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Climb "n" Stairs

Certification: Advanced Level Accuracy: 0% Submissions: 0 Points: 15

Write a C++ program to find the number of ways to climb `n` stairs using dynamic programming. You can climb either 1 or 2 stairs at a time.

Example 1
    

  • Input: n = 2
    • 

  • Output: 2
    • 

  • Explanation:
   
      
   
    • Step 1: Define the base cases: 1 way to climb 0 stairs, 1 way to climb 1 stair.
      • 
   
    • Step 2: For n = 2, calculate the number of ways by adding the ways to reach (n-1) and (n-2).
      • 
   
    • Step 3: There are 2 distinct ways to climb 2 stairs:
      
        
      
      1. 1 step + 1 step
        2. 
      
      2. 2 steps at once
        3. 
      
      
   
      • 
   
    • Step 4: Return the total number of ways: 2.
      • 
   
    

    •
Example 2
    

  • Input: n = 3
    • 

  • Output: 3
    • 

  • Explanation:
   
      
   
    • Step 1: Define the base cases: 1 way to climb 0 stairs, 1 way to climb 1 stair.
      • 
   
    • Step 2: Calculate ways[2] = ways[1] + ways[0] = 1 + 1 = 2.
      • 
   
    • Step 3: Calculate ways[3] = ways[2] + ways[1] = 2 + 1 = 3.
      • 
   
    • Step 4: There are 3 distinct ways to climb 3 stairs:
      
        
      
      1. 1 step + 1 step + 1 step
        2. 
      
      2. 1 step + 2 steps
        3. 
      
      3. 2 steps + 1 step
        4. 
      
      
   
      • 
   
    • Step 5: Return the total number of ways: 3.
      • 
   
    

    •
Constraints
    

  • 1 ≤ n ≤ 45
    • 

  • Time Complexity: O(n)
    • 

  • Space Complexity: O(n)
    •
ArraysDynamic Programming ZomatoSamsung
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Hint
Solution

Solution Hints

     
  • Use dynamic programming to solve this problem.
    •  
  • Create an array to store the number of ways to reach each step.
    •  
  • The number of ways to reach the nth step is the sum of the ways to reach the (n-1)th step and the (n-2)th step.
    •  
  • Initialize the base cases: 1 way to reach the 1st step and 2 ways to reach the 2nd step.
    •

Steps to solve by this approach:

 Step 1: Handle base case: if n=1, return 1 directly.

 Step 2: Create a DP array of size n+1 to store number of ways to reach each step.

 Step 3: Initialize base cases: dp[1] = 1 (one way to reach first step) and dp[2] = 2 (two ways to reach second step).

 Step 4: For each step i from 3 to n, compute dp[i] = dp[i-1] + dp[i-2].

 Step 5: Return dp[n] as the result.

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