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Commit 9829ba4

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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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"source": [
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"## 3 Basic steps of Recursion:\n",
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"1) Base Case\n",
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"2) Induction Hypothesis\n",
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"3) Induction Step"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"def fact(n):\n",
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" if n == 0:\n",
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" return 1\n",
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" return n*fact(n-1)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"def fact(n):\n",
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" if n == 0:\n",
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" return 1\n",
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" smallOutput = fact(n-1)\n",
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" return n*smallOutput"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"58\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"2350561331282878571829474910515074683828862318181142924420699914240000000000000"
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]
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},
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"execution_count": 3,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"n = int(input())\n",
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"fact(n)"
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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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"source": [
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"### Sum of 'n' natural numbers:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"metadata": {},
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"outputs": [],
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"source": [
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"def sum(n):\n",
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" if n == 1:\n",
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" return 1\n",
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" return n + sum(n-1)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"10\n",
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"5050\n",
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"500500\n"
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]
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}
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],
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"source": [
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"n = int(input())\n",
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"sum(n)\n",
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"print(sum(n + 90))\n",
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"print(sum(n + 990))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"def sum(n):\n",
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" if n == 1:\n",
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" return 1\n",
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" smallOutput = sum(n-1)\n",
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" return n + smallOutput"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"10\n",
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"55\n",
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"3628800\n"
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]
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}
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],
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"source": [
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"n = int(input())\n",
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"print(sum(n))\n",
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"print(fact(n))"
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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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"source": [
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"### Power of a number"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 54,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"2 5\n",
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"1\n",
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"2\n",
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"3\n",
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"4\n",
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"5\n",
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"None\n"
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]
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}
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],
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"source": [
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"str = input().split()\n",
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"x, n = int(str[0]), int(str[1])\n",
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"\n",
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"def power(x,n):\n",
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" if n == 0:\n",
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" return 1\n",
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" power(x,n-1)\n",
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" print(n)\n",
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" x = x * x\n",
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" \n",
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"print(power(x,n))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": [
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"def func(num):\n",
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" return func(num-1)\n",
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"num = 5\n",
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"ans = func(num-1)\n",
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"print(ans)\n",
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"\n",
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"# Results in Recursion Error"
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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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"source": [
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"### Print numbers from 1 to n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 49,
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"metadata": {},
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"outputs": [],
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"source": [
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"def print_1_to_n(n):\n",
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" if n == 0:\n",
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" return n\n",
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" print_1_to_n(n-1)\n",
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" print(n)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 51,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"10\n",
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"1\n",
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"2\n",
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"3\n",
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"4\n",
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"5\n",
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"6\n",
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"7\n",
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"8\n",
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"9\n",
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"10\n"
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]
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}
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],
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"source": [
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"n = int(input())\n",
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"print_1_to_n(n)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 56,
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"metadata": {},
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"outputs": [],
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"source": [
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"def print_n_to_1(n):\n",
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" if n == 0:\n",
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" return n\n",
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" print(n)\n",
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" print_n_to_1(n-1)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 57,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"10\n",
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"10\n",
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"9\n",
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"8\n",
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"7\n",
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"6\n",
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"5\n",
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"4\n",
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"3\n",
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"2\n",
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"1\n"
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]
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}
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],
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"source": [
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"n = int(input())\n",
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"print_n_to_1(n)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 58,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"5 3 1 "
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]
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}
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],
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"source": [
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"#Predict the Output:\n",
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"def printNumbers(n):\n",
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" if(n<0):\n",
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" return\n",
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" print(n,end=\" \")\n",
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" printNumbers(n-2)\n",
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"num = 5\n",
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"printNumbers(num)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.7.3"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}

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