Translate all code to English (#1836)

* Review the EN heading format.

* Fix pythontutor headings.

* Fix pythontutor headings.

* bug fixes

* Fix headings in **/summary.md

* Revisit the CN-to-EN translation for Python code using Claude-4.5

* Revisit the CN-to-EN translation for Java code using Claude-4.5

* Revisit the CN-to-EN translation for Cpp code using Claude-4.5.

* Fix the dictionary.

* Fix cpp code translation for the multipart strings.

* Translate Go code to English.

* Update workflows to test EN code.

* Add EN translation for C.

* Add EN translation for CSharp.

* Add EN translation for Swift.

* Trigger the CI check.

* Revert.

* Update en/hash_map.md

* Add the EN version of Dart code.

* Add the EN version of Kotlin code.

* Add missing code files.

* Add the EN version of JavaScript code.

* Add the EN version of TypeScript code.

* Fix the workflows.

* Add the EN version of Ruby code.

* Add the EN version of Rust code.

* Update the CI check for the English version  code.

* Update Python CI check.

* Fix cmakelists for en/C code.

* Fix Ruby comments

en/codes/ruby/chapter_computational_complexity/iteration.rb

@@ -0,0 +1,79 @@
+=begin
+File: iteration.rb
+Created Time: 2024-03-30
+Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com), Cy (9738314@gmail.com)
+=end
+
+### for loop ###
+def for_loop(n)
+  res = 0
+
+  # Sum 1, 2, ..., n-1, n
+  for i in 1..n
+    res += i
+  end
+
+  res
+end
+
+### while loop ###
+def while_loop(n)
+  res = 0
+  i = 1 # Initialize condition variable
+
+  # Sum 1, 2, ..., n-1, n
+  while i <= n
+    res += i
+    i += 1 # Update condition variable
+  end
+
+  res
+end
+
+### while loop (two updates) ###
+def while_loop_ii(n)
+  res = 0
+  i = 1 # Initialize condition variable
+
+  # Sum 1, 4, 10, ...
+  while i <= n
+    res += i
+    # Update condition variable
+    i += 1
+    i *= 2
+  end
+
+  res
+end
+
+### Nested for loop ###
+def nested_for_loop(n)
+  res = ""
+
+  # Loop i = 1, 2, ..., n-1, n
+  for i in 1..n
+    # Loop j = 1, 2, ..., n-1, n
+    for j in 1..n
+      res += "(#{i}, #{j}), "
+    end
+  end
+
+  res
+end
+
+### Driver Code ###
+if __FILE__ == $0
+  n = 5
+
+  res = for_loop(n)
+  puts "\nFor loop sum result res = #{res}"
+
+  res = while_loop(n)
+  puts "\nWhile loop sum result res = #{res}"
+
+  res = while_loop_ii(n)
+  puts "\nWhile loop (two updates) sum result res = #{res}"
+
+  res = nested_for_loop(n)
+  puts "\nNested for loop traversal result #{res}"
+end

en/codes/ruby/chapter_computational_complexity/recursion.rb

@@ -0,0 +1,70 @@
+=begin
+File: recursion.rb
+Created Time: 2024-03-30
+Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
+=end
+
+### Recursion ###
+def recur(n)
+  # Termination condition
+  return 1 if n == 1
+  # Recurse: recursive call
+  res = recur(n - 1)
+  # Return: return result
+  n + res
+end
+
+### Use iteration to simulate recursion ###
+def for_loop_recur(n)
+  # Use an explicit stack to simulate the system call stack
+  stack = []
+  res = 0
+
+  # Recurse: recursive call
+  for i in n.downto(0)
+    # Simulate "recurse" with "push"
+    stack << i
+  end
+  # Return: return result
+  while !stack.empty?
+    res += stack.pop
+  end
+
+  # res = 1+2+3+...+n
+  res
+end
+
+### Tail recursion ###
+def tail_recur(n, res)
+  # Termination condition
+  return res if n == 0
+  # Tail recursive call
+  tail_recur(n - 1, res + n)
+end
+
+### Fibonacci sequence: recursion ###
+def fib(n)
+  # Termination condition f(1) = 0, f(2) = 1
+  return n - 1 if n == 1 || n == 2
+  # Recursive call f(n) = f(n-1) + f(n-2)
+  res = fib(n - 1) + fib(n - 2)
+  # Return result f(n)
+  res
+end
+
+### Driver Code ###
+if __FILE__ == $0
+  n = 5
+
+  res = recur(n)
+  puts "\nRecursion sum result res = #{res}"
+
+  res = for_loop_recur(n)
+  puts "\nUsing iteration to simulate recursion sum result res = #{res}"
+
+  res = tail_recur(n, 0)
+  puts "\nTail recursion sum result res = #{res}"
+
+  res = fib(n)
+  puts "\nThe #{n}th Fibonacci number is #{res}"
+end

en/codes/ruby/chapter_computational_complexity/space_complexity.rb

@@ -0,0 +1,92 @@
+=begin
+File: space_complexity.rb
+Created Time: 2024-03-30
+Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
+=end
+
+require_relative '../utils/list_node'
+require_relative '../utils/tree_node'
+require_relative '../utils/print_util'
+
+### Function ###
+def function
+  # Perform some operations
+  0
+end
+
+### Constant time ###
+def constant(n)
+  # Constants, variables, objects occupy O(1) space
+  a = 0
+  nums = [0] * 10000
+  node = ListNode.new
+
+  # Variables in the loop occupy O(1) space
+  (0...n).each { c = 0 }
+  # Functions in the loop occupy O(1) space
+  (0...n).each { function }
+end
+
+### Linear time ###
+def linear(n)
+  # A list of length n occupies O(n) space
+  nums = Array.new(n, 0)
+
+  # A hash table of length n occupies O(n) space
+  hmap = {}
+  for i in 0...n
+    hmap[i] = i.to_s
+  end
+end
+
+### Linear space (recursive) ###
+def linear_recur(n)
+  puts "Recursion n = #{n}"
+  return if n == 1
+  linear_recur(n - 1)
+end
+
+### Quadratic time ###
+def quadratic(n)
+  # 2D list uses O(n^2) space
+  Array.new(n) { Array.new(n, 0) }
+end
+
+### Quadratic space (recursive) ###
+def quadratic_recur(n)
+  return 0 unless n > 0
+
+  # Array nums has length n, n-1, ..., 2, 1
+  nums = Array.new(n, 0)
+  quadratic_recur(n - 1)
+end
+
+### Exponential space (build full binary tree) ###
+def build_tree(n)
+  return if n == 0
+
+  TreeNode.new.tap do |root|
+    root.left = build_tree(n - 1)
+    root.right = build_tree(n - 1)
+  end
+end
+
+### Driver Code ###
+if __FILE__ == $0
+  n = 5
+
+  # Constant order
+  constant(n)
+
+  # Linear order
+  linear(n)
+  linear_recur(n)
+
+  # Exponential order
+  quadratic(n)
+  quadratic_recur(n)
+
+  # Exponential order
+  root = build_tree(n)
+  print_tree(root)
+end

en/codes/ruby/chapter_computational_complexity/time_complexity.rb

@@ -0,0 +1,165 @@
+=begin
+File: time_complexity.rb
+Created Time: 2024-03-30
+Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
+=end
+
+### Constant time ###
+def constant(n)
+  count = 0
+  size = 100000
+
+  (0...size).each { count += 1 }
+
+  count
+end
+
+### Linear time ###
+def linear(n)
+  count = 0
+  (0...n).each { count += 1 }
+  count
+end
+
+### Linear time (array traversal) ###
+def array_traversal(nums)
+  count = 0
+
+  # Number of iterations is proportional to the array length
+  for num in nums
+    count += 1
+  end
+
+  count
+end
+
+### Quadratic time ###
+def quadratic(n)
+  count = 0
+
+  # Number of iterations is quadratically related to the data size n
+  for i in 0...n
+    for j in 0...n
+      count += 1
+    end
+  end
+
+  count
+end
+
+### Quadratic time (bubble sort) ###
+def bubble_sort(nums)
+  count = 0  # Counter
+
+  # Outer loop: unsorted range is [0, i]
+  for i in (nums.length - 1).downto(0)
+    # Inner loop: swap the largest element in the unsorted range [0, i] to the rightmost end of that range
+    for j in 0...i
+      if nums[j] > nums[j + 1]
+        # Swap nums[j] and nums[j + 1]
+        tmp = nums[j]
+        nums[j] = nums[j + 1]
+        nums[j + 1] = tmp
+        count += 3 # Element swap includes 3 unit operations
+      end
+    end
+  end
+
+  count
+end
+
+### Exponential time (iterative) ###
+def exponential(n)
+  count, base = 0, 1
+
+  # Cells divide into two every round, forming sequence 1, 2, 4, 8, ..., 2^(n-1)
+  (0...n).each do
+    (0...base).each { count += 1 }
+    base *= 2
+  end
+
+  # count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1
+  count
+end
+
+### Exponential time (recursive) ###
+def exp_recur(n)
+  return 1 if n == 1
+  exp_recur(n - 1) + exp_recur(n - 1) + 1
+end
+
+### Logarithmic time (iterative) ###
+def logarithmic(n)
+  count = 0
+
+  while n > 1
+    n /= 2
+    count += 1
+  end
+
+  count
+end
+
+### Logarithmic time (recursive) ###
+def log_recur(n)
+  return 0 unless n > 1
+  log_recur(n / 2) + 1
+end
+
+### Linearithmic time ###
+def linear_log_recur(n)
+  return 1 unless n > 1
+
+  count = linear_log_recur(n / 2) + linear_log_recur(n / 2)
+  (0...n).each { count += 1 }
+
+  count
+end
+
+### Factorial time (recursive) ###
+def factorial_recur(n)
+  return 1 if n == 0
+
+  count = 0
+  # Split from 1 into n
+  (0...n).each { count += factorial_recur(n - 1) }
+
+  count
+end
+
+### Driver Code ###
+if __FILE__ == $0
+  # You can modify n to run and observe the trend of the number of operations for various complexities
+  n = 8
+  puts "Input data size n = #{n}"
+
+  count = constant(n)
+  puts "Constant-time operations count = #{count}"
+
+  count = linear(n)
+  puts "Linear-time operations count = #{count}"
+  count = array_traversal(Array.new(n, 0))
+  puts "Linear-time (array traversal) operations count = #{count}"
+
+  count = quadratic(n)
+  puts "Quadratic-time operations count = #{count}"
+  nums = Array.new(n) { |i| n - i } # [n, n-1, ..., 2, 1]
+  count = bubble_sort(nums)
+  puts "Quadratic-time (bubble sort) operations count = #{count}"
+
+  count = exponential(n)
+  puts "Exponential-time (iterative) operations count = #{count}"
+  count = exp_recur(n)
+  puts "Exponential-time (recursive) operations count = #{count}"
+
+  count = logarithmic(n)
+  puts "Logarithmic-time (iterative) operations count = #{count}"
+  count = log_recur(n)
+  puts "Logarithmic-time (recursive) operations count = #{count}"
+
+  count = linear_log_recur(n)
+  puts "Linearithmic-time (recursive) operations count = #{count}"
+
+  count = factorial_recur(n)
+  puts "Factorial-time (recursive) operations count = #{count}"
+end

en/codes/ruby/chapter_computational_complexity/worst_best_time_complexity.rb

@@ -0,0 +1,35 @@
+=begin
+File: worst_best_time_complexity.rb
+Created Time: 2024-03-30
+Author: Xuan Khoa Tu Nguyen (ngxktuzkai2000@gmail.com)
+=end
+
+### Generate array with elements: 1, 2, ..., n, shuffled ###
+def random_numbers(n)
+  # Generate array nums =: 1, 2, 3, ..., n
+  nums = Array.new(n) { |i| i + 1 }
+  # Randomly shuffle array elements
+  nums.shuffle!
+end
+
+### Find index of number 1 in array nums ###
+def find_one(nums)
+  for i in 0...nums.length
+    # When element 1 is at the head of the array, best time complexity O(1) is achieved
+    # When element 1 is at the tail of the array, worst time complexity O(n) is achieved
+    return i if nums[i] == 1
+  end
+
+  -1
+end
+
+### Driver Code ###
+if __FILE__ == $0
+  for i in 0...10
+    n = 100
+    nums = random_numbers(n)
+    index = find_one(nums)
+    puts "\nArray [ 1, 2, ..., n ] after shuffling = #{nums}"
+    puts "Index of number 1 is #{index}"
+  end
+end