From 00e233507a6e81f7142fa0d9addd23a2b1287928 Mon Sep 17 00:00:00 2001
From: Andrey Golikov <aregularmailaddress@gmail.com>
Date: Fri, 17 Feb 2023 17:19:12 +0600
Subject: [PATCH] Initial commit

---
 task1.ipynb | 205 ++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 205 insertions(+)
 create mode 100644 task1.ipynb

diff --git a/task1.ipynb b/task1.ipynb
new file mode 100644
index 0000000..88abd88
--- /dev/null
+++ b/task1.ipynb
@@ -0,0 +1,205 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from typing import Callable"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "precision = 3\n",
+    "eps = 1 / precision\n",
+    "\n",
+    "def dichotomy(a: float, b: float, func: Callable[[float], float]) -> float:\n",
+    "    while True:\n",
+    "        x = (a + b) / 2\n",
+    "\n",
+    "        x1 = x - eps / 2\n",
+    "        f1 = func(x1)\n",
+    "\n",
+    "        x2 = x + eps / 2\n",
+    "        f2 = func(x2)\n",
+    "\n",
+    "        if f1 > f2:\n",
+    "            a = x1\n",
+    "        else:\n",
+    "            b = x2\n",
+    "        \n",
+    "        if abs(a - b) <= 2 * eps:\n",
+    "            break\n",
+    "    return round(func((a + b) / 2), precision)\n",
+    "\n",
+    "\n",
+    "def fibonacci(a: float, b: float, func: Callable[[float], float]) -> float:\n",
+    "    n: int = 1000\n",
+    "    fibonacciSequence = [1, 1]\n",
+    "    \n",
+    "    for i in range(1, n - 1):\n",
+    "        fibonacciSequence.append(fibonacciSequence[i - 1] + fibonacciSequence[i])\n",
+    "    \n",
+    "    L = b - a\n",
+    "    while n > 2:\n",
+    "        x1 = a + L * fibonacciSequence[n - 2] / fibonacciSequence[n - 1]\n",
+    "        x2 = b - L * fibonacciSequence[n - 2] / fibonacciSequence[n - 1]\n",
+    "\n",
+    "        f1 = func(x1)\n",
+    "        f2 = func(x2)\n",
+    "\n",
+    "        if f1 > f2:\n",
+    "            b = x1\n",
+    "            f1 = f2\n",
+    "            x1 = x2\n",
+    "            L = b - a\n",
+    "            x2 = a + (b - x1)\n",
+    "            f2 = func(x2)\n",
+    "        else:\n",
+    "            a = x2\n",
+    "            f2 = f1\n",
+    "            x2 = x1\n",
+    "            L = b - a\n",
+    "            x1 = b - (x2 - a)\n",
+    "            f1 = func(x1)\n",
+    "        \n",
+    "        n -= 1\n",
+    "    return round(min(f1, f2), precision)\n",
+    "\n",
+    "\n",
+    "def goldenRatio(a: float, b: float, func: Callable[[float], float]) -> float:\n",
+    "    ratio = 0.618\n",
+    "    while True:\n",
+    "        L: float = abs(a - b)\n",
+    "\n",
+    "        x1 = a + L * ratio\n",
+    "        x2 = b - L * ratio\n",
+    "\n",
+    "        f1 = func(x1)\n",
+    "        f2 = func(x2)\n",
+    "\n",
+    "        if f1 > f2:\n",
+    "            b = x1\n",
+    "            f1 = f2\n",
+    "            x1 = x2\n",
+    "            L = b - a\n",
+    "            x2 = a + (b - x1)\n",
+    "            f2 = func(x2)\n",
+    "        else:\n",
+    "            a = x2\n",
+    "            f2 = f1\n",
+    "            x2 = x1\n",
+    "            L = b - a\n",
+    "            x1 = b - (x2 - a)\n",
+    "            f1 = func(x1)\n",
+    "        \n",
+    "        if L <= eps:\n",
+    "            break\n",
+    "    return round(min(f1, f2), precision)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "func = lambda x: (x - 15)**2 + 5\n",
+    "a = 12\n",
+    "b = 20"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "5.0003370667"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "dichotomy(a, b, func)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "5.0"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "fibonacci(a, b, func)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "5.0000883205"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "goldenRatio(a, b, func)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.10.4"
+  },
+  "orig_nbformat": 4,
+  "vscode": {
+   "interpreter": {
+    "hash": "d68a9a56d9a25e4bd7befbd53d862537883bbf75717698e3f2bd31fa571ddf98"
+   }
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}