Climbing Stairs Problem in DSA Go - Build from Scratch

Climbing Stairs Problem

📖 Scenario: Imagine you are climbing 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 slice dp of length n+1 to store the number of ways to reach each step.

Use a loop to calculate the number of ways to climb the stairs using dynamic programming.

Print the final number of ways stored in dp[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, moving through game levels, or planning routes.

💼 Career

Understanding dynamic programming and iterative solutions is important for software engineering roles that involve optimization, algorithm design, and problem solving.

1

Setup 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 Go

// Create a variable called n and set it to 5
// Your code here

Hint

Use n := 5 to create the variable for total steps.

2

Initialize dp slice for dynamic programming

Add a slice called dp of length n+1 to store the number of ways to reach each step. Initialize dp[0] and dp[1] to 1.

DSA Go

package main

import "fmt"

func main() {
    n := 5
    // Create a slice dp of length n+1
    // Initialize dp[0] and dp[1] to 1
    // Your code here
}

Hint

Use make([]int, n+1) to create the slice and set the first two values 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 dp[i] to dp[i-1] + dp[i-2] to calculate the number of ways to reach step i.

DSA Go

package main

import "fmt"

func main() {
    n := 5
    dp := make([]int, n+1)
    dp[0] = 1
    dp[1] = 1
    // Use a for loop from i = 2 to n
    // Calculate dp[i] = dp[i-1] + dp[i-2]
    // Your code here
}

Hint

Use a for loop starting at 2 and update dp[i] by adding dp[i-1] and dp[i-2].

4

Print the total number of ways to climb

Print the value of dp[n] which holds the total number of ways to climb the staircase.

DSA Go

package main

import "fmt"

func main() {
    n := 5
    dp := make([]int, n+1)
    dp[0] = 1
    dp[1] = 1
    for i := 2; i <= n; i++ {
        dp[i] = dp[i-1] + dp[i-2]
    }
    // Print dp[n]
    // Your code here
}

Hint

Use fmt.Println(dp[n]) to print the result.

Practice

1. What does the Climbing Stairs problem ask you to find?
Given n steps, how many distinct ways can you climb to the top if you can take 1 or 2 steps at a time?

easy

A. The total number of distinct ways to reach the top

B. The minimum number of steps to reach the top

C. The maximum number of steps you can take at once

D. The number of steps you skip

Solution

1. Step 1: Understand the problem statement

   The problem asks for the count of different ways to climb to the top by taking 1 or 2 steps at a time.

2. Step 2: Identify what is being counted

   We count all possible sequences of 1-step and 2-step moves that sum to n steps.

3. Final Answer:

   The total number of distinct ways to reach the top -> Option A

4. Quick Check:

   Counting sequences of 1 or 2 steps = total ways [OK]

Hint: Count sequences of 1 or 2 steps summing to n [OK]

Common Mistakes:

• Confusing number of ways with minimum steps
• Thinking about maximum steps allowed
• Counting skipped steps instead of ways

2. Which Go function signature correctly represents a function to solve the Climbing Stairs problem for n steps?

easy

A. func climbStairs(n int) bool

B. func climbStairs(n string) string

C. func climbStairs() int

D. func climbStairs(n int) int

Solution

1. Step 1: Identify input and output types

   The input is the number of steps (integer), output is the count of ways (integer).

2. Step 2: Match function signature

   Only func climbStairs(n int) int matches input int and output int.

3. Final Answer:

   func climbStairs(n int) int -> Option D

4. Quick Check:

   Input int, output int = correct signature [OK]

Hint: Input and output both must be int for steps and ways [OK]

Common Mistakes:

• Using string instead of int for steps
• Missing input parameter
• Returning bool instead of int

3. What is the output of this Go code for n = 4?

func climbStairs(n int) int {
    if n <= 2 {
        return n
    }
    a, b := 1, 2
    for i := 3; i <= n; i++ {
        a, b = b, a+b
    }
    return b
}

fmt.Println(climbStairs(4))

medium

A. 7

B. 6

C. 5

D. 4

Solution

1. Step 1: Trace initial values and loop

   Start with a=1, b=2. Loop i=3 to 4:
   i=3: a=2, b=3
   i=4: a=3, b=5

2. Step 2: Return final value

   Return b=5 after loop ends.

3. Final Answer:

   5 -> Option C

4. Quick Check:

   Ways for 4 steps = 5 [OK]

Hint: Use Fibonacci-like addition for steps count [OK]

Common Mistakes:

• Returning a instead of b
• Off-by-one error in loop range
• Incorrect initial values

4. Find the error in this Go code for climbing stairs:

func climbStairs(n int) int {
    if n == 1 {
        return 1
    }
    a, b := 1, 2
    for i := 2; i <= n; i++ {
        a, b = b, a+b
    }
    return b
}

medium

A. Return statement should return a instead of b

B. Loop starts at wrong index causing extra iteration

C. Initial values of a and b are incorrect

D. Missing base case for n == 2

Solution

1. Step 1: Analyze loop start and iterations

   Loop starts at i=2 but initial values already cover steps 1 and 2, causing one extra iteration.

2. Step 2: Correct loop start

   Loop should start at i=3 to avoid counting extra ways.

3. Final Answer:

   Loop starts at wrong index causing extra iteration -> Option B

4. Quick Check:

   Loop index off by one causes wrong count [OK]

Hint: Start loop at 3 when initial values cover steps 1 and 2 [OK]

Common Mistakes:

• Starting loop at 2 instead of 3
• Changing initial values incorrectly
• Returning wrong variable

5. You want to find the number of ways to climb 10 steps but can take 1, 2, or 3 steps at a time. How would you modify the climbing stairs approach?

hard

A. Use dynamic programming with dp[i] = dp[i-1] + dp[i-2] + dp[i-3]

B. Use the same formula dp[i] = dp[i-1] + dp[i-2]

C. Only count ways taking 3 steps at a time

D. Multiply the number of ways for 1 and 2 steps

Solution

1. Step 1: Understand the new step options

   Now you can take 1, 2, or 3 steps at a time, so ways to reach step i depend on previous 3 steps.

2. Step 2: Formulate recurrence relation

   Number of ways dp[i] = dp[i-1] + dp[i-2] + dp[i-3] to include all possibilities.

3. Final Answer:

   Use dynamic programming with dp[i] = dp[i-1] + dp[i-2] + dp[i-3] -> Option A

4. Quick Check:

   Include all step sizes in sum for dp [OK]

Hint: Sum ways from last 3 steps for 1,2,3 step moves [OK]

Common Mistakes:

• Using old formula for only 1 or 2 steps
• Ignoring 3-step moves
• Multiplying counts instead of adding