Climbing Stairs Problem in DSA Typescript - Build from Scratch

Climbing Stairs Problem

📖 Scenario: Imagine you want to climb a staircase that has a certain number of steps. You can climb either 1 step or 2 steps at a time. You want to find out how many different ways you can reach the top.

🎯 Goal: Build a program that calculates the number of distinct ways to climb to the top of a staircase with n steps, where you can take either 1 or 2 steps at a time.

📋 What You'll Learn

Create a variable n to represent the total number of steps in the staircase.

Create a variable ways to store the number of ways to climb each step.

Use a loop to calculate the number of ways to reach each step from 1 to n.

Print the total number of ways to climb n steps.

💡 Why This Matters

🌍 Real World

This problem models situations where you need to count different ways to reach a goal with limited moves, like climbing stairs or steps in a game.

💼 Career

Understanding this problem helps with learning dynamic programming, a key skill in software engineering and coding interviews.

1

Set up the total number of steps

Create a variable called n and set it to 5 to represent the total number of steps in the staircase.

DSA Typescript

# Your code here

Hint

Use const n = 5; to set the number of steps.

2

Create an array to store ways to climb

Create an array called ways with length n + 1. Initialize ways[0] to 1 and ways[1] to 1. This array will store the number of ways to reach each step.

DSA Typescript

const n = 5;
// Your code here

Hint

Use new Array(n + 1).fill(0) to create the array and set the first two values to 1.

3

Calculate ways to climb each step

Use a for loop with variable i from 2 to n inclusive. Inside the loop, set ways[i] to ways[i - 1] + ways[i - 2] to calculate the number of ways to reach step i.

DSA Typescript

const n = 5;
const ways = new Array(n + 1).fill(0);
ways[0] = 1;
ways[1] = 1;
// Your code here

Hint

Use a loop from 2 to n and update ways[i] by adding the two previous values.

4

Print the total number of ways

Print the value of ways[n] to display the total number of ways to climb n steps.

DSA Typescript

const n = 5;
const ways = new Array(n + 1).fill(0);
ways[0] = 1;
ways[1] = 1;
for (let i = 2; i <= n; i++) {
    ways[i] = ways[i - 1] + ways[i - 2];
}
// Your code here

Hint

Use console.log(ways[n]) to print the result.