Add lru_cache section

Functional_Programming/Functional_Programming.ipynb

@@ -1233,6 +1233,72 @@
         }
       ]
     },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "3RXw2BcA21La"
+      },
+      "source": [
+        "> The lru_cache decorator\n",
+        "\n",
+        "Another useful usage of a decorator is caching.\n",
+        "In python, the **lru_cache** remember the value from previous calls.\n",
+        "\n",
+        "Using a cache in a function that calculate the same value multiple time reduce drastically the amount of computation involved : "
+      ]
+    },
+    {
+      "cell_type": "code",
+      "metadata": {
+        "id": "VswQfp534Xh2",
+        "outputId": "05043055-3af0-44b2-bc7a-fd4ffac463ba",
+        "colab": {
+          "base_uri": "https://localhost:8080/"
+        }
+      },
+      "source": [
+        "from functools import lru_cache\n",
+        "import timeit\n",
+        "\n",
+        "def fib(n = 10):\n",
+        "    if n == 0:\n",
+        "        return 0\n",
+        "    if n == 1:\n",
+        "        return 1\n",
+        "    return fib(n - 1) + fib(n - 2)\n",
+        "\n",
+        "@lru_cache()\n",
+        "def fib_opt(n = 10):\n",
+        "    if n == 0:\n",
+        "        return 0\n",
+        "    if n == 1:\n",
+        "        return 1\n",
+        "    return fib(n - 1) + fib(n - 2)\n",
+        "\n",
+        "time1 = timeit.timeit(fib, number=100)\n",
+        "time2 = timeit.timeit(fib_opt, number=100)\n",
+        "print(time1, time2)"
+      ],
+      "execution_count": 1,
+      "outputs": [
+        {
+          "output_type": "stream",
+          "text": [
+            "0.0025363270000013927 3.17219999885765e-05\n"
+          ],
+          "name": "stdout"
+        }
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "xOc2_UGA4jLf"
+      },
+      "source": [
+        "The example above (using the fibonacci function) show the difference of time elapsed between a function using a cache and one that isn't."
+      ]
+    },
     {
       "cell_type": "markdown",
       "metadata": {
@@ -2095,4 +2161,4 @@
       ]
     }
   ]
-}
+}