?? LeetCode: Climbing Stairs Problem - Intuition(DP/Fibonacci) Behind the Solution ??♂??

Problem statement: https://leetcode.com/problems/climbing-stairs/description/

You're climbing a staircase with n steps, and you can take either?1 or 2 steps at each step. how many distinct ways are there to reach the top? ??

?? Breaking Down the Intuition:

This problem can be broken down into smaller sub-problems. To reach the nth step, you can:

1. Climb from the (n-1)th step by taking 1 step ??
2. Climb from the (n-2)th step by taking 2 steps ????

This means the total number of ways to reach step n is the sum of the ways to reach (n-1) and (n-2).

This is a dynamic programming problem similar to the Fibonacci Sequence.

?? Dynamic Programming Approach: We create an array step_count to store the number of ways to reach each step. We initialize:

• step_count[0] = 1: There's 1 way to "reach" the base (doing nothing).
• step_count[1] = 1: There's 1 way to reach the first step (taking 1 step).

Then, we iterate from 2 to n and fill the step_count array using:

step_count[i] = step_count[i-1] + step_count[i-2]        

This represents the two options for reaching step i.

class Solution(object):
    def climbStairs(self, n):
        step_count = [0]*(n+1)
        step_count[0] = 1
        step_count[1] = 1
        if n == 1: return 1
        for i in range(2, n+1):
            step_count[i] = step_count[i-1] + step_count[i-2]
        
        return step_count[n]
        

?? Key Takeaway: This problem demonstrates how breaking down complex problems into overlapping sub-problems can simplify the solution! Dynamic programming helps us avoid recalculating redundant steps, leading to an efficient solution. ????