1143. Longest Common Subsequence

1. Question

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.

2. Examples

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.

3. Constraints

• 1 <= text1.length, text2.length <= 1000
• text1 and text2consist of only lowercase English characters.

4. References

来源：力扣（LeetCode） 链接：https://leetcode-cn.com/problems/longest-common-subsequence 著作权归领扣网络所有。商业转载请联系官方授权，非商业转载请注明出处。

5. Solutions

维护一个二维数组，用于计算最长公共子序列。如果i和j位置的字母相同，则为最长的（左上对角）数+1。如果不同，就是上或者左的最大值。

class Solution {
  public int longestCommonSubsequence(String text1, String text2) {
    int[][] arr = new int[text1.length() + 1][text2.length() + 1];

    for (int i = 1; i <= text1.length(); i++) {
      for (int j = 1; j <= text2.length(); j++) {
        if (text1.charAt(i - 1) == text2.charAt(j - 1)) {
          arr[i][j] = arr[i - 1][j - 1] + 1;
        } else {
          arr[i][j] = Math.max(arr[i - 1][j], arr[i][j - 1]);
        }
      }
    }
    return arr[text1.length()][text2.length()];
  }
}