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‎EXERCISES/Exercises_Lecture_03.ipynb‎

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{
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"nbformat": 4,
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"nbformat_minor": 0,
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"metadata": {
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"colab": {
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"name": "SesionThree_Exercises.ipynb",
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"provenance": [],
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"collapsed_sections": [],
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"toc_visible": true
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},
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"kernelspec": {
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"name": "python3",
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"display_name": "Python 3"
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}
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},
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "KKn8pLWhJ0X9"
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},
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"source": [
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"# PYTHON COURSE FOR SCIENTIFIC PROGRAMMING \n",
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"**Contributors:** \\\n",
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"Artur Llabrés Brustenga: Artur.Llabres@e-campus.uab.cat \\\n",
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"Gerard Navarro Pérez: Gerard.NavarroP@e-campus.uab.cat \\\n",
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"Arnau Parrilla Gibert: Arnau.Parrilla@e-campus.uab.cat \\\n",
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"Jan Scarabelli Calopa:Jan.Scarabelli@e-campus.uab.cat \\\n",
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"Xabier Oyanguren Asua: Xabier.Oyanguren@e-campus.uab.cat \\\n",
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"\n",
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"Course material can be found at: https://llacorp.github.io/Python-Course-for-Scientific-Programming/ "
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "eYqb_LTserLh"
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},
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"source": [
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"# LESSON 3 EXERCISES"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "-rYMKOqDez5v"
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},
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"source": [
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"## <ins>Exercise 1</ins>:"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "0-NaBG9XhgU8"
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},
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"source": [
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"Write a Python function to check whether a number is perfect or not. It should return `True` or `False`.\r\n",
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"\r\n",
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"***Wikipedia source***: In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself (also known as its aliquot sum). Equivalently, a perfect number is a number that is half the sum of all of its positive divisors (including itself). \r\n",
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"<ins>For example</ins>: The first perfect number is 6, because 1, 2, and 3 are its proper positive divisors, and 1 + 2 + 3 = 6. Equivalently, the number 6 is equal to half the sum of all its positive divisors: ( 1 + 2 + 3 + 6 ) / 2 = 6. The next perfect number is 28 = 1 + 2 + 4 + 7 + 14. This is followed by the perfect numbers 496 and 8128."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "tR4v1HGeiApl"
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},
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"source": [
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"**SOLUTION**:"
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/"
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},
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"id": "4Iciqs4Sh-ar",
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"outputId": "f423d936-ccad-401d-ef14-e115c40708cb"
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},
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"source": [
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"def perfect_number(n):\r\n",
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" sum = 0\r\n",
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" for x in range(1, n):\r\n",
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" if n % x == 0:\r\n",
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" sum += x\r\n",
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" return sum == n\r\n",
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" \r\n",
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"print(perfect_number(6))"
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],
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"execution_count": null,
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"outputs": [
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{
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"output_type": "stream",
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"text": [
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"True\n"
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],
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"name": "stdout"
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}
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "0IZIsOxNjbhw"
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},
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"source": [
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"## <ins>Exercise 2</ins>:"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "PVlUe6mHjpeU"
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},
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"source": [
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"Write two Python functions to find the $F_n$ Fibonacci number using an iterative method and recursion. The only argument is `n`.\r\n",
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"\r\n",
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"***Wikipedia source***: In mathematics, the Fibonacci numbers, commonly denoted $F_n$, form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from 0 and 1. That is,\r\n",
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"\r\n",
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"$$F_{0}=0,\\quad F_{1}=1,$$\r\n",
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"and\r\n",
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"$$F_{n}=F_{n-1}+F_{n-2}$$\r\n",
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"for $n > 1$. \r\n",
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"The beginning of the sequence is thus:\r\n",
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"$$0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55,...$$\r\n",
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"\r\n",
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"<ins>For example</ins>: The Fibonacci number $F_7$ equals $13$, so the functions should return this value."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "XKhg1tVkjkto"
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},
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"source": [
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"**SOLUTION**:"
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "pKC9NZDYjnkg"
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},
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"source": [
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"def F_iter(n):\r\n",
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" if (n == 0):\r\n",
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" return 0\r\n",
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" elif (n == 1):\r\n",
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" return 1\r\n",
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" elif (n > 1):\r\n",
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" fn = 0\r\n",
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" fn1 = 1\r\n",
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" fn2 = 2\r\n",
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" for i in range(3, n):\r\n",
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" fn = fn1 + fn2\r\n",
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" fn1 = fn2\r\n",
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" fn2 = fn\r\n",
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" return fn\r\n",
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"\r\n",
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"def F(n):\r\n",
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" if (n == 0):\r\n",
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" return 0\r\n",
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" elif (n == 1):\r\n",
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" return 1\r\n",
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" elif (n > 1):\r\n",
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" return (F(n-1) + F(n-2))"
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],
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "code",
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/"
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},
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"id": "vmuuU6Qb4tHO",
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"outputId": "bc611b30-0594-4b6c-9efb-f6ff2c8507f0"
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},
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"source": [
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"print(F_iter(7))\r\n",
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"print(F(7))"
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],
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"execution_count": null,
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"outputs": [
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{
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"output_type": "stream",
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"text": [
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"13\n",
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"13\n"
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],
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"name": "stdout"
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}
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "bcsyVRrLjeNA"
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},
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"source": [
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"## <ins>Exercise 3</ins>:"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "mq5VNFVZjqdm"
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},
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"source": [
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"Write a Python program to create a dictionary from a string.\r\n",
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"\r\n",
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"***Note***: Track the count of the letters from the string. \r\n",
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"<ins>For example</ins>: The string 'scn2python' should output: `{'s': 1, 'c': 1, 'n': 2, '2': 1, 'p': 1, 'y': 1, 't': 1, 'h': 1, 'o': 1}`"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "w0UpFVuBjlXc"
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},
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"source": [
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"**SOLUTION**:"
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "enTtP8kljoZa",
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"colab": {
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"base_uri": "https://localhost:8080/"
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},
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"outputId": "3dfbcf73-0805-4853-a8c6-1c5949ea70a3"
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},
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"source": [
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"str1 = 'scn2python' \r\n",
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"my_dict = {}\r\n",
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"for letter in str1:\r\n",
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" if (my_dict.get(letter) == None):\r\n",
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" my_dict[letter] = 1\r\n",
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" else:\r\n",
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" my_dict[letter] += 1\r\n",
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"print(my_dict)"
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],
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"execution_count": null,
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"outputs": [
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{
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"output_type": "stream",
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"text": [
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"{'s': 1, 'c': 1, 'n': 2, '2': 1, 'p': 1, 'y': 1, 't': 1, 'h': 1, 'o': 1}\n"
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],
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"name": "stdout"
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}
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "ngPDJ-pSjgGb"
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},
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"source": [
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"## <ins>Exercise 4</ins>:"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "oMSJ_bvjjrNC"
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},
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"source": [
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""
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "JtjyQi2ujlzw"
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},
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"source": [
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"**SOLUTION**:"
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "ByVIxIpPjo32"
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},
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"source": [
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""
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],
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"execution_count": null,
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"outputs": []
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}
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]
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}

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