leetcode 718最长重复子数组 不连续 - DP&LCS leetcode583. 两个字符串的删除操作 最长重复子序列

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'''
最长重复子数组  子数组是连续的  类似LCS ，LCS是不要求连续的
递推式：
A[i] = B[j]时：memo[i][j] = memo[i-1][j-1] + 1
第一行或第一列，A[i] = B[j]时：memo[i][j] = 1 
其他情况 memo[i][j] = 0

LCS 递推式：字符串A B
A[i] = B[j]时：LCS[i，j] = LCS[i-1，j-1]  + 1
A[i] ！= B[j]时：LCS[i，j] = max(LCS[i-1，j-1],LCS[i-1，j],LCS[i，j-1])
根据递推式构造LCS矩阵

'''


def findLength(A, B):
    max_num = 0
    memo = [ [0 for i in range(len(A))] for j in range(len(B))]
    for m in range(len(A)):
        for n in range(len(B)):
            if m > 0 and n > 0 and A[m] == B[n]:
                memo[m][n] = memo[m-1][n-1] + 1
                max_num = max(max_num,memo[m][n])
            elif (m == 0 or n == 0)and  A[m] == B[n]:
                memo[m][n] = 1
                max_num = max(max_num, memo[m][n])
            else:
                continue
    print(max_num)
    return max_num

A = [0,1,1,1,0]
B = [1,1,1,1,1]
findLength(A, B)

leetcode 583两个字符串的删除操作.

任意删除一个字符为一次操作，最少几次操作可以使两次字符串相等

def minDistance(self, word1, word2):
        """
        最长子序列LCS，注意越界的问题初始化列表时+1    
        返回值返回倒数第二个元素
        """
        n,m = len(word1),len(word2)
        if n == 0:
            return m
        if m == 0:
            return n
        if word1 == word2:
            return 0
        if n == 1 and m == 1 and word1 != word2:
            return 2
        ans = [[0 for i in range(m+1)] for j in range(n+1)]
        for i in range(n):
            for j in range(m):
                if word1[i] == word2[j]:
                    ans[i][j] = ans[i-1][j-1] + 1
                else:
                    ans[i][j] = max(ans[i-1][j],ans[i][j-1])
        return m + n - 2*ans[-2][-2]