translation: Add Python and Java code for EN version (#1345)

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* Add Python and Java code for EN version

en/codes/python/chapter_computational_complexity/iteration.py

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+"""
+File: iteration.py
+Created Time: 2023-08-24
+Author: krahets (krahets@163.com)
+"""
+
+
+def for_loop(n: int) -> int:
+    """for loop"""
+    res = 0
+    # Loop sum 1, 2, ..., n-1, n
+    for i in range(1, n + 1):
+        res += i
+    return res
+
+
+def while_loop(n: int) -> int:
+    """while loop"""
+    res = 0
+    i = 1  # Initialize condition variable
+    # Loop sum 1, 2, ..., n-1, n
+    while i <= n:
+        res += i
+        i += 1  # Update condition variable
+    return res
+
+
+def while_loop_ii(n: int) -> int:
+    """while loop (two updates)"""
+    res = 0
+    i = 1  # Initialize condition variable
+    # Loop sum 1, 4, 10, ...
+    while i <= n:
+        res += i
+        # Update condition variable
+        i += 1
+        i *= 2
+    return res
+
+
+def nested_for_loop(n: int) -> str:
+    """Double for loop"""
+    res = ""
+    # Loop i = 1, 2, ..., n-1, n
+    for i in range(1, n + 1):
+        # Loop j = 1, 2, ..., n-1, n
+        for j in range(1, n + 1):
+            res += f"({i}, {j}), "
+    return res
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    n = 5
+    res = for_loop(n)
+    print(f"\nfor loop sum result res = {res}")
+
+    res = while_loop(n)
+    print(f"\nwhile loop sum result res = {res}")
+
+    res = while_loop_ii(n)
+    print(f"\nwhile loop (two updates) sum result res = {res}")
+
+    res = nested_for_loop(n)
+    print(f"\nDouble for loop traversal result {res}")

en/codes/python/chapter_computational_complexity/recursion.py

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+"""
+File: recursion.py
+Created Time: 2023-08-24
+Author: krahets (krahets@163.com)
+"""
+
+
+def recur(n: int) -> int:
+    """Recursion"""
+    # Termination condition
+    if n == 1:
+        return 1
+    # Recursive: recursive call
+    res = recur(n - 1)
+    # Return: return result
+    return n + res
+
+
+def for_loop_recur(n: int) -> int:
+    """Simulate recursion with iteration"""
+    # Use an explicit stack to simulate the system call stack
+    stack = []
+    res = 0
+    # Recursive: recursive call
+    for i in range(n, 0, -1):
+        # Simulate "recursive" by "pushing onto the stack"
+        stack.append(i)
+    # Return: return result
+    while stack:
+        # Simulate "return" by "popping from the stack"
+        res += stack.pop()
+    # res = 1+2+3+...+n
+    return res
+
+
+def tail_recur(n, res):
+    """Tail recursion"""
+    # Termination condition
+    if n == 0:
+        return res
+    # Tail recursive call
+    return tail_recur(n - 1, res + n)
+
+
+def fib(n: int) -> int:
+    """Fibonacci sequence: Recursion"""
+    # Termination condition f(1) = 0, f(2) = 1
+    if n == 1 or n == 2:
+        return n - 1
+    # Recursive call f(n) = f(n-1) + f(n-2)
+    res = fib(n - 1) + fib(n - 2)
+    # Return result f(n)
+    return res
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    n = 5
+    res = recur(n)
+    print(f"\nRecursive function sum result res = {res}")
+
+    res = for_loop_recur(n)
+    print(f"\nSimulate recursion with iteration sum result res = {res}")
+
+    res = tail_recur(n, 0)
+    print(f"\nTail recursive function sum result res = {res}")
+
+    res = fib(n)
+    print(f"\nThe n th term of the Fibonacci sequence is {res}")

en/codes/python/chapter_computational_complexity/space_complexity.py

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+"""
+File: space_complexity.py
+Created Time: 2022-11-25
+Author: krahets (krahets@163.com)
+"""
+
+import sys
+from pathlib import Path
+
+sys.path.append(str(Path(__file__).parent.parent))
+from modules import ListNode, TreeNode, print_tree
+
+
+def function() -> int:
+    """Function"""
+    # Perform some operations
+    return 0
+
+
+def constant(n: int):
+    """Constant complexity"""
+    # Constants, variables, objects occupy O(1) space
+    a = 0
+    nums = [0] * 10000
+    node = ListNode(0)
+    # Variables in a loop occupy O(1) space
+    for _ in range(n):
+        c = 0
+    # Functions in a loop occupy O(1) space
+    for _ in range(n):
+        function()
+
+
+def linear(n: int):
+    """Linear complexity"""
+    # A list of length n occupies O(n) space
+    nums = [0] * n
+    # A hash table of length n occupies O(n) space
+    hmap = dict[int, str]()
+    for i in range(n):
+        hmap[i] = str(i)
+
+
+def linear_recur(n: int):
+    """Linear complexity (recursive implementation)"""
+    print("Recursive n =", n)
+    if n == 1:
+        return
+    linear_recur(n - 1)
+
+
+def quadratic(n: int):
+    """Quadratic complexity"""
+    # A two-dimensional list occupies O(n^2) space
+    num_matrix = [[0] * n for _ in range(n)]
+
+
+def quadratic_recur(n: int) -> int:
+    """Quadratic complexity (recursive implementation)"""
+    if n <= 0:
+        return 0
+    # Array nums length = n, n-1, ..., 2, 1
+    nums = [0] * n
+    return quadratic_recur(n - 1)
+
+
+def build_tree(n: int) -> TreeNode | None:
+    """Exponential complexity (building a full binary tree)"""
+    if n == 0:
+        return None
+    root = TreeNode(0)
+    root.left = build_tree(n - 1)
+    root.right = build_tree(n - 1)
+    return root
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    n = 5
+    # Constant complexity
+    constant(n)
+    # Linear complexity
+    linear(n)
+    linear_recur(n)
+    # Quadratic complexity
+    quadratic(n)
+    quadratic_recur(n)
+    # Exponential complexity
+    root = build_tree(n)
+    print_tree(root)

en/codes/python/chapter_computational_complexity/time_complexity.py

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+"""
+File: time_complexity.py
+Created Time: 2022-11-25
+Author: krahets (krahets@163.com)
+"""
+
+
+def constant(n: int) -> int:
+    """Constant complexity"""
+    count = 0
+    size = 100000
+    for _ in range(size):
+        count += 1
+    return count
+
+
+def linear(n: int) -> int:
+    """Linear complexity"""
+    count = 0
+    for _ in range(n):
+        count += 1
+    return count
+
+
+def array_traversal(nums: list[int]) -> int:
+    """Linear complexity (traversing an array)"""
+    count = 0
+    # Loop count is proportional to the length of the array
+    for num in nums:
+        count += 1
+    return count
+
+
+def quadratic(n: int) -> int:
+    """Quadratic complexity"""
+    count = 0
+    # Loop count is squared in relation to the data size n
+    for i in range(n):
+        for j in range(n):
+            count += 1
+    return count
+
+
+def bubble_sort(nums: list[int]) -> int:
+    """Quadratic complexity (bubble sort)"""
+    count = 0  # Counter
+    # Outer loop: unsorted range is [0, i]
+    for i in range(len(nums) - 1, 0, -1):
+        # Inner loop: swap the largest element in the unsorted range [0, i] to the right end of the range
+        for j in range(i):
+            if nums[j] > nums[j + 1]:
+                # Swap nums[j] and nums[j + 1]
+                tmp: int = nums[j]
+                nums[j] = nums[j + 1]
+                nums[j + 1] = tmp
+                count += 3  # Element swap includes 3 individual operations
+    return count
+
+
+def exponential(n: int) -> int:
+    """Exponential complexity (loop implementation)"""
+    count = 0
+    base = 1
+    # Cells split into two every round, forming the sequence 1, 2, 4, 8, ..., 2^(n-1)
+    for _ in range(n):
+        for _ in range(base):
+            count += 1
+        base *= 2
+    # count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1
+    return count
+
+
+def exp_recur(n: int) -> int:
+    """Exponential complexity (recursive implementation)"""
+    if n == 1:
+        return 1
+    return exp_recur(n - 1) + exp_recur(n - 1) + 1
+
+
+def logarithmic(n: int) -> int:
+    """Logarithmic complexity (loop implementation)"""
+    count = 0
+    while n > 1:
+        n = n / 2
+        count += 1
+    return count
+
+
+def log_recur(n: int) -> int:
+    """Logarithmic complexity (recursive implementation)"""
+    if n <= 1:
+        return 0
+    return log_recur(n / 2) + 1
+
+
+def linear_log_recur(n: int) -> int:
+    """Linear logarithmic complexity"""
+    if n <= 1:
+        return 1
+    count: int = linear_log_recur(n // 2) + linear_log_recur(n // 2)
+    for _ in range(n):
+        count += 1
+    return count
+
+
+def factorial_recur(n: int) -> int:
+    """Factorial complexity (recursive implementation)"""
+    if n == 0:
+        return 1
+    count = 0
+    # From 1 split into n
+    for _ in range(n):
+        count += factorial_recur(n - 1)
+    return count
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    # Can modify n to experience the trend of operation count changes under various complexities
+    n = 8
+    print("Input data size n =", n)
+
+    count: int = constant(n)
+    print("Constant complexity operation count =", count)
+
+    count: int = linear(n)
+    print("Linear complexity operation count =", count)
+    count: int = array_traversal([0] * n)
+    print("Linear complexity (traversing an array) operation count =", count)
+
+    count: int = quadratic(n)
+    print("Quadratic complexity operation count =", count)
+    nums = [i for i in range(n, 0, -1)]  # [n, n-1, ..., 2, 1]
+    count: int = bubble_sort(nums)
+    print("Quadratic complexity (bubble sort) operation count =", count)
+
+    count: int = exponential(n)
+    print("Exponential complexity (loop implementation) operation count =", count)
+    count: int = exp_recur(n)
+    print("Exponential complexity (recursive implementation) operation count =", count)
+
+    count: int = logarithmic(n)
+    print("Logarithmic complexity (loop implementation) operation count =", count)
+    count: int = log_recur(n)
+    print("Logarithmic complexity (recursive implementation) operation count =", count)
+
+    count: int = linear_log_recur(n)
+    print("Linear logarithmic complexity (recursive implementation) operation count =", count)
+
+    count: int = factorial_recur(n)
+    print("Factorial complexity (recursive implementation) operation count =", count)

en/codes/python/chapter_computational_complexity/worst_best_time_complexity.py

@@ -0,0 +1,36 @@
+"""
+File: worst_best_time_complexity.py
+Created Time: 2022-11-25
+Author: krahets (krahets@163.com)
+"""
+
+import random
+
+
+def random_numbers(n: int) -> list[int]:
+    """Generate an array with elements: 1, 2, ..., n, order shuffled"""
+    # Generate array nums =: 1, 2, 3, ..., n
+    nums = [i for i in range(1, n + 1)]
+    # Randomly shuffle array elements
+    random.shuffle(nums)
+    return nums
+
+
+def find_one(nums: list[int]) -> int:
+    """Find the index of number 1 in array nums"""
+    for i in range(len(nums)):
+        # When element 1 is at the start of the array, achieve best time complexity O(1)
+        # When element 1 is at the end of the array, achieve worst time complexity O(n)
+        if nums[i] == 1:
+            return i
+    return -1
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    for i in range(10):
+        n = 100
+        nums: list[int] = random_numbers(n)
+        index: int = find_one(nums)
+        print("\nThe array [ 1, 2, ..., n ] after being shuffled =", nums)
+        print("Index of number 1 =", index)