import tkinter as tk from tkinter import ttk, scrolledtext, messagebox import random import math import threading # 生成题目与答案的函数 def generate_problems(n=500): problems = [] for i in range(n): t = i % 10 # 用不同类型的题 if t == 0: # 简单四则运算，保证整数结果 a = random.randint(1, 50) b = random.randint(1, 50) op = random.choice(['+', '-', '*', '//']) if op == '//': b = random.randint(1, 10) expr = f"{a*b} // {b}" ans = (a*b) // b text = f"计算：{expr}（整除）" else: expr = f"{a} {op} {b}" ans = eval(expr) text = f"计算：{expr}" problems.append((f"#{i+1} {text}", str(ans), f"解析：{expr} 的结果是 {ans}")) elif t == 1: # 小数运算 a = round(random.uniform(1, 20), 2) b = round(random.uniform(1, 20), 2) expr = f"{a} + {b}" ans = round(a + b, 4) problems.append((f"#{i+1} 计算：{a} + {b}", str(ans), f"解析：{a} + {b} = {ans}")) elif t == 2: # 一元二次方程求根（整数系数） a = random.randint(1, 5) b = random.randint(-10, 10) c = random.randint(-10, 10) disc = b*b - 4*a*c if disc < 0: # 改为有实根 c = b*b // (4*a) disc = b*b - 4*a*c r1 = (-b + math.sqrt(disc)) / (2*a) r2 = (-b - math.sqrt(disc)) / (2*a) text = f"求方程 {a}x^2 + ({b})x + ({c}) = 0 的根" ans = f"x1={round(r1,6)}, x2={round(r2,6)}" problems.append((f"#{i+1} {text}", ans, f"解析：判别式={disc}，两根如上。")) elif t == 3: # 完整平方或因式分解 a = random.randint(1,5) b = random.randint(1,10) text = f"因式分解：{a}x^2 + {2*a*b}x + {a*b*b}" ans = f"({a}x + {a*b})^2" if a!=0 else f"{a*b*b}" problems.append((f"#{i+1} {text}", ans, f"解析：这是完全平方。")) elif t == 4: # 基本三角恒等式判断 theta = random.choice([0, 30, 45, 60, 90]) text = f"计算 sin({theta}°), cos({theta}°), tan({theta}°)" def deg_to_val(d): if d==0: return (0,1,0) if d==30: return (0.5, math.sqrt(3)/2, 1/math.sqrt(3)) if d==45: return (math.sqrt(2)/2, math.sqrt(2)/2, 1) if d==60: return (math.sqrt(3)/2, 0.5, math.sqrt(3)) if d==90: return (1,0,float('inf')) s,c,tanv = deg_to_val(theta) ans = f"sin={round(s,6)}, cos={round(c,6)}, tan={round(tanv,6) if tanv!=float('inf') else '无穷'}" problems.append((f"#{i+1} {text}", ans, f"解析：常见角值。")) elif t == 5: # 导数：多项式 a = random.randint(1,5) b = random.randint(-5,5) c = random.randint(-5,5) text = f"求导：f(x)={a}x^2 + {b}x + {c}" ans = f"f'(x)={2*a}x + {b}" problems.append((f"#{i+1} {text}", ans, f"解析：多项式求导。")) elif t == 6: # 积分：简单多项式不定积分 a = random.randint(1,5) b = random.randint(-5,5) text = f"求不定积分：∫ ({a}x + {b}) dx" ans = f"{a/2}x^2 + {b}x + C" problems.append((f"#{i+1} {text}", ans, "解析：按幂次积分。")) elif t == 7: # 组合数或排列数 n0 = random.randint(5,15) k0 = random.randint(0,n0) from math import comb val = comb(n0,k0) text = f"计算组合数 C({n0},{k0})" problems.append((f"#{i+1} {text}", str(val), f"解析：组合数值为 {val}")) elif t == 8: # 等比或等差数列求和 a1 = random.randint(1,10) d = random.randint(1,5) n0 = random.randint(3,10) s = n0*(2*a1+(n0-1)*d)//2 text = f"等差数列前 {n0} 项和，首项={a1}, 公差={d}" problems.append((f"#{i+1} {text}", str(s), f"解析：使用前 n 项和公式。")) else: # 随机文本题（例如证明或恒等式） text = f"判断或说明：下列恒等式是否成立（例）：sin^2 x + cos^2 x = 1" ans = "成立" problems.append((f"#{i+1} {text}", ans, "解析：基本三角恒等式。")) return problems class MathQuizApp(tk.Tk): def __init__(self): super().__init__() self.title("数学公式查询器") self.geometry("900x600") self.problems = generate_problems(500) # 左侧题目列表 left_frame = ttk.Frame(self) left_frame.pack(side=tk.LEFT, fill=tk.Y, padx=5, pady=5) lbl = ttk.Label(left_frame, text="题目列表（双击查看）") lbl.pack(anchor="w") self.listbox = tk.Listbox(left_frame, width=40, height=30) for p in self.problems: self.listbox.insert(tk.END, p[0]) self.listbox.pack(side=tk.LEFT, fill=tk.Y) self.listbox.bind("", self.on_select) scrollbar = ttk.Scrollbar(left_frame, orient="vertical", command=self.listbox.yview) scrollbar.pack(side=tk.RIGHT, fill=tk.Y) self.listbox.config(yscrollcommand=scrollbar.set) # 右侧显示区 right_frame = ttk.Frame(self) right_frame.pack(side=tk.RIGHT, fill=tk.BOTH, expand=True, padx=5, pady=5) btn_frame = ttk.Frame(right_frame) btn_frame.pack(fill=tk.X) self.random_btn = ttk.Button(btn_frame, text="随机抽题", command=self.random_problem) self.random_btn.pack(side=tk.LEFT, padx=5, pady=5) self.show_answer_btn = ttk.Button(btn_frame, text="显示答案/解析", command=self.show_answer) self.show_answer_btn.pack(side=tk.LEFT, padx=5, pady=5) self.search_var = tk.StringVar() search_entry = ttk.Entry(btn_frame, textvariable=self.search_var) search_entry.pack(side=tk.LEFT, padx=5) search_entry.bind("", lambda e: self.search()) search_btn = ttk.Button(btn_frame, text="搜索", command=self.search) search_btn.pack(side=tk.LEFT, padx=5) self.problem_title = ttk.Label(right_frame, text="题目将显示在此处", font=("Arial", 14)) self.problem_title.pack(anchor="nw", pady=5) self.problem_text = scrolledtext.ScrolledText(right_frame, wrap=tk.WORD, height=12) self.problem_text.pack(fill=tk.BOTH, expand=True, padx=5, pady=5) ans_lbl = ttk.Label(right_frame, text="答案/解析：") ans_lbl.pack(anchor="nw") self.answer_text = scrolledtext.ScrolledText(right_frame, wrap=tk.WORD, height=8, foreground="blue") self.answer_text.pack(fill=tk.BOTH, expand=True, padx=5, pady=5) self.answer_text.config(state=tk.DISABLED) # 状态栏 self.status = ttk.Label(self, text="共 500 题", relief=tk.SUNKEN, anchor="w") self.status.pack(side=tk.BOTTOM, fill=tk.X) # 当前索引 self.current_index = None def on_select(self, event=None): sel = self.listbox.curselection() if not sel: return idx = sel[0] self.show_problem(idx) def show_problem(self, idx): title, ans, parse = self.problems[idx] self.current_index = idx self.problem_title.config(text=title) self.problem_text.delete(1.0, tk.END) # 显示题目详情（题目文本可能需要更多信息） self.problem_text.insert(tk.END, title + "\n\n" + "（详细说明）") self.answer_text.config(state=tk.NORMAL) self.answer_text.delete(1.0, tk.END) self.answer_text.insert(tk.END, "(答案已隐藏，点击“显示答案/解析”查看)") self.answer_text.config(state=tk.DISABLED) self.status.config(text=f"第 {idx+1} 题，共 {len(self.problems)} 题") def show_answer(self): if self.current_index is None: messagebox.showinfo("提示", "请先选择题目或随机抽题。") return _, ans, parse = self.problems[self.current_index] self.answer_text.config(state=tk.NORMAL) self.answer_text.delete(1.0, tk.END) self.answer_text.insert(tk.END, f"答案：{ans}\n\n{parse}") self.answer_text.config(state=tk.DISABLED) def random_problem(self): idx = random.randint(0, len(self.problems)-1) # 选中列表对应项 self.listbox.selection_clear(0, tk.END) self.listbox.selection_set(idx) self.listbox.see(idx) self.show_problem(idx) def search(self): key = self.search_var.get().strip() if not key: messagebox.showinfo("提示", "请输入搜索关键词（例如：sin, 求导, 等差）") return found = [] for i, p in enumerate(self.problems): if key.lower() in p[0].lower() or key.lower() in p[2].lower(): found.append(i) if not found: messagebox.showinfo("搜索结果", "未找到匹配题目") return # 高亮并跳转到第一个找到的 idx = found[0] self.listbox.selection_clear(0, tk.END) self.listbox.selection_set(idx) self.listbox.see(idx) self.show_problem(idx) messagebox.showinfo("搜索结果", f"找到 {len(found)} 条匹配，已跳转到第一个。") if __name__ == "__main__": app = MathQuizApp() app.mainloop()