import 'dart:math';

String lcsRecursion(String a, String b) {
  int aLen = a.length;
  int bLen = b.length;

  if (aLen == 0 || bLen == 0) {
    return "";
  } else if (a[aLen-1] == b[bLen-1]) {
    return lcsRecursion(a.substring(0,aLen-1),b.substring(0,bLen-1)) + a[aLen-1];
  } else {
    var x = lcsRecursion(a, b.substring(0,bLen-1));
    var y = lcsRecursion(a.substring(0,aLen-1), b);
    return (x.length > y.length) ? x : y;
  }
}

String lcsDynamic(String a, String b) {
  var lengths = new List<List<int>>.generate(a.length + 1,
      (_) => new List.filled(b.length+1, 0), growable: false);

  // row 0 and column 0 are initialized to 0 already
  for (int i = 0; i < a.length; i++) {
    for (int j = 0; j < b.length; j++) {
      if (a[i] == b[j]) {
        lengths[i+1][j+1] = lengths[i][j] + 1;
      } else {
        lengths[i+1][j+1] = max(lengths[i+1][j], lengths[i][j+1]);
      }
    }
  }

  // read the substring out from the matrix
  StringBuffer reversedLcsBuffer = new StringBuffer();
  for (int x = a.length, y = b.length; x != 0 && y != 0;) {
    if (lengths[x][y] == lengths[x-1][y]) {
      x--;
    } else if (lengths[x][y] == lengths[x][y-1]) {
      y--;
    } else {
      assert(a[x-1] == b[y-1]);
      reversedLcsBuffer.write(a[x-1]);
      x--;
      y--;
    }
  }

  // reverse String
  var reversedLCS = reversedLcsBuffer.toString();
  var lcsBuffer = new StringBuffer();
  for(var i = reversedLCS.length - 1; i>=0; i--) {
    lcsBuffer.write(reversedLCS[i]);
  }
  return lcsBuffer.toString();
}

void main() {
  print("lcsDynamic('1234', '1224533324') =  ${lcsDynamic('1234', '1224533324')}");
  print("lcsDynamic('thisisatest', 'testing123testing') = ${lcsDynamic('thisisatest', 'testing123testing')}");
  print("lcsDynamic('', 'x') = ${lcsDynamic('', 'x')}");
  print("lcsDynamic('x', 'x') = ${lcsDynamic('x', 'x')}");
  print('');
  print("lcsRecursion('1234', '1224533324') = ${lcsRecursion('1234', '1224533324')}");
  print("lcsRecursion('thisisatest', 'testing123testing') = ${lcsRecursion('thisisatest', 'testing123testing')}");
  print("lcsRecursion('', 'x') = ${lcsRecursion('', 'x')}");
  print("lcsRecursion('x', 'x') = ${lcsRecursion('x', 'x')}");
}