Climbing Stairs Problem in DSA C - Build from Scratch

Climbing Stairs Problem

📖 Scenario: Imagine you are climbing a staircase with 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 an integer variable n with the value 5 (number of steps).

Create an integer array ways of size n+1 to store the number of ways to reach each step.

Initialize the base cases for ways[0] and ways[1].

Use a for loop with variable i from 2 to n to fill the ways array using the relation ways[i] = ways[i-1] + ways[i-2].

Print the number of ways to reach step n.

💡 Why This Matters

🌍 Real World

This problem models situations where you have multiple ways to reach a goal step-by-step, such as climbing stairs or moving through stages in a process.

💼 Career

Understanding dynamic programming and iterative solutions is important for software development roles that involve optimization and algorithm design.

1

Create the number of steps variable

Create an integer variable called n and set it to 5.

DSA C

# Your code here

Hint

Use int n = 5; to create the variable.

2

Create and initialize the ways array

Create an integer array called ways of size n + 1. Initialize ways[0] to 1 and ways[1] to 1.

DSA C

int n = 5;
// Your code here

Hint

Remember array size is n + 1. Initialize the first two elements to 1.

3

Calculate ways to climb using a loop

Use a for loop with variable i from 2 to n inclusive. Inside the loop, set ways[i] = ways[i - 1] + ways[i - 2].

DSA C

int n = 5;
int ways[6];
ways[0] = 1;
ways[1] = 1;
// Your code here

Hint

Use the formula to fill the array from step 2 to step n.

4

Print the total number of ways

Print the value of ways[n] using printf with the format "%d\n".

DSA C

int n = 5;
int ways[6];
ways[0] = 1;
ways[1] = 1;
for (int i = 2; i <= n; i++) {
    ways[i] = ways[i - 1] + ways[i - 2];
}
// Your code here

Hint

Use printf("%d\n", ways[n]); to print the result.