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].
int longestCommonSubsequence(string text1, string text2) {
int m = text1.size(), n = text2.size();
vector<vector<int>> dp(m + 1, vector<int>(n + 1, 0));
for (int i = 1;
i <= m;
i++) {
for (int j = 1;
j <= n;
j++) {
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?
