LeetCode in Racket

70. Climbing Stairs

Easy

You are climbing a staircase. It takes n steps to reach the top.

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

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

Solution

(define (clmHelp n hTable)
	(cond
		; base cases
		((= 1 n) 1)
		((= 2 n) 2)
		((hash-ref hTable n #f) (hash-ref hTable n))

		; inductive case
		(else
			(let*
				; the local variables
				(
					(a (clmHelp (- n 1) hTable))
					(b (clmHelp (- n 2) hTable))
					(numPos (+ a b))
				)

				; the body
				(hash-set! hTable n numPos)
				numPos
			)
		)
	)
)

(define/contract (climb-stairs n)
	(-> exact-integer? exact-integer?)
	(local
		; local definitions
		((define hTable (make-hash)))

		; function body
		(clmHelp n hTable)
	)
)

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