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Dynamic Programming

15. Climbing Stairs

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

Each time, you can either climb 1 step or 2 steps. In how many distinct ways can you climb to the top?

Examples

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

Estas subiendo una escalera. Se necesitan n escalones para llegar a la cima.

En cada movimiento puedes subir 1 escalon o 2 escalones. De cuantas formas distintas puedes llegar a la cima?

Ejemplos

Ejemplo 1

Entrada: n = 2
Salida: 2
Explicacion: Hay dos formas de llegar a la cima:
  1. 1 escalon + 1 escalon
  2. 2 escalones

Ejemplo 2

Entrada: n = 3
Salida: 3
Explicacion: Hay tres formas de llegar a la cima:
  1. 1 escalon + 1 escalon + 1 escalon
  2. 1 escalon + 2 escalones
  3. 2 escalones + 1 escalon

Restricciones

  • 1 <= n <= 45
climbing_stairs.py 
# Climbing stairs: count distinct ways to reach step n (Fibonacci approach)
n: int = 8
one: int = 1
two: int = 1

# Iterate n times, shifting the two-variable window forward
for i in range(n):
    temp: int = one
    one = one + two
    two = temp

print(temp)
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