JavaAlgorithms/DynamicProgramming/LongestCommonSubsequence.java

package DynamicProgramming;

class LongestCommonSubsequence {

  public static String getLCS(String str1, String str2) {

    // At least one string is null
    if (str1 == null || str2 == null) return null;

    // At least one string is empty
    if (str1.length() == 0 || str2.length() == 0) return "";

    String[] arr1 = str1.split("");
    String[] arr2 = str2.split("");

    // lcsMatrix[i][j]  = LCS of first i elements of arr1 and first j characters of arr2
    int[][] lcsMatrix = new int[arr1.length + 1][arr2.length + 1];

    for (int i = 0; i < arr1.length + 1; i++) lcsMatrix[i][0] = 0;
    for (int j = 1; j < arr2.length + 1; j++) lcsMatrix[0][j] = 0;
    for (int i = 1; i < arr1.length + 1; i++) {
      for (int j = 1; j < arr2.length + 1; j++) {
        if (arr1[i - 1].equals(arr2[j - 1])) {
          lcsMatrix[i][j] = lcsMatrix[i - 1][j - 1] + 1;
        } else {
          lcsMatrix[i][j] =
              lcsMatrix[i - 1][j] > lcsMatrix[i][j - 1] ? lcsMatrix[i - 1][j] : lcsMatrix[i][j - 1];
        }
      }
    }
    return lcsString(str1, str2, lcsMatrix);
  }

  public static String lcsString(String str1, String str2, int[][] lcsMatrix) {
    StringBuilder lcs = new StringBuilder();
    int i = str1.length(), j = str2.length();
    while (i > 0 && j > 0) {
      if (str1.charAt(i - 1) == str2.charAt(j - 1)) {
        lcs.append(str1.charAt(i - 1));
        i--;
        j--;
      } else if (lcsMatrix[i - 1][j] > lcsMatrix[i][j - 1]) {
        i--;
      } else {
        j--;
      }
    }
    return lcs.reverse().toString();
  }

  public static void main(String[] args) {
    String str1 = "DSGSHSRGSRHTRD";
    String str2 = "DATRGAGTSHS";
    String lcs = getLCS(str1, str2);

    // Print LCS
    if (lcs != null) {
      System.out.println("String 1: " + str1);
      System.out.println("String 2: " + str2);
      System.out.println("LCS: " + lcs);
      System.out.println("LCS length: " + lcs.length());
    }
  }
}