
+    55
+    """
+    fib_number = 0
+    what_to_add = 1  # to get to the next fib number
+    for _ in range(n):
+        what_to_add, fib_number = fib_number, fib_number + what_to_add
+    return fib_number
+
+# List comprehension practice
+
+xs = range(-10, 11)
+ys = [x*x - 2*x + 1 for x in xs]
+
+xs_where_y_is_below_10 = [x for x in xs if x*x - 2*x + 1 < 10]
+xs_where_y_is_below_10 = [xs[i] for i in range(len(xs)) if ys[i] < 10]
+
+# Tree recursion practice
+
+goal = 21
+
+def play(strategy0, strategy1, n=0, who = 0, announce=False):
+    "Play twenty-one starting at n and return the index of the winner."
+    strategies = [strategy0, strategy1]
+    while n < goal:
+        n = n + strategies[who](n)
+        if announce:
+            print('Player', who, 'increases n to', n)
+        who = 1 - who
+    return who
+
+def two_strat(n):
+    "Always choose 2."
+    return 2
+
+def interactive(n):
+    "Ask the user."
+    choice = input('Pick 1, 2, or 3: ')
+    if choice in ['1', '2', '3']:
+        return int(choice)
+    else:
+        print('Invalid choice!')
+        return interactive(n)
+
+def best(n, other_strategy):
+    """Return an best strategy against other_strategy.
+
+    >>> beat_two_strat = lambda n: best(n, two_strat)
+    >>> winner(20, beat_two_strat, two_strat)
+    1
+    >>> winner(19, beat_two_strat, two_strat)
+    0
+    >>> winner(15, beat_two_strat, two_strat)
+    0
+    >>> winner(0, beat_two_strat, two_strat)
+    0
+    """
+    plan = lambda future_n: best(future_n, other_strategy)
+    for choice in range(1, 4):
+        if play(plan, other_strategy, n + choice, 1) == 0:
+            return choice
+    return 1
+
+perfect = lambda n: best(n, perfect)
+

hw/hw04/hw04.py

@@ -1,6 +1,3 @@
-LAB_SOURCE_FILE=__file__
-
-
 HW_SOURCE_FILE=__file__
 
 
@@ -35,13 +32,13 @@ def digit_distance(n):
 
     >>> digit_distance(3)
     0
-    >>> digit_distance(777)
+    >>> digit_distance(777) # 0 + 0
     0
-    >>> digit_distance(314)
+    >>> digit_distance(314) # 2 + 3
     5
-    >>> digit_distance(31415926535)
+    >>> digit_distance(31415926535) # 2 + 3 + 3 + 4 + ... + 2
     32
-    >>> digit_distance(3464660003)
+    >>> digit_distance(3464660003)  # 1 + 2 + 2 + 2 + ... + 3
     16
     >>> from construct_check import check
     >>> # ban all loops

hw/hw04/index.html

@@ -210,9 +210,9 @@ <h2 id="getting-started-videos" class="no-toc">Getting Started Videos</h2>
 <blockquote><p>To see these videos, you should be logged into your berkeley.edu email.</p></blockquote>
 
 
-            <iframe width="560" height="315" src="https://youtube.com/embed/videoseries?list=PLx38hZJ5RLZd69lK3GQh_OH1u_xmVdBe5"
-                frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" aria-label = "hw3-getstarted"
-                allowfullscreen></iframe><p><a href='https://youtu.be/playlist?list=PLx38hZJ5RLZd69lK3GQh_OH1u_xmVdBe5'> YouTube link </a></p>
+            <iframe width="560" height="315" src="https://youtube.com/embed/videoseries?list=PLx38hZJ5RLZd3VypdvCJVp_nN_ihhDFXi"
+                frameborder="0" allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" aria-label = "c88c-hw4-getstarted"
+                allowfullscreen></iframe><p><a href='https://youtu.be/playlist?list=PLx38hZJ5RLZd3VypdvCJVp_nN_ihhDFXi'> YouTube link </a></p>
 </div>
 
 
@@ -224,7 +224,7 @@ <h3 id="q1-num-eights">Q1: Num Eights</h3>
 
 <p><strong>Important:</strong>
 Use recursion; the tests will fail if you use any assignment statements or loops.
-(You can, however, use function definitions if you'd like.)</p>
+(You can define new functions, but don't put assignment statements there either.)</p>
 
 <solution>
 
@@ -272,32 +272,28 @@ <h3 id="q2-digit-distance">Q2: Digit Distance</h3>
 consecutive digits. For example:</p>
 
 <ul>
-  <li>The digit distance of <code>6</code> is <code>0</code>.</li>
   <li>The digit distance of <code>61</code> is <code>5</code>, as the absolute value of <code>6 &#x2d; 1</code> is <code>5</code>.</li>
-  <li>The digit distance of <code>71253</code> is <code>12</code> (<code>6 + 1 + 3 + 2</code>).</li>
+  <li>The digit distance of <code>71253</code> is <code>12</code> (<code>abs(7&#x2d;1) + abs(1&#x2d;2) + abs(2&#x2d;5) + abs(5&#x2d;3)</code> = <code>6 + 1 + 3 + 2</code>).</li>
+  <li>The digit distance of <code>6</code> is <code>0</code> because there are no pairs of consecutive digits.</li>
 </ul>
 
-<p>Write a function that determines the digit distance of a given positive integer.
+<p>Write a function that determines the digit distance of a positive integer.
 You must use recursion or the tests will fail.</p>
 
-<blockquote><p><strong>Hint:</strong> There are multiple valid ways of solving this problem!
-If you're stuck, try writing out an iterative solution
-first, and then convert your iterative solution into a recursive one.</p></blockquote>
-
 <solution>
 
 <pre><code>def digit_distance(n):
     &quot;&quot;&quot;Determines the digit distance of n.
 
     &gt;&gt;&gt; digit_distance(3)
     0
-    &gt;&gt;&gt; digit_distance(777)
+    &gt;&gt;&gt; digit_distance(777) # 0 + 0
     0
-    &gt;&gt;&gt; digit_distance(314)
+    &gt;&gt;&gt; digit_distance(314) # 2 + 3
     5
-    &gt;&gt;&gt; digit_distance(31415926535)
+    &gt;&gt;&gt; digit_distance(31415926535) # 2 + 3 + 3 + 4 + ... + 2
     32
-    &gt;&gt;&gt; digit_distance(3464660003)
+    &gt;&gt;&gt; digit_distance(3464660003)  # 1 + 2 + 2 + 2 + ... + 3
     16
     &gt;&gt;&gt; from construct_check import check
     &gt;&gt;&gt; # ban all loops
@@ -316,8 +312,6 @@ <h3 id="q2-digit-distance">Q2: Digit Distance</h3>
         </script>
         <br/>
 
-</p>
-
 <!--  -->
 
 
@@ -333,7 +327,7 @@ <h3 id="q3-interleaved-sum">Q3: Interleaved Sum</h3>
 returns <code>1 + 2*2 + 3 + 4*4 + 5 = 29</code>.</p>
 
 <blockquote><p><strong>Important:</strong> Implement this function without using any loops or directly testing if a number
-is odd or even -- aka modulos (<code>%</code>) are not allowed! Instead of directly checking whether a number
+is odd or even (no using <code>%</code>). Instead of directly checking whether a number
 is even or odd, start with 1, which you know is an odd number.</p>
 
 <p><strong>Hint:</strong> Introduce an inner helper function that takes an odd number <code>k</code> and
@@ -392,7 +386,7 @@ <h1 id="submit-assignment">Submit Assignment</h1>
 <h1 id="just-for-fun-questions">Just For Fun Questions</h1>
 
 
-<p>The questions below are out of scope for 61A. You can try them if you want an extra challenge, but they're just puzzles that are not required for the course. Almost all students will skip them, and that's fine. We will <strong>not</strong> be prioritizing support for these questions on Ed or during Office Hours.</p>
+<p>The questions below are optional and not representative of exam questions. You can try them if you want an extra challenge, but they're just puzzles that are not required for the course. Almost all students will skip them, and that's fine. We will <strong>not</strong> be prioritizing support for these questions on Ed or during office hours.</p>
 
 
 <h3 id="q4-towers-of-hanoi">Q4: Towers of Hanoi</h3>