task2 solution

Author: proton

week3/quicksort/interview-questions/task2/solution.rb

@@ -1,82 +1,39 @@
-# def merge_sort(array, start: nil, finish: nil, buffer: nil)
-#   return if start == finish
-
-#   mid = (finish - start) / 2 + start
-
-#   merge_sort(array, start: start,   finish: mid,    buffer: buffer)
-#   merge_sort(array, start: mid + 1, finish: finish, buffer: buffer)
-
-#   i = 0
-#   j = 0
-#   b = 0
-#   loop do
-#     remaining = (j + mid + 1)..finish if i == mid + 1 - start
-#     remaining = (i + start)..mid      if j == finish - mid
-#     if remaining
-#       remaining.each do |k|
-#         buffer[b] = array[k]
-#         b += 1
-#       end
-#       break
-#     end
-#     x = array[i + start]
-#     y = array[j + mid + 1]
-#     if x < y
-#       buffer[b] = x
-#       i += 1
-#     else
-#       buffer[b] = y
-#       j += 1
-#     end
-#     b += 1
-#   end
-#   (0...b).each do |k|
-#     array[start + k] = buffer[k]
-#   end
-
-#   array
-# end
-
-# n = 10
-# a = n.times.map { rand(0..99) }.sort + n.times.map { rand(0..99) }.sort
-# b = Array.new(n)
-
-# p a
-
-# k = 0
-# i = 0
-# j = n
-
-# while k < n do
-#   if a[i] <= a[j]
-#     b[k] = a[i]
-#     a[i] = nil
-#     i += 1
-#   else
-#     b[k] = a[j]
-#     a[j] = nil
-#     j += 1
-#   end
-#   k += 1
-# end
-
-# i = 2 * n - 1
-# k = 2 * n - 1
-# while k >= n do
-#   if a[i]
-#     a[k] = a[i] unless k == i
-#     k -= 1
-#   end
-#   i -= 1
-# end
-
-# b.each_with_index do |e, i|
-#   a[i] = e
-# end
-
-# merge_sort(a, start: n, finish: 2*n - 1, buffer: b)
-
-# p b
-# p a
-# p a.sort
-# p a == a.sort
+def kth(array1, array2, k)
+  return kth(array2, array1, k)     if array1.size > array2.size
+  return array2[k]                  if array1.empty?
+  return [array1[0], array2[0]].min if k == 0
+
+  low  = [0, k - array2.size].max
+  high = [k, array1.size    ].min
+
+  while low <= high
+    partition1 = (low + high) / 2
+    partition2 = k - partition1
+
+    max_left_1  = partition1 > 0           ? array1[partition1 - 1] : Float::NEGATIVE_INFINITY
+    max_left_2  = partition2 > 0           ? array2[partition2 - 1] : Float::NEGATIVE_INFINITY
+    min_right_1 = partition1 < array1.size ? array1[partition1]     : Float::INFINITY
+    min_right_2 = partition2 < array2.size ? array2[partition2]     : Float::INFINITY
+
+    if max_left_1 <= min_right_2 && max_left_2 <= min_right_1
+      return [min_right_1, min_right_2].min
+    elsif max_left_1 > min_right_2
+      high = partition1 - 1
+    else
+      low  = partition1 + 1
+    end
+  end
+end
+
+# Given two sorted arrays `a[]` and `b[]`, of lengths `n1` and `n2` and an integer `0 ≤ k < n1 + n2`
+n = 10
+n1 = n
+n2 = n
+
+a = n1.times.map { rand(10..99) }.sort
+b = n2.times.map { rand(10..99) }.sort
+k = rand(0...(n1 + n2))
+
+c = (a + b).sort
+
+p kth(a, b, k) == c[k]

week3/quicksort/interview-questions/task3/solution.rb

@@ -1,82 +1,25 @@
-# def merge_sort(array, start: nil, finish: nil, buffer: nil)
-#   return if start == finish
 
-#   mid = (finish - start) / 2 + start
 
-#   merge_sort(array, start: start,   finish: mid,    buffer: buffer)
-#   merge_sort(array, start: mid + 1, finish: finish, buffer: buffer)
 
-#   i = 0
-#   j = 0
-#   b = 0
-#   loop do
-#     remaining = (j + mid + 1)..finish if i == mid + 1 - start
-#     remaining = (i + start)..mid      if j == finish - mid
-#     if remaining
-#       remaining.each do |k|
-#         buffer[b] = array[k]
-#         b += 1
-#       end
-#       break
-#     end
-#     x = array[i + start]
-#     y = array[j + mid + 1]
-#     if x < y
-#       buffer[b] = x
-#       i += 1
-#     else
-#       buffer[b] = y
-#       j += 1
-#     end
-#     b += 1
-#   end
-#   (0...b).each do |k|
-#     array[start + k] = buffer[k]
-#   end
 
-#   array
-# end
 
-# n = 10
-# a = n.times.map { rand(0..99) }.sort + n.times.map { rand(0..99) }.sort
-# b = Array.new(n)
 
-# p a
+----------------------------------
 
-# k = 0
-# i = 0
-# j = n
+Hint: determine the
+(
+�
+/
+10
+)
+�
+ℎ
+(n/10)
+th
+  largest key using quickselect and check if it occurs more than
+�
+/
+10
+n/10 times.
 
-# while k < n do
-#   if a[i] <= a[j]
-#     b[k] = a[i]
-#     a[i] = nil
-#     i += 1
-#   else
-#     b[k] = a[j]
-#     a[j] = nil
-#     j += 1
-#   end
-#   k += 1
-# end
-
-# i = 2 * n - 1
-# k = 2 * n - 1
-# while k >= n do
-#   if a[i]
-#     a[k] = a[i] unless k == i
-#     k -= 1
-#   end
-#   i -= 1
-# end
-
-# b.each_with_index do |e, i|
-#   a[i] = e
-# end
-
-# merge_sort(a, start: n, finish: 2*n - 1, buffer: b)
-
-# p b
-# p a
-# p a.sort
-# p a == a.sort
+Alternate solution hint: use 9 counters.