master-algorithms-py/math_logic_dp/climbing_stairs.py

'''
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 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]

def climb_stairs_memoization(n: int) -> int:
        memo = {}    
        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]


if __name__ == "__main__":
    print(climb_stairs_o2n(4))
    print(climb_stairs_memoization(4))
    print(climb_stairs_optimized(4))
    print(climb_stairs_tabulation(4))