Climbing stairs (Tabulation)

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

Building upon understanding of Climbing stairs (Memoization). Tabulation essentially reconstructs the cache.

Start with the foundation – the base cases, which are the simplest solutions. Then, layer by layer, use the results of the previous layers to calculate the solutions for the next level. This way, we systematically build up the entire solution, avoiding redundant calculations and ensuring efficiency. It is like building a pyramid.

The underlying calculation logic remains fundamentally identical to the original recursive approach, albeit executed in reverse order.

• Python
• Javascript
•  Run

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

  if n == 1:
    return 1

  if n == 2:
    return 2

  result = 0
  prev_1 = 2
  prev_2 = 1

  for i in range(3, n + 1):
    result = prev_1 + prev_2
    prev_2 = prev_1
    prev_1 = result
  
  return result

n = 5

print(climb(n))

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

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

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

  let result = 0;
  let prev_1 = 2;
  let prev_2 = 1;

  for (let i = 3; i <= n; i++) {
    result = prev_1 + prev_2;
    prev_2 = prev_1;
    prev_1 = result;
  }
  
  return result;
}

const n = 5;

console.log(climb(n));