一个“一笔画”问题的求解器
作者：互联网
回老家跟侄子玩，因为不想惯着他玩手机的臭毛病，就跟他玩一些纸笔游戏，比如这个：
从起点出发抵达终点，如何在不走重复格子的前提下，走过尽可能多的格子，并吃到尽可能多的金币？其中，黑色格子是墙壁不能走。
感觉还挺有意思的，不妨就来写一个“一笔画”的求解器，找出所有最优的轨迹。
思路：
可以先输出所有从起点到终点的轨迹，然后建立一个评分系统对所有轨迹进行评估：每走一个格子+1分，每吃一个金币+1分，最后输出评分最高的轨迹即可。
Step1：建模
一个如图的迷宫可以很自然地用矩阵描述，对于每一个元素，值0表示空格子，值1表示金币，值-1表示墙壁，值2表示起点，值3表示终点。
import numpy as np ROW, COL = 6, 4 maze = np.zeros((ROW,COL)) START = (0, 3) OUT = (5, 0) maze[START] = 2 maze[OUT] = 3 maze[1, 1] = 1 maze[5, 3] = 1 maze[2, 1] = -1 maze[4, 2] = -1View Code
Step2：寻迹算法
一条轨迹可以拆分成多个“步”，在走每一步之前，所作的事情是一样的：找到下一步能到达的合法位置，然后选择其中一个。如果新位置是死路或者是终点，那么结束或输出该轨迹，并返回到上一步所在的位置，选择其他步。这一过程可以很好地由递归函数表达：
def step(start, track, env):
x, y = start
next_pos = []
for i, j in [(x-1, y), (x+1, y), (x, y-1), (x, y+1)]:
if 0 <= i <= ROW-1 and 0 <= j <= COL-1: # 边界限制
if (i, j) in track: # 重复的格子不能走
continue
if env[i,j] == -1: # 有墙壁的格子不能走
continue
next_pos.append((i, j))
for i, j in next_pos:
track_new = track.copy()
track_new.append((i, j))
if (i, j) == OUT:
global tracks
tracks.append(track_new)
return
start_new = (i, j)
step(start_new, track_new, env)
运行一下：
tracks = [] step(START, [START], maze) print(len(tracks))
输出为192，说明从起点到终点的轨迹有192条
Step3：评分器
每走一个格子+1分，每吃一个金币+1分，输出评分最高的轨迹。
def findOptimalTracks(tracks):
# 统计所有track的分数
# 分数：每走过一个格子+1，若是金币格子则额外+1
scores = []
for track in tracks:
score = 0
if (1, 1) in track:
score += 1
if (5, 3) in track:
score += 1
score += len(track)
scores.append(score)
tracks_optimal = []
maxScore = max(scores)
for i, score in enumerate(scores):
if score == maxScore:
tracks_optimal.append(tracks[i])
return tracks_optimal
运行一下：
tracks_optimal = findOptimalTracks(tracks) print(len(tracks_optimal))
输出为9，说明最优的轨迹有9条。
Step4：可视化
其实事情到上一步就已经结束了，这里就当看个乐子吧！用pygame把所有轨迹呈现出来：
class tracksRender():
def __init__(self, tracks, env):
pygame.init()
SIZE = 75
ROW, COL = env.shape
self.window = pygame.display.set_mode((COL*SIZE, ROW*SIZE))
pygame.display.set_caption('一笔画')
self.running = True
self.clock = pygame.time.Clock() # 帧数控制
self.time = time.time() # 时间控制
self.INTERVAL = 0.1 # 动作间隔
self.FPS = 30 # 帧数
self.env = env
self.tracks = tracks
self.track = [] # 存放当前将显示的轨迹
self.track_render = [] # 存放当前显示的部分轨迹
def processInput(self):
for event in pygame.event.get():
# 按下右上角的退出键
if event.type == pygame.QUIT:
self.running = False
break
def update(self):
if time.time() - self.time < self.INTERVAL: # 设定更新间隔
return
if self.tracks == []: # 如果已经显示完所有轨迹 则函数返回
return
if self.track == []: # 如果当前轨迹已经完全显示 则显示下一条轨迹
self.track = self.tracks.pop(0)
self.track_render = []
self.track_render.append(self.track.pop(0))
self.time = time.time()
def render(self):
SIZE = 75
ROW, COL = self.env.shape
BGCOLOR = (226, 240, 217) # 浅草绿
self.window.fill(BGCOLOR)
DarkKhaki = (189, 183, 107) # 深卡其布
Wall = (139, 126, 102) # 灰墙
Orange = (255, 165, 0) # 橘子
DodgerBlue = (30, 144, 255) # 道奇蓝
Gold = (255, 215, 0) # 黄金
Font = pygame.font.SysFont('arial', 40)
# 画分隔线
for i in range(ROW + 1):
pygame.draw.line(self.window, DarkKhaki, (0, i*SIZE), (COL*SIZE, i*SIZE), 3)
for i in range(COL + 1):
pygame.draw.line(self.window, DarkKhaki, (i*SIZE, 0), (i*SIZE, ROW*SIZE), 3)
# 画特殊格子
for i in range(ROW):
for j in range(COL):
if self.env[i, j] == -1: # 墙壁
pygame.draw.polygon(self.window, Wall,
((j*SIZE, i*SIZE), ((j+1)*SIZE, i*SIZE), ((j+1)*SIZE, (i+1)*SIZE), (j*SIZE, (i+1)*SIZE))
,0)
if self.env[i, j] == 2: # 起点
Start_text = Font.render('S', True, Orange)
self.window.blit(Start_text, ((j+0.3)*SIZE, (i+0.2)*SIZE))
if self.env[i, j] == 3: # 终点
Start_text = Font.render('E', True, DodgerBlue)
self.window.blit(Start_text, ((j+0.3)*SIZE, (i+0.2)*SIZE))
if self.env[i, j] == 1: # 金币
pygame.draw.circle(self.window, Gold, ((j+0.5)*SIZE,(i+0.5)*SIZE), 20)
# 画轨迹线
if len(self.track_render) > 1:
for i, point in enumerate(self.track_render):
if i == 0: continue
x_, y_ = self.track_render[i-1]
x, y = point
pygame.draw.line(self.window, Orange, ((y_+0.5)*SIZE, (x_+0.5)*SIZE), ((y+0.5)*SIZE, (x+0.5)*SIZE), 5)
pygame.display.update() # 刷新显示
def run(self):
while self.running:
self.processInput()
self.update()
self.render()
self.clock.tick(self.FPS)
效果如下：
整体代码如下：
"""
走迷宫
玩家从起点出发，到达终点走出迷宫
迷宫可由矩阵描述，例如以下6×4的迷宫
[ 0 0 0 2
0 1 0 0
0 -1 0 0
0 0 0 0
0 0 -1 0
3 0 0 1 ]
其中，2表示起点，3表示终点，-1表示墙壁（无法行动到该位置），1表示金币
问，如何在不走重复格子的前提下，走出迷宫，并吃到最多的金币，且走过最多的格子？请打印路径
"""
import numpy as np
import pygame
import time
def step(start, track, env):
x, y = start
next_pos = []
for i, j in [(x-1, y), (x+1, y), (x, y-1), (x, y+1)]:
if 0 <= i <= ROW-1 and 0 <= j <= COL-1: # 边界限制
if (i, j) in track: # 重复的格子不走
continue
if env[i,j] == -1: # 有墙壁的格子不能走
continue
next_pos.append((i, j))
for i, j in next_pos:
track_new = track.copy()
track_new.append((i, j))
if (i, j) == OUT:
global tracks
tracks.append(track_new)
return
start_new = (i, j)
step(start_new, track_new, env)
def findOptimalTracks(tracks):
# 统计所有track的分数
# 分数：每走过一个格子+1，若是金币格子则额外+1
scores = []
for track in tracks:
score = 0
if (1, 1) in track:
score += 1
if (5, 3) in track:
score += 1
score += len(track)
scores.append(score)
tracks_optimal = []
maxScore = max(scores)
for i, score in enumerate(scores):
if score == maxScore:
tracks_optimal.append(tracks[i])
return tracks_optimal
class tracksRender():
def __init__(self, tracks, env):
pygame.init()
SIZE = 75
ROW, COL = env.shape
self.window = pygame.display.set_mode((COL*SIZE, ROW*SIZE))
pygame.display.set_caption('一笔画')
self.running = True
self.clock = pygame.time.Clock() # 帧数控制
self.time = time.time() # 时间控制
self.INTERVAL = 0.1 # 动作间隔
self.FPS = 30 # 帧数
self.env = env
self.tracks = tracks
self.track = [] # 存放当前将显示的轨迹
self.track_render = [] # 存放当前显示的部分轨迹
def processInput(self):
for event in pygame.event.get():
# 按下右上角的退出键
if event.type == pygame.QUIT:
self.running = False
break
def update(self):
if time.time() - self.time < self.INTERVAL: # 设定更新间隔
return
if self.tracks == []: # 如果已经显示完所有轨迹 则函数返回
return
if self.track == []: # 如果当前轨迹已经完全显示 则显示下一条轨迹
self.track = self.tracks.pop(0)
self.track_render = []
self.track_render.append(self.track.pop(0))
self.time = time.time()
def render(self):
SIZE = 75
ROW, COL = self.env.shape
BGCOLOR = (226, 240, 217) # 浅草绿
self.window.fill(BGCOLOR)
DarkKhaki = (189, 183, 107) # 深卡其布
Wall = (139, 126, 102) # 灰墙
Orange = (255, 165, 0) # 橘子
DodgerBlue = (30, 144, 255) # 道奇蓝
Gold = (255, 215, 0) # 黄金
Font = pygame.font.SysFont('arial', 40)
# 画分隔线
for i in range(ROW + 1):
pygame.draw.line(self.window, DarkKhaki, (0, i*SIZE), (COL*SIZE, i*SIZE), 3)
for i in range(COL + 1):
pygame.draw.line(self.window, DarkKhaki, (i*SIZE, 0), (i*SIZE, ROW*SIZE), 3)
# 画特殊格子
for i in range(ROW):
for j in range(COL):
if self.env[i, j] == -1: # 墙壁
pygame.draw.polygon(self.window, Wall,
((j*SIZE, i*SIZE), ((j+1)*SIZE, i*SIZE), ((j+1)*SIZE, (i+1)*SIZE), (j*SIZE, (i+1)*SIZE))
,0)
if self.env[i, j] == 2: # 起点
Start_text = Font.render('S', True, Orange)
self.window.blit(Start_text, ((j+0.3)*SIZE, (i+0.2)*SIZE))
if self.env[i, j] == 3: # 终点
Start_text = Font.render('E', True, DodgerBlue)
self.window.blit(Start_text, ((j+0.3)*SIZE, (i+0.2)*SIZE))
if self.env[i, j] == 1: # 金币
pygame.draw.circle(self.window, Gold, ((j+0.5)*SIZE,(i+0.5)*SIZE), 20)
# 画轨迹线
if len(self.track_render) > 1:
for i, point in enumerate(self.track_render):
if i == 0: continue
x_, y_ = self.track_render[i-1]
x, y = point
pygame.draw.line(self.window, Orange, ((y_+0.5)*SIZE, (x_+0.5)*SIZE), ((y+0.5)*SIZE, (x+0.5)*SIZE), 5)
pygame.display.update() # 刷新显示
def run(self):
while self.running:
self.processInput()
self.update()
self.render()
self.clock.tick(self.FPS)
if __name__ == "__main__":
ROW, COL = 6, 4
maze = np.zeros((ROW,COL))
START = (0, 3)
OUT = (5, 0)
maze[START] = 2
maze[OUT] = 3
maze[1, 1] = 1
maze[5, 3] = 1
maze[2, 1] = -1
maze[4, 2] = -1
print(' Maze:\n', maze)
tracks = []
step(START, [START], maze)
tracks_optimal = findOptimalTracks(tracks)
tracksRender = tracksRender(tracks_optimal, maze)
tracksRender.run()
pygame.quit()
View Code
标签：笔画,求解,track,self,问题,tracks,pygame,maze,SIZE 来源： https://www.cnblogs.com/wsy950409/p/15819523.html