feat: add get_primes_in_range & get_prime_factorization to pre-algebra notebook

notebooks/pre-algebra/unit1.ipynb

@@ -38,7 +38,7 @@
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   {
    "cell_type": "code",
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@@ -85,7 +85,7 @@
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@@ -130,7 +130,7 @@
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@@ -158,7 +158,7 @@
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@@ -186,7 +186,7 @@
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@@ -224,7 +224,7 @@
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@@ -260,7 +260,7 @@
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    "source": [
@@ -279,6 +279,99 @@
     "assert is_composite(59) == False\n",
     "assert is_composite(72) == True"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Write a program that finds all prime numbers of a positive integer `n` in the range `[n, end]`.**\n",
+    "\n",
+    "- Assume that `n` and `end` are positive integers greater than or equal to 1.\n",
+    "\n",
+    "For example for `n = 1` and `end = 20`, the output of `get_primes_in_range(1, 20)` may be:\n",
+    "\n",
+    "```\n",
+    "{2, 3, 5, 7, 11, 13, 17, 19}\n",
+    "```"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 51,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def get_primes_in_range(n: int, end: int) -> set:\n",
+    "    primes: set = set()\n",
+    "    for num in range(n, end + 1):\n",
+    "        if is_prime(num):\n",
+    "            primes.add(num)\n",
+    "    return primes\n",
+    "\n",
+    "assert get_primes_in_range(1, 1) == set()\n",
+    "assert get_primes_in_range(1, 2) == {2}\n",
+    "assert get_primes_in_range(1, 20) == {2, 3, 5, 7, 11, 13, 17, 19}\n",
+    "assert get_primes_in_range(3, 20) == {3, 5, 7, 11, 13, 17, 19}\n",
+    "assert get_primes_in_range(1, 50) == {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47}\n",
+    "assert get_primes_in_range(32, 85) == {37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Write a program that determines the prime factorization of a positive integer `n`.**\n",
+    "\n",
+    "For example for `n = 12`, the output of `get_prime_factorization(12)` may be:\n",
+    "\n",
+    "```\n",
+    "{2: 2, 3: 1}\n",
+    "```\n",
+    "\n",
+    "This means the prime factorization of 12 is $2^2 \\times 3^1$, where the keys are the prime factors and the values are the exponents."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 52,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def get_prime_factorization(n: int) -> dict:\n",
+    "    if n == 1: return {}\n",
+    "    prime_factors: dict = {}\n",
+    "    primes_of_n: set = get_primes_in_range(1, n)\n",
+    "    current_num: int = n\n",
+    "    for prime in primes_of_n:\n",
+    "        while current_num % prime == 0:\n",
+    "            current_num //= prime\n",
+    "            if prime not in prime_factors:\n",
+    "                prime_factors[prime] = 1\n",
+    "            else:\n",
+    "                prime_factors[prime] += 1\n",
+    "        if current_num in primes_of_n:\n",
+    "            if current_num not in prime_factors:\n",
+    "                prime_factors[current_num] = 1\n",
+    "            else:\n",
+    "                prime_factors[current_num] += 1\n",
+    "            break\n",
+    "        elif current_num == 1:\n",
+    "            break\n",
+    "    return prime_factors\n",
+    "\n",
+    "assert get_prime_factorization(1) == {}\n",
+    "assert get_prime_factorization(2) == {2: 1}\n",
+    "assert get_prime_factorization(3) == {3: 1}\n",
+    "assert get_prime_factorization(4) == {2: 2}\n",
+    "assert get_prime_factorization(5) == {5: 1}\n",
+    "assert get_prime_factorization(6) == {2: 1, 3: 1}\n",
+    "assert get_prime_factorization(10) == {2: 1, 5: 1}\n",
+    "assert get_prime_factorization(12) == {2: 2, 3: 1}\n",
+    "assert get_prime_factorization(13) == {13: 1}\n",
+    "assert get_prime_factorization(20) == {2: 2, 5: 1}\n",
+    "assert get_prime_factorization(75) == {3: 1, 5: 2}\n",
+    "assert get_prime_factorization(750) == {2: 1, 3: 1, 5: 3}"
+   ]
   }
  ],
  "metadata": {