// find best threshold value to separate list1 (smaller values) from list2 (bigger values), minimizing false positives + false negatives

// returns (threshold, false positives, false negatives)

static T3<Double, Int, Int> findBestThreshold(Cl<Double> list1, Cl<Double> list2) {

  if (empty(list1) || empty(list2)) null;

  // get basic treshold & number of false positives/negatives

  T3<Double, Int, Int> t = findThreshold_unmoved(list1, list2);

  double threshold = t.a;

  int falsePositives = t.b, falseNegatives = t.c;

  // get all values in a sorted list

  L<Double> l = sorted(concatLists(list1, list2));

  int i = binarySearch_insertionPoint(l, threshold);

  ifdef findBestThreshold_debug

    printVars_str("Initial threshold.", +i, l := l(l), +threshold, +falsePositives, +falseNegatives);

  endifdef

  while (falsePositives <= falseNegatives && i > 0) {

    int i2 = i-1;

    double threshold2 = avg(l.get(i2), l.get(i2+1));

    int falsePositives2 = countPred(list1, d -> d > threshold2); // this is unoptimized

    int falseNegatives2 = countPred(list2, d -> d <= threshold2);

    ifdef findBestThreshold_debug

      printVars_str("Stepped down.", +i2, l := l(l), +threshold2, +falsePositives2, +falseNegatives2);

    endifdef

    // is new result better than old result?

    if (falsePositives2+falseNegatives2 <= falsePositives+falseNegatives) { // not getting worse

      i = i2;

      threshold = threshold2;

      falsePositives = falsePositives2;

      falseNegatives = falseNegatives2;

    } else break;

  }

  while (falseNegatives <= falsePositives && i+2 < l(l)) {

    int i2 = i+1;

    double threshold2 = avg(l.get(i2), l.get(i2+1));

    int falsePositives2 = countPred(list1, d -> d > threshold2);

    int falseNegatives2 = countPred(list2, d -> d <= threshold2);

    ifdef findBestThreshold_debug

      printVars_str("Stepped up.", +i2, l := l(l), +threshold2, +falsePositives2, +falseNegatives2);

    endifdef

    // is new result better than old result?

    if (falsePositives2+falseNegatives2 <= falsePositives+falseNegatives) { // not getting worse

      i = i2;

      threshold = threshold2;

      falsePositives = falsePositives2;

      falseNegatives = falseNegatives2;

    } else break;

  }

  ret t3(threshold, falsePositives, falseNegatives);

}