Climbing stairs (Memoization)

There are n stairs, and a person standing at the bottom can climb either 1 stair or 2 stairs at a time, count the number of ways that a person can reach at the top.

Hint

This algorithm uses memoization to improve performance. It's same as the recursive version of Climbing stairs, but with a special 'cache' to store results. The 'cache key' is crucial. It's how we identify and store past results. Sometimes we need one key, sometimes multiple keys. We add code to:

Initialize cache to store results.
Using the key to check cached result. If the result is not found in the cache, do the calculation and save the result in cache.
Return the cached result.

Python
Javascript

# Python implementation

cache = {}

def climb(n):
  if n < 1:
    return 0

  if n == 1:
    return 1

  if n == 2:
    return 2

  if n not in cache:
    cache[n] = climb(n - 1) + climb(n - 2)
  
  return cache[n]

n = 5

print(climb(n))

// Javascript implementation

const cache = {}

function climb(n) {
  if (n < 1) {
    return 0;
  }

  if (n == 1) {
    return 1;
  }

  if (n === 2) {
    return 2;
  }

  if (cache[n] === undefined) {
    cache[n] = climb(n - 1) + climb(n - 2);
  } 
  
  return cache[n];
}

const n = 5;

console.log(climb(n));