From 5a2156d0ce402ec5352706111d33f2cba30215f2 Mon Sep 17 00:00:00 2001
From: sidaksohi <31377210+sidaksohi@users.noreply.github.com>
Date: Sun, 22 Aug 2021 15:23:32 -0700
Subject: [PATCH 1/3] Added climbing-stairs solution, with description

---
 dynamic_programming/climbing-stairs.rb | 58 ++++++++++++++++++++++++++
 1 file changed, 58 insertions(+)
 create mode 100644 dynamic_programming/climbing-stairs.rb

diff --git a/dynamic_programming/climbing-stairs.rb b/dynamic_programming/climbing-stairs.rb
new file mode 100644
index 0000000..8b510fe
--- /dev/null
+++ b/dynamic_programming/climbing-stairs.rb
@@ -0,0 +1,58 @@
+#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
\ No newline at end of file

From 4a38db07649b2d9cf357a925e19aea26d8bac151 Mon Sep 17 00:00:00 2001
From: sidaksohi <31377210+sidaksohi@users.noreply.github.com>
Date: Sun, 22 Aug 2021 15:25:24 -0700
Subject: [PATCH 2/3] Rename climbing-stairs.rb to climbing_stairs.rb

---
 dynamic_programming/{climbing-stairs.rb => climbing_stairs.rb} | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)
 rename dynamic_programming/{climbing-stairs.rb => climbing_stairs.rb} (99%)

diff --git a/dynamic_programming/climbing-stairs.rb b/dynamic_programming/climbing_stairs.rb
similarity index 99%
rename from dynamic_programming/climbing-stairs.rb
rename to dynamic_programming/climbing_stairs.rb
index 8b510fe..8b7e26e 100644
--- a/dynamic_programming/climbing-stairs.rb
+++ b/dynamic_programming/climbing_stairs.rb
@@ -55,4 +55,4 @@ def recurse(n, memo)
     return memo[n] if memo[n]
     
     memo[n] = recurse(n - 1, memo) + recurse(n - 2, memo)
-end
\ No newline at end of file
+end

From 70a1b9353a01f5e9dbab3e2d030fb906060f9bab Mon Sep 17 00:00:00 2001
From: sidaksohi <31377210+sidaksohi@users.noreply.github.com>
Date: Tue, 24 Aug 2021 18:33:53 -0700
Subject: [PATCH 3/3] Update climbing_stairs.rb

---
 dynamic_programming/climbing_stairs.rb | 15 ++++++++++++++-
 1 file changed, 14 insertions(+), 1 deletion(-)

diff --git a/dynamic_programming/climbing_stairs.rb b/dynamic_programming/climbing_stairs.rb
index 8b7e26e..8f058b7 100644
--- a/dynamic_programming/climbing_stairs.rb
+++ b/dynamic_programming/climbing_stairs.rb
@@ -41,7 +41,7 @@ def climb_stairs(n)
     memo[0] = 1
     memo[1] = 1
     
-    return memo[n] if n <= 1 && n >= 0
+    return memo[n] if n == 0 || n == 1
     
     (2..n).each do |n|
       recurse(n, memo)
@@ -56,3 +56,16 @@ def recurse(n, memo)
     
     memo[n] = recurse(n - 1, memo) + recurse(n - 2, memo)
 end
+
+
+puts climb_stairs(2)
+# => 2
+
+puts climb_stairs(4)
+# => 5
+
+puts climb_stairs(10)
+# => 89
+
+puts climb_stairs(45)
+# => 1836311903