刷题第四十五天 1143. 最长公共子序列 1035. 不相交的线 53. 最大子数组和

class Solution:
    def longestCommonSubsequence(self, text1: str, text2: str) -> int:
        #dp[i][j] 以i-1 和j-1字符结尾的两个序列拥有的最长公共子序列长度
        #
        dp = [[0]*(len(text1) + 1) for _ in range(len(text2) + 1)]
        result = 0
        for i in range(1, len(text2) + 1):
            for j in range(1, len(text1) + 1):
                if text2[i - 1] == text1[j - 1]:
                    dp[i][j] = dp[i - 1][j - 1] + 1
                else: #不相等的情况要考虑是因为本题可以不连续，所以在不连续的时候要把之前的最大值保留下来
                    dp[i][j] = max(dp[i][j - 1], dp[i - 1][j])
                if dp[i][j] > result:
                    result = dp[i][j]
        return result

#不相等的情况要考虑是因为本题可以不连续，所以在不连续的时候要把之前的最大值保留下来

class Solution:
    def maxUncrossedLines(self, nums1: List[int], nums2: List[int]) -> int:
        dp = [[0]*(len(nums2) + 1) for _ in range(len(nums1) + 1)]
        result = 0
        for i in range(1, len(nums1) + 1):
            for j in range(1, len(nums2) + 1):
                if nums1[i - 1] == nums2[j - 1]:
                    dp[i][j] = dp[i - 1][j - 1] + 1
                else:
                    dp[i][j] = max(dp[i - 1][j], dp[i][j - 1])
                if dp[i][j] > result:
                    result = dp[i][j]
        return result

class Solution:
    def maxSubArray(self, nums: List[int]) -> int:
        #dp[i]: 以i结尾的数组最大和
        #dp[i] = max(nums[i], dp[i - 1] + nums[i])
        dp = [0] * (len(nums))
        dp[0] = nums[0]
        result = dp[0]
        for i in range(1, len(nums)):
            dp[i] = max(nums[i], dp[i - 1] + nums[i])
            if dp[i] > result:
                result = dp[i]
        return result