Given n stairs and we have 2 colour yellow and green the task is that we have to paint given stairs by given colour with condition is that we cannot paints two yellow steps directly after each other.
Input : n = 1 Output : 2 A single stair can be colored either as green or yellow. Input : n = 3 Output : 5
Case 1: When we have 1 stair, we can paint either yellow or green.
Case 2: When we have 2 stairs, we can paint first stair by either yellow or green but for next stair we can only paint by green because we cannot paint two yellow steps directly after each other. So total cases are three YG, GG, GY.
Case 3: When we have 3 stairs then we can paint it by in 5 ways.
If we take a closer look, we can notice that it follows Fibonacci Series.
Time Complexity : O(n)
Extra Space : O(n)
We can solve this problem in O(Log n) time also using matrix exponentiation solution for n-th Fibonacci Number.
- Ways to paint N paintings such that adjacent paintings don't have same colors
- Number of ways to paint a tree of N nodes with K distinct colors with given conditions
- Ways to color a 3*N board using 4 colors
- Number of ways to form an array with distinct adjacent elements
- Permutations of string such that no two vowels are adjacent
- Maximum sum of difference of adjacent elements
- Generate permutations with only adjacent swaps allowed
- Arrange first N natural numbers such that absolute difference between all adjacent elements > 1
- Different ways to represent N as sum of K non-zero integers
- Count of different ways to express N as the sum of 1, 3 and 4
- Ways to represent a number as a sum of 1's and 2's
- Ways to select one or more pairs from two different sets
- Count possible ways to construct buildings
- Number of ways to reach the end of matrix with non-zero AND value
- Number of ways to pair people
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.