Longest Common Subsequence
Given two sequences, find the length of their longest common subsequence. A subsequence is a sequence that appears in the same relative order, but not necessarily contiguous.
Constraints:
- 1 <= text1.length, text2.length <= 1000
Examples:
Input: text1 = "abcde", text2 = "ace"
Output: 3
Explanation: The longest common subsequence is "ace"
Solutions
Dynamic Programming
Time: O(m*n)Space: O(m*n)
The dynamic programming approach involves creating a 2D array dp where dp[i][j] represents the length of the longest common subsequence of the first i characters of text1 and the first j characters of text2. The final answer is stored in dp[m][n].
def longestCommonSubsequence(text1, text2):
m, n = len(text1), len(text2); dp = [[0] * (n + 1) for _ in range(m + 1)]; for i in range(1, m + 1):
for j in range(1, n + 1):
if text1[i - 1] == text2[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[m][n]Follow-up:
What if the input sequences are very large and we need to find the actual longest common subsequence, not just its length?
