feat: update day28_416.py

feat: update day28_416.py

Author: hj.tian

leetcode75/day28_416.py

@@ -0,0 +1,132 @@
+from typing import List
+
+
+class Solution:
+ def canPartition(self, nums: List[int]) -> bool:
+ """
+ 1 5 11 5
+ 0 T T T F
+ 1 T T T F
+ 2 F F F F
+ 3 F F F F
+ 4 F F F F
+ 5 F T T F
+ 6 F T T F
+ 7 F F F F
+ 8 F F F F
+ 9 F F F F
+ 10 F F F F
+ 11 F F T F
+
+ dp[row][col]: 表示前col个元素是否可以构成row这个数字
+ dp[row][col] = dp[row][col-1] or dp[row-nums[col]][col-1]
+ 状态压缩: col 只与 col-1 有关
+ dp[row] = dp[row] or dp[row-nums[col]], row 从后往前, 从前往后不行是因为 col 会覆盖 col-1
+ """
+ total = sum(nums)
+ if total % 2 > 0 or len(nums) <= 1:
+ return False
+ target = total // 2
+ dp = [False for _ in range(target + 1)]
+ dp[0] = True
+ if nums[0] <= target:
+ dp[nums[0]] = True
+ for col in range(1, len(nums)):
+ for row in range(target, 0, -1):
+ dp[row] = dp[row] or (row >= nums[col] and dp[row - nums[col]])
+ if dp[target] is True:
+ return True
+ return False
+
+
+# class Solution:
+# def canPartition(self, nums: List[int]) -> bool:
+# """
+# 1 5 11 5
+# 0 T T T F
+# 1 T T T F
+# 2 F F F F
+# 3 F F F F
+# 4 F F F F
+# 5 F T T F
+# 6 F T T F
+# 7 F F F F
+# 8 F F F F
+# 9 F F F F
+# 10 F F F F
+# 11 F F T F
+
+# dp[row][col]: 表示前col个元素是否可以构成row这个数字
+# dp[row][col] = dp[row][col-1] or dp[row-nums[col]][col-1]
+# """
+# total = sum(nums)
+# if total % 2 > 0 or len(nums) <= 1:
+# return False
+# target = total // 2
+# dp = [[False for _ in nums] for _ in range(total + 1)]
+# dp[0][0] = dp[nums[0]][0] = True
+# for col in range(1, len(nums)):
+# for row in range(target + 1):
+# dp[row][col] = dp[row][col - 1] or (row >= nums[col] and dp[row - nums[col]][col - 1])
+# if dp[target][col] is True:
+# return True
+# return False
+
+
+# class Solution:
+# def canPartition(self, nums: List[int]) -> bool:
+# """
+# (11,0)
+# (10,1) (11,1)
+# (5,2) (10,2) (6,2) (11,2)
+# - (5,3) - (6,3) (0,3) (11,3)
+# (0,4)
+# 超时的原因在于重复计数子问题 2**N
+# 记录 (target, index) 的解避免重复计算
+# """
+# total = sum(nums)
+# if total % 2 > 0 or len(nums) <= 1:
+# return False
+# memory = dict()
+# return self.search(nums, total // 2, 0, memory)
+
+# def search(self, nums: List[int], target: int, index: int, memory: dict) -> bool:
+# if target == 0:
+# return True
+# if target < 0:
+# return False
+# if index >= len(nums):
+# return False
+# if memory.get((target, index)) in (True, False):
+# return memory[(target, index)]
+# got = self.search(nums, target - nums[index], index + 1, memory)
+# memory[(target - nums[index], index + 1)] = got
+# not_got = self.search(nums, target, index + 1, memory)
+# memory[(target, index + 1)] = not_got
+# return got or not_got
+
+
+# class Solution:
+# def canPartition(self, nums: List[int]) -> bool:
+# # 暴力搜索 Timeout
+# total = sum(nums)
+# if total % 2 > 0 or len(nums) <= 1:
+# return False
+# nums.sort()
+# return self.search(nums, total // 2, 0)
+
+# def search(self, nums: List[int], target: int, index: int):
+# if target == 0:
+# return True
+# if target < 0:
+# return False
+# if index >= len(nums):
+# return False
+# return self.search(nums, target - nums[index], index + 1) or self.search(nums, target, index + 1)
+
+
+if __name__ == "__main__":
+ # assert Solution().canPartition(nums=[1, 5, 11, 5]) is True
+ # assert Solution().canPartition(nums=[1, 2, 3, 5]) is False
+ # assert Solution().canPartition(nums=[9, 5]) is False
+ assert Solution().canPartition(nums=[14, 9, 8, 4, 3, 2]) is True