第五章 数组和广义表

系列文章目录

---

文章目录

• 系列文章目录
• 前言
• 一、约瑟夫环问题
• 总结

---

前言

---

一、约瑟夫环问题

核心代码

//用一维数组p[0..n-1]存放n个人（1，2，...，n）
void josephus(int n,int m)
{  int p[MaxSize];
   int i,j,t;
   for (i=0;i<n;i++)		//构建初始序列（1，2，...，n）
     p[i]=i+1;
   t=0;				//首次报数的起始位置
   printf("出列顺序:");
   for (i=n;i>=1;i--)	  	//i为数组p中当前的人数，出列一次，人数减1
   {  t=(t+m-1)%i;		//t为出列者的编号
      printf("%d ",p[t]);	//编号为t的元素出列
      for (j=t+1;j<=i-1;j++)	//后面的元素前移一个位置
        p[j-1]=p[j];
   }
   printf("\n");
}

代码实现的动态展示图，通过cursor实现

import matplotlib.pyplot as plt
import matplotlib.animation as animation
import numpy as np
from matplotlib.patches import Circle, FancyBboxPatch
import matplotlib.patches as mpatches
from matplotlib.widgets import Button
import matplotlib.patches as patches

# 设置中文字体
plt.rcParams['font.sans-serif'] = ['SimHei', 'Microsoft YaHei']
plt.rcParams['axes.unicode_minus'] = False

class JosephusVisualizer:
    def __init__(self, n=8, m=4):
        self.n = n
        self.m = m
        self.people = list(range(1, n+1))  # 人员编号
        self.current_index = 0  # 当前报数位置
        self.count = 1  # 当前报数
        self.exited = []  # 已出列的人员
        self.remaining = self.people.copy()  # 剩余人员
        self.animation_frames = []
        self.is_paused = False  # 暂停状态
        
        # 计算出列顺序
        self.exit_order = self.calculate_exit_order()
        
        # 生成详细的演示步骤
        self.detailed_steps = self.generate_detailed_steps()
        
    def calculate_exit_order(self):
        """计算约瑟夫问题的出列顺序"""
        people = list(range(1, self.n + 1))
        exit_order = []
        index = 0
        
        while people:
            index = (index + self.m - 1) % len(people)
            exit_order.append(people.pop(index))
            
        return exit_order
    
    def generate_detailed_steps(self):
        """生成详细的演示步骤，包括报数过程"""
        detailed_steps = []
        people = list(range(1, self.n + 1))
        index = 0
        step_num = 1
        
        while people:
            step_info = {
                'step': step_num,
                'remaining': people.copy(),
                'current_index': index,
                'counting_sequence': [],
                'exit_person': None
            }
            
            # 生成报数序列
            counting = []
            for i in range(self.m):
                current_person = people[(index + i) % len(people)]
                counting.append((current_person, i + 1))
            step_info['counting_sequence'] = counting
            step_info['exit_person'] = people[(index + self.m - 1) % len(people)]
            
            detailed_steps.append(step_info)
            
            # 移除出列的人
            index = (index + self.m - 1) % len(people)
            people.pop(index)
            step_num += 1
            
        return detailed_steps
    
    def create_frame(self, frame_num):
        """创建动画帧"""
        fig, ax = plt.subplots(figsize=(14, 12))
        ax.set_xlim(-7, 7)
        ax.set_ylim(-7, 7)
        ax.set_aspect('equal')
        
        # 标题
        title = f"约瑟夫问题演示 (n={self.n}, m={self.m})\n"
        if frame_num < len(self.detailed_steps):
            step_info = self.detailed_steps[frame_num]
            title += f"第{step_info['step']}步: 第{step_info['exit_person']}号出列"
        else:
            title += "演示完成"
        ax.set_title(title, fontsize=16, fontweight='bold', color='red')
        
        # 绘制圆圈
        circle = Circle((0, 0), 4, fill=False, color='blue', linewidth=2)
        ax.add_patch(circle)
        
        # 计算人员位置
        positions = []
        for i in range(self.n):
            angle = 2 * np.pi * i / self.n - np.pi/2  # 从12点钟方向开始
            x = 3.5 * np.cos(angle)
            y = 3.5 * np.sin(angle)
            positions.append((x, y))
        
        # 绘制人员
        for i, (x, y) in enumerate(positions):
            person_num = i + 1
            
            # 确定颜色和样式
            if frame_num < len(self.detailed_steps):
                step_info = self.detailed_steps[frame_num]
                
                if person_num not in step_info['remaining']:
                    # 已出列 - 灰色
                    color = 'lightgray'
                    edgecolor = 'gray'
                    alpha = 0.5
                elif person_num == step_info['exit_person']:
                    # 当前出列 - 红色
                    color = 'red'
                    edgecolor = 'darkred'
                    alpha = 1.0
                elif person_num in [p[0] for p in step_info['counting_sequence']]:
                    # 正在报数 - 橙色
                    color = 'orange'
                    edgecolor = 'darkorange'
                    alpha = 1.0
                else:
                    # 正常 - 绿色
                    color = 'lightgreen'
                    edgecolor = 'green'
                    alpha = 1.0
            else:
                # 演示完成
                color = 'lightgray'
                edgecolor = 'gray'
                alpha = 0.5
            
            # 绘制人员圆圈
            person = Circle((x, y), 0.4, facecolor=color, edgecolor=edgecolor, alpha=alpha, linewidth=2)
            ax.add_patch(person)
            
            # 添加编号
            ax.text(x, y, str(person_num), ha='center', va='center', fontsize=12, fontweight='bold')
            
            # 如果正在报数，显示报数
            if frame_num < len(self.detailed_steps):
                step_info = self.detailed_steps[frame_num]
                for person, count in step_info['counting_sequence']:
                    if person == person_num:
                        ax.text(x, y-0.6, f"({count})", ha='center', va='center', 
                               fontsize=10, fontweight='bold', color='red')
        
        # 添加说明文字
        if frame_num < len(self.detailed_steps):
            step_info = self.detailed_steps[frame_num]
            info_text = f"剩余人数: {len(step_info['remaining'])}\n"
            info_text += f"出列顺序: {[s['exit_person'] for s in self.detailed_steps[:frame_num+1]]}"
            
            # 报数过程说明
            counting_text = "报数过程:\n"
            for person, count in step_info['counting_sequence']:
                counting_text += f"第{person}号报{count}\n"
            counting_text += f"第{step_info['exit_person']}号报到{self.m}，出列！"
        else:
            info_text = f"最终出列顺序: {[s['exit_person'] for s in self.detailed_steps]}"
            counting_text = "演示完成！"
        
        ax.text(-6.5, -6, info_text, fontsize=11, bbox=dict(boxstyle="round,pad=0.3", facecolor="yellow", alpha=0.7))
        ax.text(-6.5, 6, counting_text, fontsize=11, bbox=dict(boxstyle="round,pad=0.3", facecolor="lightblue", alpha=0.7))
        
        ax.axis('off')
        return fig
    
    def create_animation(self):
        """创建完整动画，包含暂停按钮"""
        frames = len(self.detailed_steps) + 1  # 包括初始状态
        
        fig, ax = plt.subplots(figsize=(14, 12))
        ax.set_xlim(-7, 7)
        ax.set_ylim(-7, 7)
        ax.set_aspect('equal')
        
        # 删除暂停按钮相关代码
        
        def animate(frame_num):
            # 删除暂停检查
            ax.clear()
            ax.set_xlim(-7, 7)
            ax.set_ylim(-7, 7)
            ax.set_aspect('equal')
            
            # 标题
            title = f"约瑟夫环问题演示 (n={self.n}, m={self.m})\n"
            if frame_num < len(self.detailed_steps):
                step_info = self.detailed_steps[frame_num]
                title += f"第{step_info['step']}步: 第{step_info['exit_person']}号出列"
            else:
                title += "演示完成"
            ax.set_title(title, fontsize=16, fontweight='bold', color='red')
            
            # 绘制圆圈
            circle = Circle((0, 0), 4, fill=False, color='blue', linewidth=2)
            ax.add_patch(circle)
            
            # 计算人员位置
            positions = []
            for i in range(self.n):
                angle = 2 * np.pi * i / self.n - np.pi/2
                x = 3.5 * np.cos(angle)
                y = 3.5 * np.sin(angle)
                positions.append((x, y))
            
            # 绘制人员
            for i, (x, y) in enumerate(positions):
                person_num = i + 1
                
                if frame_num < len(self.detailed_steps):
                    step_info = self.detailed_steps[frame_num]
                    
                    if person_num not in step_info['remaining']:
                        color = 'lightgray'
                        edgecolor = 'gray'
                        alpha = 0.5
                    elif person_num == step_info['exit_person']:
                        color = 'red'
                        edgecolor = 'darkred'
                        alpha = 1.0
                    elif person_num in [p[0] for p in step_info['counting_sequence']]:
                        color = 'orange'
                        edgecolor = 'darkorange'
                        alpha = 1.0
                    else:
                        color = 'lightgreen'
                        edgecolor = 'green'
                        alpha = 1.0
                else:
                    color = 'lightgray'
                    edgecolor = 'gray'
                    alpha = 0.5
                
                person = Circle((x, y), 0.4, facecolor=color, edgecolor=edgecolor, alpha=alpha, linewidth=2)
                ax.add_patch(person)
                ax.text(x, y, str(person_num), ha='center', va='center', fontsize=12, fontweight='bold')
                
                # 修复报数显示覆盖问题：调整报数数字的位置
                if frame_num < len(self.detailed_steps):
                    step_info = self.detailed_steps[frame_num]
                    for person, count in step_info['counting_sequence']:
                        if person == person_num:
                            # 使用更大的偏移距离，确保不重叠
                            base_offset = 1.5  # 基础偏移距离
                            
                            # 根据人数和位置进一步调整
                            if self.n <= 6:
                                # 人数少时使用更大的偏移
                                offset_distance = base_offset + 0.5
                            else:
                                offset_distance = base_offset
                            
                            # 计算报数数字的偏移位置 - 向外偏移
                            angle = 2 * np.pi * i / self.n - np.pi/2
                            # 向外偏移，确保在圆圈外
                            offset_x = offset_distance * np.cos(angle)
                            offset_y = offset_distance * np.sin(angle)
                            
                            text_x = x + offset_x
                            text_y = y + offset_y
                            
                            # 确保报数数字在安全位置
                            distance_from_center = np.sqrt(text_x**2 + text_y**2)
                            min_safe_distance = 5.0  # 最小安全距离
                            
                            if distance_from_center < min_safe_distance:
                                # 向外调整到安全距离
                                scale_factor = min_safe_distance / distance_from_center
                                text_x = text_x * scale_factor
                                text_y = text_y * scale_factor
                            
                            # 添加背景框，使报数数字更清晰
                            ax.text(text_x, text_y, f"({count})", ha='center', va='center', 
                                   fontsize=11, fontweight='bold', color='red',
                                   bbox=dict(boxstyle="round,pad=0.2", facecolor="white", alpha=0.8, edgecolor="red"))
            
            # 添加说明文字
            if frame_num < len(self.detailed_steps):
                step_info = self.detailed_steps[frame_num]
                info_text = f"剩余人数: {len(step_info['remaining'])}\n"
                info_text += f"出列顺序: {[s['exit_person'] for s in self.detailed_steps[:frame_num+1]]}"
                
                counting_text = "报数过程:\n"
                for person, count in step_info['counting_sequence']:
                    counting_text += f"第{person}号报{count}\n"
                counting_text += f"第{step_info['exit_person']}号报到{self.m}，出列！"
            else:
                info_text = f"最终出列顺序: {[s['exit_person'] for s in self.detailed_steps]}"
                counting_text = "演示完成！"
            
            ax.text(-6.5, -6, info_text, fontsize=11, bbox=dict(boxstyle="round,pad=0.3", facecolor="yellow", alpha=0.7))
            ax.text(-6.5, 6, counting_text, fontsize=11, bbox=dict(boxstyle="round,pad=0.3", facecolor="lightblue", alpha=0.7))
            
            ax.axis('off')
        
        anim = animation.FuncAnimation(fig, animate, frames=frames, interval=3000, repeat=True)
        return anim, fig
    
    # 删除toggle_pause方法，因为不再需要
    
    def show_static_frames(self):
        """显示静态帧，便于理解每一步"""
        frames = len(self.detailed_steps) + 1
        
        for i in range(frames):
            fig = self.create_frame(i)
            plt.show()

# 创建可视化器
josephus = JosephusVisualizer(n=8, m=4)

print("约瑟夫问题 (n=8, m=4) 的出列顺序:")
print(f"初始序列: {list(range(1, 9))}")
print(f"出列顺序: {josephus.exit_order}")
print("\n正在生成动画...")

# 创建动画
anim, fig = josephus.create_animation()

# 保存为GIF
print("正在保存动画为GIF文件...")
try:
    anim.save('josephus_demo.gif', 
              writer='pillow', 
              fps=0.33,  # 改为每3秒/帧，播放更流畅
              dpi=100)
    print("动画已保存为 'josephus_demo.gif'")
except Exception as e:
    print(f"保存失败: {e}")
    print("请确保已安装 pillow 库")

print("您也可以运行 josephus.show_static_frames() 来查看静态帧")
# 删除暂停按钮相关提示

# 显示动画
plt.show()

2023级王同学做的思维导图，做得比较全，我贴上来。

总结

提示：这里对文章进行总结：

例如：以上就是今天要讲的内容，本文仅仅简单介绍约瑟夫环的问题。