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Commit 327bf56

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feat: add python solution to lc problem: No.1728 (#1848)
No.1728.Cat and Mouse II
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‎solution/1700-1799/1728.Cat and Mouse II/README.md‎

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<!-- 这里可写当前语言的特殊实现逻辑 -->
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```python
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class Solution:
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def canMouseWin(self, grid: List[str], catJump: int, mouseJump: int) -> bool:
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dirs = [0, 1, 0, -1, 0]
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m = len(grid)
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n = len(grid[0])
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nFloors = 0
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cat = 0 # cat's position
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mouse = 0 # mouse's position
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def hash(i: int, j: int) -> int:
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return i * n + j
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for i in range(m):
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for j in range(n):
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if grid[i][j] != "#":
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nFloors += 1
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if grid[i][j] == "C":
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cat = hash(i, j)
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elif grid[i][j] == "M":
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mouse = hash(i, j)
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# dp(i, j, k) := True if mouse can win w//
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# Cat on (i // 8, i % 8), mouse on (j // 8, j % 8), and turns = k
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@functools.lru_cache(None)
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def dp(cat: int, mouse: int, turn: int) -> bool:
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# We already search whole touchable grid
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if turn == nFloors * 2:
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return False
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if turn % 2 == 0:
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# mouse's turn
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i = mouse // n
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j = mouse % n
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for k in range(4):
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for jump in range(mouseJump + 1):
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x = i + dirs[k] * jump
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y = j + dirs[k + 1] * jump
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if x < 0 or x == m or y < 0 or y == n:
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break
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if grid[x][y] == "#":
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break
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if grid[x][y] == "F": # Mouse eats the food, so mouse win
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return True
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if dp(cat, hash(x, y), turn + 1):
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return True
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# Mouse can't win, so mouse lose
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return False
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else:
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# cat's turn
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i = cat // n
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j = cat % n
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for k in range(4):
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for jump in range(catJump + 1):
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x = i + dirs[k] * jump
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y = j + dirs[k + 1] * jump
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if x < 0 or x == m or y < 0 or y == n:
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break
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if grid[x][y] == "#":
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break
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if grid[x][y] == "F": # Cat eats the food, so mouse lose
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return False
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nextCat = hash(x, y)
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if nextCat == mouse: # Cat catches mouse, so mouse lose
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return False
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if not dp(nextCat, mouse, turn + 1):
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return False
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# Cat can't win, so mouse win
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return True
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return dp(cat, mouse, 0)
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```
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‎solution/1700-1799/1728.Cat and Mouse II/README_EN.md‎

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### **Python3**
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```python
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class Solution:
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def canMouseWin(self, grid: List[str], catJump: int, mouseJump: int) -> bool:
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dirs = [0, 1, 0, -1, 0]
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m = len(grid)
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n = len(grid[0])
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nFloors = 0
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cat = 0 # cat's position
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mouse = 0 # mouse's position
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def hash(i: int, j: int) -> int:
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return i * n + j
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for i in range(m):
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for j in range(n):
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if grid[i][j] != "#":
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nFloors += 1
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if grid[i][j] == "C":
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cat = hash(i, j)
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elif grid[i][j] == "M":
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mouse = hash(i, j)
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# dp(i, j, k) := True if mouse can win w//
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# Cat on (i // 8, i % 8), mouse on (j // 8, j % 8), and turns = k
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@functools.lru_cache(None)
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def dp(cat: int, mouse: int, turn: int) -> bool:
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# We already search whole touchable grid
108+
if turn == nFloors * 2:
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return False
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if turn % 2 == 0:
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# mouse's turn
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i = mouse // n
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j = mouse % n
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for k in range(4):
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for jump in range(mouseJump + 1):
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x = i + dirs[k] * jump
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y = j + dirs[k + 1] * jump
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if x < 0 or x == m or y < 0 or y == n:
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break
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if grid[x][y] == "#":
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break
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if grid[x][y] == "F": # Mouse eats the food, so mouse win
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return True
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if dp(cat, hash(x, y), turn + 1):
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return True
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# Mouse can't win, so mouse lose
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return False
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else:
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# cat's turn
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i = cat // n
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j = cat % n
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for k in range(4):
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for jump in range(catJump + 1):
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x = i + dirs[k] * jump
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y = j + dirs[k + 1] * jump
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if x < 0 or x == m or y < 0 or y == n:
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break
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if grid[x][y] == "#":
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break
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if grid[x][y] == "F": # Cat eats the food, so mouse lose
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return False
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nextCat = hash(x, y)
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if nextCat == mouse: # Cat catches mouse, so mouse lose
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return False
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if not dp(nextCat, mouse, turn + 1):
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return False
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# Cat can't win, so mouse win
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return True
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return dp(cat, mouse, 0)
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```
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class Solution:
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def canMouseWin(self, grid: List[str], catJump: int, mouseJump: int) -> bool:
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dirs = [0, 1, 0, -1, 0]
4+
m = len(grid)
5+
n = len(grid[0])
6+
nFloors = 0
7+
cat = 0 # cat's position
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mouse = 0 # mouse's position
9+
10+
def hash(i: int, j: int) -> int:
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return i * n + j
12+
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for i in range(m):
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for j in range(n):
15+
if grid[i][j] != "#":
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nFloors += 1
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if grid[i][j] == "C":
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cat = hash(i, j)
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elif grid[i][j] == "M":
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mouse = hash(i, j)
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# dp(i, j, k) := True if mouse can win w//
23+
# Cat on (i // 8, i % 8), mouse on (j // 8, j % 8), and turns = k
24+
@functools.lru_cache(None)
25+
def dp(cat: int, mouse: int, turn: int) -> bool:
26+
# We already search whole touchable grid
27+
if turn == nFloors * 2:
28+
return False
29+
30+
if turn % 2 == 0:
31+
# mouse's turn
32+
i = mouse // n
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j = mouse % n
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for k in range(4):
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for jump in range(mouseJump + 1):
36+
x = i + dirs[k] * jump
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y = j + dirs[k + 1] * jump
38+
if x < 0 or x == m or y < 0 or y == n:
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break
40+
if grid[x][y] == "#":
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break
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if grid[x][y] == "F": # Mouse eats the food, so mouse win
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return True
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if dp(cat, hash(x, y), turn + 1):
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return True
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# Mouse can't win, so mouse lose
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return False
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else:
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# cat's turn
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i = cat // n
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j = cat % n
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for k in range(4):
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for jump in range(catJump + 1):
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x = i + dirs[k] * jump
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y = j + dirs[k + 1] * jump
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if x < 0 or x == m or y < 0 or y == n:
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break
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if grid[x][y] == "#":
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break
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if grid[x][y] == "F": # Cat eats the food, so mouse lose
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return False
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nextCat = hash(x, y)
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if nextCat == mouse: # Cat catches mouse, so mouse lose
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return False
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if not dp(nextCat, mouse, turn + 1):
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return False
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# Cat can't win, so mouse win
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return True
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return dp(cat, mouse, 0)

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