Streamline previous content
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13 changed files with 5091 additions and 3409 deletions
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@ -91,7 +91,7 @@
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" Args:\n",
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" n (int): seconds until the party begins\n",
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" \"\"\"\n",
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" if n == 0: # base case\n",
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" if n == 0: # = base case\n",
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" print(\"Happy New Year!\")\n",
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" else:\n",
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" print(n)\n",
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@ -222,7 +222,7 @@
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" Returns:\n",
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" factorial (int)\n",
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" \"\"\"\n",
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" if n == 0:\n",
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" if n == 0: # = base case\n",
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" return 1\n",
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" else:\n",
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" recurse = factorial(n - 1)\n",
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@ -323,7 +323,7 @@
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" Returns:\n",
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" factorial (int)\n",
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" \"\"\"\n",
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" if n == 0:\n",
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" if n == 0: # = base case\n",
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" return 1\n",
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" return n * factorial(n - 1)"
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]
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@ -517,7 +517,7 @@
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" Returns:\n",
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" gcd (int)\n",
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" \"\"\"\n",
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" if b == 0:\n",
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" if b == 0: # = base case\n",
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" return a \n",
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" return gcd(b, a % b)"
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]
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@ -787,9 +787,9 @@
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" Returns:\n",
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" ith_fibonacci (int)\n",
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" \"\"\"\n",
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" if i == 0:\n",
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" if i == 0: # = first base case\n",
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" return 0\n",
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" elif i == 1:\n",
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" elif i == 1: # = second base case\n",
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" return 1\n",
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" return fibonacci(i - 1) + fibonacci(i - 2)"
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]
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@ -841,7 +841,7 @@
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"\n",
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"To understand this in detail, we would have to study algorithms and data structures (e.g., with [this book](https://www.amazon.de/Introduction-Algorithms-Press-Thomas-Cormen/dp/0262033844/ref=sr_1_1?__mk_de_DE=%C3%85M%C3%85%C5%BD%C3%95%C3%91&crid=1JNE8U0VZGU0O&qid=1569837169&s=gateway&sprefix=algorithms+an%2Caps%2C180&sr=8-1)), a discipline within computer science, and dive into the analysis of **[time complexity of algorithms](https://en.wikipedia.org/wiki/Time_complexity)**.\n",
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"\n",
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"Luckily, in the Fibonacci case, the inefficiency can be resolved with a **caching** (i.e., \"re-use\") strategy from the field of **[dynamic programming](https://en.wikipedia.org/wiki/Dynamic_programming)**, namely **[memoization](https://en.wikipedia.org/wiki/Memoization)**. We do so in Chapter 8, after introducing the [dictionaries](https://docs.python.org/3/library/stdtypes.html#dict) data type.\n",
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"Luckily, in the Fibonacci case, the inefficiency can be resolved with a **caching** (i.e., \"reuse\") strategy from the field of **[dynamic programming](https://en.wikipedia.org/wiki/Dynamic_programming)**, namely **[memoization](https://en.wikipedia.org/wiki/Memoization)**. We do so in [Chapter 8](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/08_mappings.ipynb#Memoization), after introducing the [dictionaries](https://docs.python.org/3/library/stdtypes.html#dict) data type.\n",
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"\n",
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"Let's measure the average run times for `fibonacci()` and varying `i` arguments with the `%%timeit` [cell magic](https://ipython.readthedocs.io/en/stable/interactive/magics.html#magic-timeit) that comes with Jupyter."
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]
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@ -859,7 +859,7 @@
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"36.5 µs ± 2.47 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
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"37.5 µs ± 4.26 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
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]
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}
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],
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@ -881,7 +881,7 @@
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"1.58 ms ± 20.7 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
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"1.49 ms ± 22.4 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)\n"
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]
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}
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],
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@ -903,7 +903,7 @@
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"194 ms ± 0 ns per loop (mean ± std. dev. of 1 run, 1 loop each)\n"
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"199 ms ± 0 ns per loop (mean ± std. dev. of 1 run, 1 loop each)\n"
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]
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}
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],
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@ -925,7 +925,7 @@
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"2.15 s ± 0 ns per loop (mean ± std. dev. of 1 run, 1 loop each)\n"
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"2.04 s ± 0 ns per loop (mean ± std. dev. of 1 run, 1 loop each)\n"
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]
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}
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],
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@ -947,7 +947,7 @@
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"5.59 s ± 0 ns per loop (mean ± std. dev. of 1 run, 1 loop each)\n"
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"5.33 s ± 0 ns per loop (mean ± std. dev. of 1 run, 1 loop each)\n"
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]
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}
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],
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@ -4011,9 +4011,9 @@
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"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
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"\u001b[0;31mRecursionError\u001b[0m Traceback (most recent call last)",
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"\u001b[0;32m<ipython-input-30-43e3ad331761>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mcountdown\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3.1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
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"\u001b[0;32m<ipython-input-1-6001bec3d961>\u001b[0m in \u001b[0;36mcountdown\u001b[0;34m(n)\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 10\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m \u001b[0mcountdown\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
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"\u001b[0;32m<ipython-input-1-d7441c038fc8>\u001b[0m in \u001b[0;36mcountdown\u001b[0;34m(n)\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 10\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m \u001b[0mcountdown\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
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"... last 1 frames repeated, from the frame below ...\n",
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"\u001b[0;32m<ipython-input-1-6001bec3d961>\u001b[0m in \u001b[0;36mcountdown\u001b[0;34m(n)\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 10\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m \u001b[0mcountdown\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
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"\u001b[0;32m<ipython-input-1-d7441c038fc8>\u001b[0m in \u001b[0;36mcountdown\u001b[0;34m(n)\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 10\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m \u001b[0mcountdown\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
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"\u001b[0;31mRecursionError\u001b[0m: maximum recursion depth exceeded while calling a Python object"
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]
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}
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"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
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"\u001b[0;31mRecursionError\u001b[0m Traceback (most recent call last)",
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"\u001b[0;32m<ipython-input-31-188b816be8b6>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mfactorial\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3.1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
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"\u001b[0;32m<ipython-input-6-88d8d933f651>\u001b[0m in \u001b[0;36mfactorial\u001b[0;34m(n)\u001b[0m\n\u001b[1;32m 10\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 11\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 12\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mfactorial\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
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"\u001b[0;32m<ipython-input-6-d41f5be5adaa>\u001b[0m in \u001b[0;36mfactorial\u001b[0;34m(n)\u001b[0m\n\u001b[1;32m 10\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;31m# = base case\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 11\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 12\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mfactorial\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
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"... last 1 frames repeated, from the frame below ...\n",
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"\u001b[0;32m<ipython-input-6-88d8d933f651>\u001b[0m in \u001b[0;36mfactorial\u001b[0;34m(n)\u001b[0m\n\u001b[1;32m 10\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 11\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 12\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mfactorial\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
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"\u001b[0;32m<ipython-input-6-d41f5be5adaa>\u001b[0m in \u001b[0;36mfactorial\u001b[0;34m(n)\u001b[0m\n\u001b[1;32m 10\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;31m# = base case\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 11\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 12\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mfactorial\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
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"\u001b[0;31mRecursionError\u001b[0m: maximum recursion depth exceeded in comparison"
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]
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}
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" raise TypeError(\"Factorial is only defined for integers\")\n",
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" elif n < 0:\n",
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" raise ValueError(\"Factorial is not defined for negative integers\")\n",
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" elif n == 0:\n",
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" elif n == 0: # = base case\n",
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" return 1\n",
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" return n * factorial(n - 1)"
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]
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"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
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"\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)",
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"\u001b[0;32m<ipython-input-35-188b816be8b6>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mfactorial\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3.1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
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"\u001b[0;32m<ipython-input-32-54b57bc2107d>\u001b[0m in \u001b[0;36mfactorial\u001b[0;34m(n)\u001b[0m\n\u001b[1;32m 13\u001b[0m \"\"\"\n\u001b[1;32m 14\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mint\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 15\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Factorial is only defined for integers\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 16\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 17\u001b[0m \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Factorial is not defined for negative integers\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;32m<ipython-input-32-ff0b507f76b8>\u001b[0m in \u001b[0;36mfactorial\u001b[0;34m(n)\u001b[0m\n\u001b[1;32m 13\u001b[0m \"\"\"\n\u001b[1;32m 14\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mint\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 15\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Factorial is only defined for integers\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 16\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 17\u001b[0m \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Factorial is not defined for negative integers\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;31mTypeError\u001b[0m: Factorial is only defined for integers"
|
||||
]
|
||||
}
|
||||
|
|
@ -4261,7 +4261,7 @@
|
|||
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
|
||||
"\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
|
||||
"\u001b[0;32m<ipython-input-36-b06b2cada645>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mfactorial\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m42\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
|
||||
"\u001b[0;32m<ipython-input-32-54b57bc2107d>\u001b[0m in \u001b[0;36mfactorial\u001b[0;34m(n)\u001b[0m\n\u001b[1;32m 15\u001b[0m \u001b[0;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Factorial is only defined for integers\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 16\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 17\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Factorial is not defined for negative integers\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 18\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 19\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;32m<ipython-input-32-ff0b507f76b8>\u001b[0m in \u001b[0;36mfactorial\u001b[0;34m(n)\u001b[0m\n\u001b[1;32m 15\u001b[0m \u001b[0;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Factorial is only defined for integers\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 16\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 17\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Factorial is not defined for negative integers\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 18\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;31m# = base case\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 19\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
|
||||
"\u001b[0;31mValueError\u001b[0m: Factorial is not defined for negative integers"
|
||||
]
|
||||
}
|
||||
|
|
@ -4565,7 +4565,7 @@
|
|||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"4.69 s ± 0 ns per loop (mean ± std. dev. of 1 run, 1 loop each)\n"
|
||||
"4.6 s ± 0 ns per loop (mean ± std. dev. of 1 run, 1 loop each)\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
@ -4790,11 +4790,11 @@
|
|||
}
|
||||
},
|
||||
"source": [
|
||||
"Recursion and the `while` statement are two sides of the same coin. Disregarding that in the case of recursion Python internally faces some additional burden for managing the stack of frames in memory, both approaches lead to the *same* computational steps in memory. More importantly, we can re-formulate a recursive implementation in an iterative way and vice versa despite one of the two ways often \"feeling\" a lot more natural given a particular problem.\n",
|
||||
"Recursion and the `while` statement are two sides of the same coin. Disregarding that in the case of recursion Python internally faces some additional burden for managing the stack of frames in memory, both approaches lead to the *same* computational steps in memory. More importantly, we can formulate any recursive implementation in an iterative way and vice versa despite one of the two ways often \"feeling\" a lot more natural given a particular problem.\n",
|
||||
"\n",
|
||||
"So how does the compound `for` statement (cf., [reference](https://docs.python.org/3/reference/compound_stmts.html#the-for-statement)) in this book's very first example fit into this picture? It is a *redundant* language construct to provide a *shorter* and more *convenient* syntax for common applications of the `while` statement. In programming, such additions to a language are called **syntactic sugar**. A cup of tea tastes better with sugar, but we may drink tea without sugar too.\n",
|
||||
"\n",
|
||||
"Consider `elements` below. Without the `for` statement, we have to manage a temporary **index variable**, `index`, to loop over all the elements and also obtain the individual elements with the `[]` operator in each iteration of the loop."
|
||||
"Consider `elements` below. Without the `for` statement, we must manage a temporary **index variable**, `index`, to loop over all the elements and also obtain the individual elements with the `[]` operator in each iteration of the loop."
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -5000,21 +5000,21 @@
|
|||
}
|
||||
},
|
||||
"source": [
|
||||
"The essential difference between the above `list` objects, `[0, 1, 2, 3, 4]` and `[1, 3, 5, 7, 9]`, and the `range` objects, `range(5)` and `range(1, 10, 2)`, is that in the former case *six* objects are created in memory *before* the `for` statement starts running, *one* `list` holding pointers to *five* `int` objects, whereas in the latter case only *one* `range` object is created that **generates** `int` objects one at a time *while* the `for`-loop runs.\n",
|
||||
"The essential difference between the above `list` objects, `[0, 1, 2, 3, 4]` and `[1, 3, 5, 7, 9]`, and the `range` objects, `range(5)` and `range(1, 10, 2)`, is that in the former case *six* objects are created in memory *before* the `for` statement starts running, *one* `list` holding references to *five* `int` objects, whereas in the latter case only *one* `range` object is created that **generates** `int` objects one at a time *while* the `for`-loop runs.\n",
|
||||
"\n",
|
||||
"However, we can loop over both of them. So a natural question to ask is why Python treats objects of *different* types in the *same* way when used with a `for` statement.\n",
|
||||
"\n",
|
||||
"So far, the overarching storyline in this book goes like this: In Python, *everything* is an object. Besides its *identity* and *value*, every object is characterized by belonging to *one data type* that determines how the object behaves and what we may do with it.\n",
|
||||
"So far, the overarching storyline in this book goes like this: In Python, *everything* is an object. Besides its *identity* and *value*, every object is characterized by \"belonging\" to *one* data type that determines how the object behaves and what we may do with it.\n",
|
||||
"\n",
|
||||
"Now, just as we classify objects by their types, we also classify these **concrete data types** (e.g., `int`, `float`, `str`, or `list`) into **abstract concepts**.\n",
|
||||
"Now, just as we classify objects by data type, we also classify these data types (e.g., `int`, `float`, `str`, or `list`) into **abstract concepts**.\n",
|
||||
"\n",
|
||||
"We did this already in [Chapter 1](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/01_elements.ipynb#Who-am-I?-And-how-many?) when we described a `list` object as \"some sort of container that holds [...] pointers to other objects\". So, abstractly speaking, **containers** are any objects that are \"composed\" of other objects and also \"manage\" how these objects are organized. `list` objects, for example, have the property that they model an internal order associated with its elements. There exist, however, other container types, many of which do *not* come with an order. So, containers primarily \"contain\" other objects and have *nothing* to do with looping.\n",
|
||||
"We did this already in [Chapter 1](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/01_elements.ipynb#Who-am-I?-And-how-many?) when we described a `list` object as \"some sort of container that holds [...] references to other objects\". So, abstractly speaking, **containers** are any objects that are \"composed\" of other objects and also \"manage\" how these objects are organized. `list` objects, for example, have the property that they model an order associated with their elements. There exist, however, other container types, many of which do *not* come with an order. So, containers primarily \"contain\" other objects and have *nothing* to do with looping.\n",
|
||||
"\n",
|
||||
"On the contrary, the abstract concept of **iterables** is all about looping: Any object that we can loop over is, by definition, an iterable. So, `range` objects, for example, are iterables that do *not* contain other objects. Moreover, looping does *not* have to occur in a *predictable* order, although this is the case for both `list` and `range` objects.\n",
|
||||
"On the contrary, the abstract concept of **iterables** is all about looping: Any object that we can loop over is, by definition, an iterable. So, `range` objects, for example, are iterables, even though they hold no references to other objects. Moreover, looping does *not* have to occur in a *predictable* order, although this is the case for both `list` and `range` objects.\n",
|
||||
"\n",
|
||||
"Typically, containers are iterables, and iterables are containers. Yet, only because these two concepts coincide often, we must not think of them as the same. Chapter 9 finally gives an explanation as to how abstract concepts are implemented and play together.\n",
|
||||
"Typically, containers are iterables, and iterables are containers. Yet, only because these two concepts coincide often, we must not think of them as the same. In [Chapter 7](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/07_sequences.ipynb#Collections-vs.-Sequences), we formalize these two concepts and introduce many more. Finally, Chapter 9 gives an explanation how abstract concepts are implemented and play together.\n",
|
||||
"\n",
|
||||
"So, `list` objects like `first_names` below are iterable containers. They implement even more abstract concepts, as [Chapter 7](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/07_sequences.ipynb#Collections-vs.-Sequences) reveals."
|
||||
"Let's continue with `first_names` below as an example an illustrate what iterable containers are."
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -5038,7 +5038,7 @@
|
|||
}
|
||||
},
|
||||
"source": [
|
||||
"The characteristic operator associated with a container type is the `in` operator: It checks if a given object evaluates equal to at least one of the objects in the container. Colloquially, it checks if an object is \"contained\" in the container. Formally, this operation is called **membership testing**."
|
||||
"The characteristic operator associated with container types is the `in` operator: It checks if a given object evaluates equal to at least one of the objects in the container. Colloquially, it checks if an object is \"contained\" in the container. Formally, this operation is called **membership testing**."
|
||||
]
|
||||
},
|
||||
{
|
||||
|
|
@ -5112,7 +5112,7 @@
|
|||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"True"
|
||||
"[0, 1, 2, 3, 4]"
|
||||
]
|
||||
},
|
||||
"execution_count": 58,
|
||||
|
|
@ -5120,6 +5120,30 @@
|
|||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"elements"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 59,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "skip"
|
||||
}
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"True"
|
||||
]
|
||||
},
|
||||
"execution_count": 59,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"3.0 in elements"
|
||||
]
|
||||
|
|
@ -5137,7 +5161,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 59,
|
||||
"execution_count": 60,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "slide"
|
||||
|
|
@ -5170,7 +5194,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 60,
|
||||
"execution_count": 61,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "fragment"
|
||||
|
|
@ -5203,7 +5227,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 61,
|
||||
"execution_count": 62,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "skip"
|
||||
|
|
@ -5236,7 +5260,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 62,
|
||||
"execution_count": 63,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "skip"
|
||||
|
|
@ -5249,7 +5273,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 63,
|
||||
"execution_count": 64,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "skip"
|
||||
|
|
@ -5297,7 +5321,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 64,
|
||||
"execution_count": 65,
|
||||
"metadata": {
|
||||
"code_folding": [],
|
||||
"slideshow": {
|
||||
|
|
@ -5338,7 +5362,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 65,
|
||||
"execution_count": 66,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "slide"
|
||||
|
|
@ -5358,7 +5382,7 @@
|
|||
"144"
|
||||
]
|
||||
},
|
||||
"execution_count": 65,
|
||||
"execution_count": 66,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
|
|
@ -5391,7 +5415,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 66,
|
||||
"execution_count": 67,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "slide"
|
||||
|
|
@ -5411,7 +5435,7 @@
|
|||
"218922995834555169026"
|
||||
]
|
||||
},
|
||||
"execution_count": 66,
|
||||
"execution_count": 67,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
|
|
@ -5444,7 +5468,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 67,
|
||||
"execution_count": 68,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "slide"
|
||||
|
|
@ -5480,7 +5504,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 68,
|
||||
"execution_count": 69,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "slide"
|
||||
|
|
@ -5500,7 +5524,7 @@
|
|||
"3628800"
|
||||
]
|
||||
},
|
||||
"execution_count": 68,
|
||||
"execution_count": 69,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
|
|
@ -5555,7 +5579,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 69,
|
||||
"execution_count": 70,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "slide"
|
||||
|
|
@ -5568,7 +5592,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 70,
|
||||
"execution_count": 71,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "-"
|
||||
|
|
@ -5592,7 +5616,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 71,
|
||||
"execution_count": 72,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "fragment"
|
||||
|
|
@ -5638,7 +5662,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 72,
|
||||
"execution_count": 73,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "slide"
|
||||
|
|
@ -5716,7 +5740,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 73,
|
||||
"execution_count": 74,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "slide"
|
||||
|
|
@ -5759,7 +5783,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 74,
|
||||
"execution_count": 75,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "slide"
|
||||
|
|
@ -5797,7 +5821,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 75,
|
||||
"execution_count": 76,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "skip"
|
||||
|
|
@ -5885,7 +5909,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 76,
|
||||
"execution_count": 77,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "slide"
|
||||
|
|
@ -5898,7 +5922,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 77,
|
||||
"execution_count": 78,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "-"
|
||||
|
|
@ -5918,7 +5942,7 @@
|
|||
"370"
|
||||
]
|
||||
},
|
||||
"execution_count": 77,
|
||||
"execution_count": 78,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
|
|
@ -5980,7 +6004,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 78,
|
||||
"execution_count": 79,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "slide"
|
||||
|
|
@ -5993,7 +6017,7 @@
|
|||
"[7, 11, 8, 5, 3, 12, 2, 6, 9, 10, 1, 4]"
|
||||
]
|
||||
},
|
||||
"execution_count": 78,
|
||||
"execution_count": 79,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
|
|
@ -6004,7 +6028,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 79,
|
||||
"execution_count": 80,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "-"
|
||||
|
|
@ -6024,7 +6048,7 @@
|
|||
"227"
|
||||
]
|
||||
},
|
||||
"execution_count": 79,
|
||||
"execution_count": 80,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
|
|
@ -6070,7 +6094,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 80,
|
||||
"execution_count": 81,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "slide"
|
||||
|
|
@ -6090,7 +6114,7 @@
|
|||
"227"
|
||||
]
|
||||
},
|
||||
"execution_count": 80,
|
||||
"execution_count": 81,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
|
|
@ -6178,7 +6202,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 81,
|
||||
"execution_count": 82,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "slide"
|
||||
|
|
@ -6191,7 +6215,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 82,
|
||||
"execution_count": 83,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "-"
|
||||
|
|
@ -6204,7 +6228,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 83,
|
||||
"execution_count": 84,
|
||||
"metadata": {
|
||||
"code_folding": [],
|
||||
"slideshow": {
|
||||
|
|
@ -6283,7 +6307,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 84,
|
||||
"execution_count": 85,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "slide"
|
||||
|
|
@ -6320,7 +6344,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 85,
|
||||
"execution_count": 86,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "slide"
|
||||
|
|
@ -6358,7 +6382,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 86,
|
||||
"execution_count": 87,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "skip"
|
||||
|
|
@ -6371,7 +6395,7 @@
|
|||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 87,
|
||||
"execution_count": 88,
|
||||
"metadata": {
|
||||
"slideshow": {
|
||||
"slide_type": "slide"
|
||||
|
|
@ -6441,7 +6465,7 @@
|
|||
"\n",
|
||||
"Second, the `while` and `for` statements are alternative and potentially more intuitive ways to express iteration as they correspond to a **forward** reasoning. The `for` statement is **syntactic sugar** that allows rewriting common occurrences of the `while` statement concisely. Python provides the `break` and `continue` statements as well as an optional `else`-clause that make working with the `for` and `while` statements even more convenient.\n",
|
||||
"\n",
|
||||
"**Iterables** are any **concrete data types** that support being looped over, for example, with the `for` statement. The idea behind iterables is an **abstract concept** that may or may not be implemented by any given concrete data type. For example, both `list` and `range` objects can be looped over. The `list` type is also a **container** as any given `list` objects \"contains\" pointers to other objects in memory. On the contrary, the `range` type does not point to any other objects but instead creates *new* `int` objects \"on the fly\" (i.e., when being looped over)."
|
||||
"**Iterables** are any **concrete data types** that support being looped over, for example, with the `for` statement. The idea behind iterables is an **abstract concept** that may or may not be implemented by any given concrete data type. For example, both `list` and `range` objects can be looped over. The `list` type is also a **container** as any given `list` objects \"contains\" references to other objects in memory. On the contrary, the `range` type does not reference any other object but instead creates *new* `int` objects \"on the fly\" (i.e., when being looped over)."
|
||||
]
|
||||
}
|
||||
],
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue