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* docs: add Japanese documents (`ja/docs`) * docs: add Japanese documents (`ja/codes`) * docs: add Japanese documents * Remove pythontutor blocks in ja/ * Add an empty at the end of each markdown file. * Add the missing figures (use the English version temporarily). * Add index.md for Japanese version. * Add index.html for Japanese version. * Add missing index.assets * Fix backtracking_algorithm.md for Japanese version. * Add avatar_eltociear.jpg. Fix image links on the Japanese landing page. * Add the Japanese banner. --------- Co-authored-by: krahets <krahets@163.com>
151 lines
4.0 KiB
Python
151 lines
4.0 KiB
Python
"""
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File: time_complexity.py
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Created Time: 2022-11-25
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Author: krahets (krahets@163.com)
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"""
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def constant(n: int) -> int:
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"""定数複雑度"""
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count = 0
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size = 100000
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for _ in range(size):
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count += 1
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return count
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def linear(n: int) -> int:
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"""線形複雑度"""
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count = 0
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for _ in range(n):
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count += 1
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return count
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def array_traversal(nums: list[int]) -> int:
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"""線形複雑度（配列の走査）"""
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count = 0
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# ループ回数は配列の長さに比例する
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for num in nums:
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count += 1
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return count
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def quadratic(n: int) -> int:
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"""二次複雑度"""
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count = 0
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# ループ回数はデータサイズnの二乗に比例する
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for i in range(n):
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for j in range(n):
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count += 1
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return count
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def bubble_sort(nums: list[int]) -> int:
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"""二次複雑度（バブルソート）"""
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count = 0 # カウンタ
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# 外側のループ: 未ソート範囲は [0, i]
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for i in range(len(nums) - 1, 0, -1):
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# 内側のループ: 未ソート範囲 [0, i] の最大要素を右端にスワップ
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for j in range(i):
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if nums[j] > nums[j + 1]:
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# nums[j] と nums[j + 1] をスワップ
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tmp: int = nums[j]
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nums[j] = nums[j + 1]
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nums[j + 1] = tmp
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count += 3 # 要素のスワップは3つの個別操作を含む
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return count
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def exponential(n: int) -> int:
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"""指数複雑度（ループ実装）"""
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count = 0
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base = 1
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# セルは毎回2つに分裂し、1, 2, 4, 8, ..., 2^(n-1) の数列を形成する
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for _ in range(n):
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for _ in range(base):
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count += 1
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base *= 2
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# count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1
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return count
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def exp_recur(n: int) -> int:
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"""指数複雑度（再帰実装）"""
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if n == 1:
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return 1
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return exp_recur(n - 1) + exp_recur(n - 1) + 1
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def logarithmic(n: int) -> int:
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"""対数複雑度（ループ実装）"""
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count = 0
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while n > 1:
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n = n / 2
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count += 1
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return count
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def log_recur(n: int) -> int:
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"""対数複雑度（再帰実装）"""
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if n <= 1:
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return 0
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return log_recur(n / 2) + 1
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def linear_log_recur(n: int) -> int:
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"""線形対数複雑度"""
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if n <= 1:
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return 1
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count: int = linear_log_recur(n // 2) + linear_log_recur(n // 2)
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for _ in range(n):
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count += 1
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return count
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def factorial_recur(n: int) -> int:
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"""階乗複雑度（再帰実装）"""
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if n == 0:
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return 1
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count = 0
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# 1つからnに分岐
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for _ in range(n):
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count += factorial_recur(n - 1)
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return count
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"""ドライバコード"""
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if __name__ == "__main__":
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# nを変更して、様々な複雑度での操作回数の変化傾向を体験できる
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n = 8
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print("入力データサイズ n =", n)
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count: int = constant(n)
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print("定数複雑度の操作回数 =", count)
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count: int = linear(n)
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print("線形複雑度の操作回数 =", count)
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count: int = array_traversal([0] * n)
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print("線形複雑度（配列の走査）の操作回数 =", count)
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count: int = quadratic(n)
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print("二次複雑度の操作回数 =", count)
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nums = [i for i in range(n, 0, -1)] # [n, n-1, ..., 2, 1]
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count: int = bubble_sort(nums)
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print("二次複雑度（バブルソート）の操作回数 =", count)
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count: int = exponential(n)
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print("指数複雑度（ループ実装）の操作回数 =", count)
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count: int = exp_recur(n)
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print("指数複雑度（再帰実装）の操作回数 =", count)
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count: int = logarithmic(n)
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print("対数複雑度（ループ実装）の操作回数 =", count)
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count: int = log_recur(n)
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print("対数複雑度（再帰実装）の操作回数 =", count)
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count: int = linear_log_recur(n)
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print("線形対数複雑度（再帰実装）の操作回数 =", count)
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count: int = factorial_recur(n)
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print("階乗複雑度（再帰実装）の操作回数 =", count) |