There exists a staircase with N steps, and you can climb up either 1 or 2 steps at a time. Given N, write a function that returns the number of unique ways you can climb the staircase. The order of the steps matters. For example, if N is 4, then there are 5 unique ways: 1, 1, 1, 1 2, 1, 1 1, 2, 1 1, 1, 2 2, 2 What if, instead of being able to cl…

daily-coding-problem-12.py

#!/usr/bin/env python

def staircase(n, X):
    cache = [0 for _ in range(n + 1)]
    cache[0] = 1
    for i in range(n + 1):
        cache[i] += sum(cache[i - x] for x in X if i - x > 0)
        cache[i] += 1 if i in X else 0
    return cache[-1]

if __name__ == "__main__":
    X = {1, 3, 5}
    print (staircase(10, X))