The number of ways to reach step n is the sum of ways to reach n-1 and n-2. This is a Fibonacci-like recurrence. To avoid exponential time, we use a simple recursion with a dictionary for memoization.

1. memo = {}.
2. solve(n):
   • Base case: If n <= 2, return n.
   • If n in memo, return memo[n].
   • memo[n] = solve(n - 1) + solve(n - 2).
   • Return memo[n].

• Time Complexity: O(N) with memoization.
• Space Complexity: O(N).

def climb_stairs(n):
    memo = {}
    def solve(n):
        if n <= 2: return n
        if n in memo: return memo[n]
        memo[n] = solve(n - 1) + solve(n - 2)
        return memo[n]
    return solve(n)