Codility ‘Ladder’ Solution

Short Problem Definition:

Count the number of different ways of climbing to the top of a ladder.




expected worst-case time complexity is O(L)

expected worst-case space complexity is O(L)


We first compute the Fibonacci sequence for the first L+2 numbers. The first two numbers are used only as fillers, so we have to index the sequence as A[idx]+1 instead of A[idx]-1. The second step is to replace the modulo operation by removing all but the n lowest bits. A discussion can be found on Stack Overflow.

def solution(A, B):
    L = max(A)
    P_max = max(B)
    fib = [0] * (L+2)
    fib[1] = 1
    for i in xrange(2, L + 2):
        fib[i] = (fib[i-1] + fib[i-2]) & ((1 << P_max) - 1)
    return_arr = [0] * len(A)
    for idx in xrange(len(A)):
        return_arr[idx] = fib[A[idx]+1] & ((1 << B[idx]) - 1)
    return return_arr

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