代码随想录算法训练营第五十三日| ● 1143.最长公共子序列 ● 1035.不相交的线 ● 53. 最大子序和 动态规划

1143.最长公共子序列：

class Solution:
    def longestCommonSubsequence(self, text1: str, text2: str) -> int:
        len1, len2 = len(text1)+1, len(text2)+1
        dp = [[0 for _ in range(len1)] for _ in range(len2)] # 先对dp数组做初始化操作
        for i in range(1, len2):
            for j in range(1, len1): # 开始列出状态转移方程
                if text1[j-1] == text2[i-1]:
                    dp[i][j] = dp[i-1][j-1]+1
                else:
                    dp[i][j] = max(dp[i-1][j], dp[i][j-1])
        return dp[-1][-1]

1035.不相交的线：

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

53. 最大子序和 动态规划

class Solution:
    def maxSubArray(self, nums: List[int]) -> int:
        if len(nums) == 0:
            return 0
        dp = [0] * len(nums)
        dp[0] = nums[0]
        result = dp[0]
        for i in range(1, len(nums)):
            dp[i] = max(dp[i-1] + nums[i], nums[i]) #状态转移公式
            result = max(result, dp[i]) #result 保存dp[i]的最大值
        return result