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Climbing Stairs

Certification: Basic Level Accuracy: 0% Submissions: 0 Points: 5

Write a C program to count the number of ways to climb a staircase. You are climbing a staircase with n steps. Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?

Example 1
    
  
  • Input: n = 2
    • 
  
  • Output: 2
    • 
  
  • Explanation: There are two ways to climb to the top.
    1. 1 step + 1 step
    2. 2 steps at once
    •
Example 2
    
  
  • Input: n = 3
    • 
  
  • Output: 3
    • 
  
  • Explanation: There are three ways to climb to the top.
    1. 1 step + 1 step + 1 step
    2. 1 step + 2 steps
    3. 2 steps + 1 step
    •
Constraints
    
  
  • 1 ≤ n ≤ 45
    • 
  
  • The answer will fit within a 32-bit integer range
    • 
  
  • Time Complexity: O(n)
    • 
  
  • Space Complexity: O(1) (for the optimized solution)
    •
NumberCognizantWalmart
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Hint
Solution

Solution Hints

    
  
  • This problem follows the Fibonacci sequence
    • 
  
  • The number of ways to reach step n is equal to the number of ways to reach step (n-1) plus the number of ways to reach step (n-2)
    • 
  
  • For n = 1, there's only 1 way: climb 1 step
    • 
  
  • For n = 2, there are 2 ways: climb 1 step + 1 step, or climb 2 steps at once
    • 
  
  • Use dynamic programming to avoid redundant calculations
    •

Steps to solve by this approach:

 Step 1: Handle base cases: for n=1, return 1; for n=2, return 2.

 Step 2: Initialize variables to track the ways to climb n-1 and n-2 steps.

 Step 3: Iterate from 3 to n, calculating the total ways for each step.

 Step 4: For each step i, the number of ways equals the sum of ways for step i-1 and step i-2.

 Step 5: Update the variables for the next iteration.

 Step 6: Return the final count which represents the total number of ways to climb n steps.

 Step 7: This solution uses O(1) space and O(n) time complexity to solve the problem efficiently.

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