2023-08-07 16:56:28 -07:00

59 lines
1.2 KiB
Python

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
# author: bt3gl
'''
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?
'''
def climb_stairs_o2n(n: int) -> int:
if n == 0 or n == 1:
return 1
return climb_stairs_o2n(n - 1) + climb_stairs_o2n(n - 2)
def climb_stairs_memoization(n: int) -> int:
memo = {}
def helper(n: int, memo: dict[int, int]) -> int:
if n == 0 or n == 1:
return 1
if n not in memo:
memo[n] = helper(n - 1, memo) + helper(n - 2, memo)
return memo[n]
return helper(n, memo)
def climb_stairs_optimized(n: int) -> int:
if n == 0 or n == 1:
return 1
prev, curr = 1, 1
for i in range(2, n + 1):
temp = curr
curr = prev + curr
prev = temp
return curr
def climb_stairs_tabulation(n: int) -> int:
if n == 0 or n == 1:
return 1
dp = [0] * (n + 1)
dp[0] = dp[1] = 1
for i in range(2, n + 1):
dp[i] = dp[i - 1] + dp[i - 2]
return dp[n]