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Fills a table where dp[i][j] is the LCS length of the first i and j characters — each cell built from its diagonal, top, or left neighbour.
Base row & column are 0 (an empty string matches nothing).
1int lcs(String text1, String text2) {2 int len1 = text1.length(), len2 = text2.length();3 int[][] dp = new int[len1+1][len2+1]; // base row/col = 04 for (int i = 1; i <= len1; i++)5 for (int j = 1; j <= len2; j++)6 if (text1.charAt(i-1) == text2.charAt(j-1)) // same character?7 dp[i][j] = dp[i-1][j-1] + 1; // extend diagonal + 18 else9 dp[i][j] = Math.max(dp[i-1][j], dp[i][j-1]); // best of up, left10 return dp[len1][len2]; // LCS length11}