期末考-1112405053-黃柏翰

weeks/week-02/solutions/1112405053/1one.py

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+
+import sys
+import re
+import random
+
+
+def generate_numbers(y: int):
+	"""Generate a deterministic sequence of y numbers.
+
+	The sequence uses y as the random seed so the same input always
+	produces the same output, which keeps the result reproducible.
+	"""
+	rng = random.Random(y)
+	upper_bound = max(10, y * 2)
+	return [rng.randint(1, upper_bound) for _ in range(y)]
+
+
+def process_input(text: str):
+	text = text.strip()
+	if not text:
+		return None
+	try:
+		y = int(text)
+	except ValueError:
+		print("請輸入整數")
+		return None
+	if y <= 0:
+		print("請輸入正整數")
+		return None
+
+	nums = generate_numbers(y)
+	print(f"目前數列：{' '.join(map(str, nums))}")
+
+	# remove duplicates while keeping original order
+	seen = set()
+	unique = []
+	for n in nums:
+		if n not in seen:
+			seen.add(n)
+			unique.append(n)
+
+	# keep numbers divisible by 5 and sort ascending
+	result = sorted(n for n in unique if n % 5 == 0)
+	return result
+
+
+def main():
+	data = sys.stdin.read()
+	if not data:
+		return
+	res = process_input(data)
+	if res is None:
+		return
+	if res:
+		print(' '.join(map(str, res)))
+	else:
+		print("NONE")
+
+
+if __name__ == '__main__':
+	main()

weeks/week-02/solutions/1112405053/2two.py

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+import sys
+
+
+def shift_letters(text: str, shift: int = 4) -> str:
+	"""Shift all English letters by 4 positions (Caesar cipher).
+	Z shifts to D, a shifts to e, etc. Non-letter characters remain unchanged."""
+	result = []
+	for char in text:
+		if 'A' <= char <= 'Z':
+			# Uppercase letters
+			new_char = chr((ord(char) - ord('A') + shift) % 26 + ord('A'))
+			result.append(new_char)
+		elif 'a' <= char <= 'z':
+			# Lowercase letters
+			new_char = chr((ord(char) - ord('a') + shift) % 26 + ord('a'))
+			result.append(new_char)
+		else:
+			# Non-letter characters remain unchanged
+			result.append(char)
+	return ''.join(result)
+
+
+def main():
+	data = sys.stdin.read()
+	if not data:
+		return
+	result = shift_letters(data.rstrip('\n'))
+	print(result)
+
+
+if __name__ == '__main__':
+	main()

weeks/week-02/solutions/1112405053/3three.py

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+import sys
+
+def to_base3(n: int) -> str:
+    if n == 0:
+        return '0'
+    digits = []
+    while n > 0:
+        digits.append(str(n % 3))
+        n //= 3
+    return ''.join(reversed(digits))
+
+
+def iterative_base3_digit_sum_steps(n: int):
+    """Return a list of step strings and the final single-digit result.
+
+    Each step string has the form: "N -> base3 -> sum: S".
+    """
+    steps = []
+    current = n
+    # handle zero explicitly
+    if current == 0:
+        steps.append("0 -> 0 -> sum: 0")
+        return steps, 0
+    b3 = to_base3(current)
+    current = sum(int(d) for d in b3)
+    steps.append(f"{n} -> {b3} -> sum: {current}")
+
+    while current >= 10:
+        digits_sum = sum(int(d) for d in str(current))
+        steps.append(f"{current} -> sum: {digits_sum}")
+        current = digits_sum
+    return steps, current
+
+
+def run_cli(data: str):
+    data = data.strip()
+    if not data:
+        return
+    try:
+        n = int(data)
+    except ValueError:
+        print("請輸入整數")
+        return
+    steps, result = iterative_base3_digit_sum_steps(n)
+    for s in steps:
+        print(s)
+    print(f"最終結果：{result}")
+
+
+def run_gui():
+    try:
+        import tkinter as tk
+        from tkinter import messagebox
+    except Exception:
+        print("無法載入 Tkinter，請使用命令列模式")
+        return
+
+    def on_compute(event=None):
+        txt_output.delete('1.0', tk.END)
+        raw = entry.get().strip()
+        if raw == '':
+            return
+        try:
+            n = int(raw)
+        except ValueError:
+            messagebox.showerror('錯誤', '請輸入整數')
+            return 
+        steps, result = iterative_base3_digit_sum_steps(n)
+        for s in steps:
+            txt_output.insert(tk.END, s + '\n')
+        txt_output.insert(tk.END, f"最終結果：{result}\n")
+
+    root = tk.Tk()
+    root.title('Base-3 迭代加總')
+
+    frm = tk.Frame(root, padx=8, pady=8)
+    frm.pack(fill=tk.BOTH, expand=True)
+
+    lbl = tk.Label(frm, text='輸入十進位整數：')
+    lbl.grid(row=0, column=0, sticky='w')
+
+    entry = tk.Entry(frm, width=30)
+    entry.grid(row=0, column=1, sticky='we')
+    entry.bind('<Return>', on_compute)
+
+    btn = tk.Button(frm, text='計算 (Enter)', command=on_compute)
+    btn.grid(row=0, column=2, padx=6)
+
+    txt_output = tk.Text(frm, height=10, width=60)
+    txt_output.grid(row=1, column=0, columnspan=3, pady=8)
+
+    # make columns expand
+    frm.columnconfigure(1, weight=1)
+
+    entry.focus()
+    root.mainloop()
+
+
+def main():
+    # If there's piped input, run CLI mode. Otherwise open GUI (pressing F5 in an editor
+    # typically runs the script directly and will show the GUI window).
+    if not sys.stdin.isatty():
+        data = sys.stdin.read()
+        run_cli(data)
+    else:
+        run_gui()
+
+
+if __name__ == '__main__':
+    main()

weeks/week-02/solutions/1112405053/4four/plot.py

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+import matplotlib
+matplotlib.use("Agg")
+import matplotlib.pyplot as plt
+import numpy as np
+
+# 維度定義
+labels = [
+    'Speed for Large N\n(大N速度)', 
+    'Speed for Small N\n(小N速度)', 
+    'No Sorting Required\n(免預先排序)', 
+    'Implementation Simplicity\n(實作簡易度)', 
+    'Worst-case Cmps\n(最壞比較次數)'
+]
+num_vars = len(labels)
+
+# 線性搜尋與二分搜尋的歸一化得分 (0~1) 
+# 數值設計呼應 README 中的多維權衡邏輯
+linear_scores = [0.1, 1.0, 1.0, 1.0, 0.1]
+binary_scores = [1.0, 0.8, 0.2, 0.6, 1.0]
+
+# 雷達圖需要首尾相連
+angles = np.linspace(0, 2 * np.pi, num_vars, endpoint=False).tolist()
+linear_scores += linear_scores[:1]
+binary_scores += binary_scores[:1]
+angles += angles[:1]
+
+fig, ax = plt.subplots(figsize=(7, 7), subplot_kw=dict(polar=True))
+
+# 畫出極座標網格與標籤
+plt.xticks(angles[:-1], labels, color='grey', size=10)
+
+# 設定 y 軸範圍與刻度
+ax.set_rlabel_position(0)
+plt.yticks([0.2, 0.4, 0.6, 0.8, 1.0], ["0.2", "0.4", "0.6", "0.8", "1.0"], color="grey", size=8)
+plt.ylim(0, 1.1)
+
+# 繪製線性搜尋
+ax.plot(angles, linear_scores, linewidth=2, linestyle='solid', label='Linear Search (線性搜尋)', color='#e74c3c')
+ax.fill(angles, linear_scores, color='#e74c3c', alpha=0.25)
+
+# 繪製二分搜尋
+ax.plot(angles, binary_scores, linewidth=2, linestyle='solid', label='Binary Search (二分搜尋)', color='#3498db')
+ax.fill(angles, binary_scores, color='#3498db', alpha=0.25)
+
+# 新增標題與圖例
+plt.title('Multi-Dimensional Trade-off: Linear vs. Binary Search\n(線性 vs 二分搜尋多維權衡雷達圖)', size=14, y=1.1, fontweight='bold')
+plt.legend(loc='upper right', bbox_to_anchor=(1.3, 1.1))
+
+# 儲存圖片
+plt.tight_layout()
+plt.savefig('assets/radar.png', dpi=300)
+print("Radar chart generated successfully at assets/radar.png")

weeks/week-02/solutions/1112405053/4four/search_eval.py

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+import timeit
+import random
+import matplotlib
+matplotlib.use("Agg")
+import matplotlib.pyplot as plt
+import numpy as np
+
+# 1. 產生升冪排序的整數陣列
+N = 100000
+# 為了確保能找到, 讓數值範圍涵蓋 153 並且有足夠的大小差距
+# 我們建立一個包含 0 到 200000 之間的奇數或特定間隔, 
+# 這裡簡單用範圍整數確保 153 必定在其中
+arr = list(range(0, N * 2, 2)) # 產生偶數陣列
+# 強制把 153 放進去，或者我們直接用連續整數確保存在與位置隨機
+arr = list(range(1, N + 1)) 
+
+target = 153 # K = 100 + 53
+
+# 2. 實作二分搜尋（計算比較次數）
+def binary_search(array, k):
+    low = 0
+    high = len(array) - 1
+    cmp_count = 0
+
+    while low <= high:
+        cmp_count += 1
+        mid = (low + high) // 2
+        if array[mid] == k:
+            return mid, cmp_count
+        elif array[mid] < k:
+            low = mid + 1
+        else:
+            high = mid - 1
+    return -1, cmp_count
+
+# 為了比對，也寫一個簡單的線性搜尋計算比較次數
+def linear_search_cmp(array, k):
+    cmp_count = 0
+    for i in range(len(array)):
+        cmp_count += 1
+        if array[i] == k:
+            return i, cmp_count
+    return -1, cmp_count
+
+# 執行搜尋並輸出結果
+idx, cmp_bin = binary_search(arr, target)
+if idx != -1:
+    print(f"FOUND {idx} cmp={cmp_bin}")
+else:
+    print(f"NOT FOUND cmp={cmp_bin}")
+
+# 3. 用 timeit 量測效能
+# 為了避免線性搜尋在前面太快找到，我們用完整跑完或多次量測的平均
+# linear_search 的原生實作供 timeit 使用
+def run_linear():
+    for x in arr:
+        if x == target:
+            break
+
+def run_binary():
+    low = 0
+    high = len(arr) - 1
+    while low <= high:
+        mid = (low + high) // 2
+        if arr[mid] == target:
+            break
+        elif arr[mid] < target:
+            low = mid + 1
+        else:
+            high = mid - 1
+
+# 由於二分搜尋極快，我們讓它執行較多次數以利量測
+t_linear = timeit.timeit(run_linear, number=100)
+t_binary = timeit.timeit(run_binary, number=100)
+
+print(f"linear: {t_linear:.6f} s")
+print(f"binary: {t_binary:.6f} s")
+
+if t_binary < t_linear:
+    print("binary faster")
+else:
+    print("linear faster")