Climbing Stairs Problem in DSA Typescript - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of climbingStairs(4) with simple recursion

What is the output of the following TypeScript function call: climbingStairs(4)?

DSA Typescript

function climbingStairs(n: number): number {
  if (n <= 2) return n;
  return climbingStairs(n - 1) + climbingStairs(n - 2);
}

console.log(climbingStairs(4));

A 7

B 6

C 4

D 5

💡 Hint

Think about how many ways to climb 3 steps and 2 steps add up for 4 steps.

The function uses recursion where climbingStairs(n) = climbingStairs(n-1) + climbingStairs(n-2). For n=4, it calculates 3 + 2 = 5.

❓ Predict Output

intermediate

Output of climbingStairs(5) with memoization

What is the output of the following TypeScript code when calling climbingStairs(5)?

DSA Typescript

function climbingStairs(n: number, memo: Record<number, number> = {}): number {
  if (n <= 2) return n;
  if (memo[n] !== undefined) return memo[n];
  memo[n] = climbingStairs(n - 1, memo) + climbingStairs(n - 2, memo);
  return memo[n];
}

console.log(climbingStairs(5));

A 8

B 7

C 5

D 10

💡 Hint

Use the relation climbingStairs(n) = climbingStairs(n-1) + climbingStairs(n-2) with memoization.

climbingStairs(5) = climbingStairs(4) + climbingStairs(3) = 5 + 3 = 8. But memoization stores results to avoid repeated calls.

🔧 Debug

advanced

Identify the error in climbingStairs iterative solution

What error will the following TypeScript code produce when calling climbingStairs(3)?

DSA Typescript

function climbingStairs(n: number): number {
  let a = 1, b = 2;
  for (let i = 3; i <= n; i++) {
    let c = a + b;
    a = b;
    b = c;
  }
  return b;
}

console.log(climbingStairs(3));

A Returns 2

B Runtime error: undefined variable

C Returns 3

D Returns 5

💡 Hint

Check initial values and loop start index carefully.

The function returns 3 for climbingStairs(3) because it correctly sums ways for steps 1 and 2 and iterates once for step 3.

🧠 Conceptual

advanced

Number of ways to climb 0 steps

According to the climbing stairs problem, how many ways are there to climb 0 steps?

A 2 ways

B 1 way (do nothing)

C Undefined

D 0 ways

💡 Hint

Think about the base case for no steps.

There is exactly 1 way to climb 0 steps: by not climbing at all. This is the base case in many solutions.

🚀 Application

expert

Minimum number of jumps to reach the top

Given an array where each element represents the maximum jump length from that position, what is the minimum number of jumps to reach the last index? For example, for [2,3,1,1,4], what is the minimum jumps needed?

A 2

B 3

C 4

D 1

💡 Hint

Try to jump to the farthest reachable index at each step.

From index 0 jump 1 step to index 1, then jump 3 steps to the last index. Total jumps = 2.