最长公共子序列
Longest Common Subsequence
题目详情
问题：最长公共子序列
考察：字符串、动态规划
来源：Citadel
链接：https://www.jointaro.com/interviews/questions/longest-common-subsequence/
Given two strings text1 and text2, return the length of their longest common subsequence. If there is no common subsequence, return 0.
A subsequence of a string is a new string generated from the original string with some characters (can be none) deleted without changing the relative order of the remaining characters.
- For example,
"ace"is a subsequence of"abcde".
A common subsequence of two strings is a subsequence that is common to both strings.
Example 1:
Input: text1 = "abcde", text2 = "ace" Output: 3 Explanation: The longest common subsequence is "ace" and its length is 3.
Example 2:
Input: text1 = "abc", text2 = "abc" Output: 3 Explanation: The longest common subsequence is "abc" and its length is 3.
Example 3:
Input: text1 = "abc", text2 = "def" Output: 0 Explanation: There is no such common subsequence, so the result is 0.
Constraints:
1 <= text1.length, text2.length <= 1000text1andtext2consist of only lowercase English characters.
解析
思路：二维 DP。若两个字符相等，dp[i][j] = dp[i-1][j-1] + 1；否则取删除任一侧字符后的较大值。
复杂度：时间 O(mn)，空间 O(mn)，可滚动优化到 O(min(m,n))。