Backup files

Author: dijonkitchen

problems/nth_root.rb

@@ -0,0 +1,33 @@
+# Calculate nth root (within givin tolerance) without standard library
+# for embedded system with little space
+
+# Root must be between 0 and number
+# Binary search of possibilites from 0 to number
+
+# Set left and right boundaries
+# While left is less than right
+#   Check if midpoint ^ n is within tolerance of number
+#     If value is too big
+#       Set right to midpoint
+#     Else
+#       Set left to midpoint
+#     Update midpoint to new average of left and right
+# Return midpoint
+
+def nth_root(number, n, tolerance = 0.001)
+  low = 0
+  high = number
+  loop do
+    midpoint = (low + high) / 2.0
+    error = midpoint**n - number
+    return midpoint if error.abs < tolerance
+    if error > 0
+      high = midpoint
+    else
+      low = midpoint
+    end
+  end
+end
+
+# Time complexity: O(log(n))
+# Space complexity: O(1)

problems/num_of_paths_to_dest.rb

@@ -0,0 +1,20 @@
+def num_of_paths_to_dest(size)
+  memo = Array.new(size, [])
+  num_of_paths_to_sq(size - 1, size - 1, memo)
+end
+
+def num_of_paths_to_sq(x, y, memo)
+  if x < 0 || y < 0
+    return 0
+  elsif x < y
+    memo[x, y] = 0
+  elsif x == 0 && y == 0
+    memo[x, y] = 1
+  elsif memo[x, y].nil?
+    memo[x, y] = num_of_paths_to_sq(x - 1, y, memo) + num_of_paths_to_sq(x, y - 1, memo)
+  end
+
+  memo[x, y]
+end
+
+puts num_of_paths_to_dest(4)

sorts/insertion_sort.rb

@@ -13,7 +13,7 @@
 
 def insertion_sort(arr)
   arr.each_with_index do |num, index|
-    prev_index = index - 1
+    prev_index = index - 1 # Check index -1 edge case
     while prev_index >= 0 && arr[prev_index] > num
       arr[prev_index + 1] = arr[prev_index]
       prev_index -= 1

spec/nth_root_spec.rb

@@ -0,0 +1,15 @@
+require_relative '../problems/nth_root'
+
+RSpec.describe 'nth root' do
+  it 'takes nth root of a number' do
+    number = 7
+    n = 3
+    expect((nth_root(number, n)**n - number).abs <= 0.001).to eq(true)
+  end
+
+  it 'takes nth root of a number' do
+    number = 4
+    n = 2
+    expect((nth_root(number, n)**n - number).abs <= 0.001).to eq(true)
+  end
+end