Some Dynamic Programming Concept

Author: Gaurav-pandey04

Dynamic Programming/Climbing_staris.ipynb

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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "4a8d9a75",
+ "metadata": {},
+ "source": [
+ "# Climibing Staris "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "6c331f02",
+ "metadata": {},
+ "source": [
+ "### Recursion"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "09992779",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "13\n"
+ ]
+ }
+ ],
+ "source": [
+ "n = 6\n",
+ "if n<2:\n",
+ " print(1)\n",
+ "\n",
+ "a, b = 1, 1\n",
+ "for _ in range(2, n+1):\n",
+ " a, b = b, a+b\n",
+ "\n",
+ "print(b)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "e5bc268f",
+ "metadata": {},
+ "source": [
+ "### Dynamic Approach"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "id": "71177526",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "8"
+ ]
+ },
+ "execution_count": 8,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "n = 5\n",
+ "dp = [0]*(n+1)\n",
+ "dp[0] = 1\n",
+ "dp[1] = 1\n",
+ "\n",
+ "for i in range(2, n+1):\n",
+ " dp[i] = dp[i-1]+dp[i-2]\n",
+ "\n",
+ "dp[n]"
+ ]
+ }
+ ],
+ "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": "3.13.3"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

Dynamic Programming/Triobannic_number.ipynb

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+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "f8990bae",
+ "metadata": {},
+ "source": [
+ "# N-th Triobnacci Number"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "id": "edee84b6",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "13"
+ ]
+ },
+ "execution_count": 2,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "n=6\n",
+ "\n",
+ "if n==0 or n==1:\n",
+ " print(n)\n",
+ "dp = [0]*(n+1)\n",
+ "dp[0], dp[1], dp[2] = 0, 1, 1\n",
+ "\n",
+ "for i in range(3, n+1):\n",
+ " dp[i] = dp[i-1] + dp[i-2] + dp[i-3]\n",
+ "\n",
+ "dp[n]"
+ ]
+ }
+ ],
+ "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": "3.13.3"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}