Your browser (Unknown 0) is no longer supported. Some parts of the website may not work correctly. Please update your browser.
respectable
Count the number of different ways of climbing to the top of a ladder.
Programming language:

You have to climb up a ladder. The ladder has exactly N rungs, numbered from 1 to N. With each step, you can ascend by one or two rungs. More precisely:

  • with your first step you can stand on rung 1 or 2,
  • if you are on rung K, you can move to rungs K + 1 or K + 2,
  • finally you have to stand on rung N.

Your task is to count the number of different ways of climbing to the top of the ladder.

For example, given N = 4, you have five different ways of climbing, ascending by:

  • 1, 1, 1 and 1 rung,
  • 1, 1 and 2 rungs,
  • 1, 2 and 1 rung,
  • 2, 1 and 1 rungs, and
  • 2 and 2 rungs.

Given N = 5, you have eight different ways of climbing, ascending by:

  • 1, 1, 1, 1 and 1 rung,
  • 1, 1, 1 and 2 rungs,
  • 1, 1, 2 and 1 rung,
  • 1, 2, 1 and 1 rung,
  • 1, 2 and 2 rungs,
  • 2, 1, 1 and 1 rungs,
  • 2, 1 and 2 rungs, and
  • 2, 2 and 1 rung.

The number of different ways can be very large, so it is sufficient to return the result modulo 2P, for a given integer P.

Write a function:

class Solution { public int[] solution(int[] A, int[] B); }

that, given two non-empty arrays A and B of L integers, returns an array consisting of L integers specifying the consecutive answers; position I should contain the number of different ways of climbing the ladder with A[I] rungs modulo 2B[I].

For example, given L = 5 and:

A[0] = 4 B[0] = 3 A[1] = 4 B[1] = 2 A[2] = 5 B[2] = 4 A[3] = 5 B[3] = 3 A[4] = 1 B[4] = 1

the function should return the sequence [5, 1, 8, 0, 1], as explained above.

Write an efficient algorithm for the following assumptions:

  • L is an integer within the range [1..50,000];
  • each element of array A is an integer within the range [1..L];
  • each element of array B is an integer within the range [1..30].
Copyright 2009–2019 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.