TheAlgorithms-Ruby/dynamic_programming/climbing-stairs.rb

#You are climbing a staircase. It takes n steps to reach the top.
#Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?

#Example 1:
#Input: n = 2
#Output: 2
#Explanation: There are two ways to climb to the top.
#1. 1 step + 1 step
#2. 2 steps

#Example 2:
#Input: n = 3
#Output: 3
#Explanation: There are three ways to climb to the top.
#1. 1 step + 1 step + 1 step
#2. 1 step + 2 steps
#3. 2 steps + 1 step

#Constraints:
#1 <= n <= 45




#Dynamic Programming, Recursive Bottom Up Approach - O(n) Time / O(n) Space
#Init memoization hash (only 1 parameter)
#Set base cases which are memo[0] = 1 and memo[1] = 1, since there are only 1 way to get to each stair
#Iterate from 2..n and call recurse(n, memo) for each value n. 
#Return memo[n].

#recurse(n, memo) - Recurrence Relation is n = (n - 1) + (n - 2)
#return memo[n] if memo[n] exists. 
#otherwise, memo[n] = recurse(n - 1, memo) + recurse(n - 2, memo)               


# @param {Integer} n
# @return {Integer}
def climb_stairs(n)
    memo = Hash.new
    
    memo[0] = 1
    memo[1] = 1
    
    return memo[n] if n <= 1 && n >= 0
    
    (2..n).each do |n|
      recurse(n, memo)
    end
    
    memo[n]
end


def recurse(n, memo)
    return memo[n] if memo[n]
    
    memo[n] = recurse(n - 1, memo) + recurse(n - 2, memo)
end