// baseset ∪ (∪ S) = XとなるようなSを求める(複数返す)
static public IEnumerable<IEnumerable<BitField>> Solve
(IEnumerable<BitField> subsets, BitField baseset = null)
{
// 自明の場合
if (subsets.Count() == 0) {
return Enumerable.Empty<IEnumerable<BitField>>();
}
if (baseset == null) {
baseset = new BitField (subsets.First().Length);
}
// １つしか選択肢がないものを抽出
var subsets1 = subsets.ToList ();
var need = new List<BitField> ();
for (int i = 0; i < baseset.Length; i ++) {
if (baseset [i])
continue;
BitField candidate = null;
int candiCount = 0;
foreach (BitField aSubset in subsets1) {
if (aSubset [i]) {
candiCount ++;
if (candidate == null)
candidate = aSubset;
else
break;
}
}
// １つも無ければエラー
if (candiCount < 1) {
return Enumerable.Empty<IEnumerable<BitField>>();
} else if (candiCount == 1) {
subsets1.Remove (candidate);
need.Add (candidate);
baseset |= candidate;
}
}
// 包含関係を除去
var subsets2 = subsets1.Where
(x => subsets1.All (y => ReferenceEquals(x, y) || !y.Contains(x)));
// 0から総当り
var first = Tuple.Create (Enumerable.Empty<BitField>(), baseset);
var candidates = first.ToEnumerable ();
while (candidates.SingleOrDefault () != null) {
var ok = candidates.Where (x => x.Item2.IsMax).Select (x => x.Item1);
if (ok.SingleOrDefault() != null) {
return ok.Select (x => x.Concat(need));
}
candidates = candidates.SelectMany
(src => subsets2
.Where(x => !src.Item2.Contains(x))
.Select(x => Tuple.Create(src.Item1.Add(x), src.Item2 | x)));
}
return Enumerable.Empty<IEnumerable<BitField>>();
}
// 包含関係
public bool Contains (BitField a)
{
var last = fields.Length - 1;
for (int i = 0; i < last; i ++) {
if ((a.fields [i] | fields [i]) != fields[i])
return false;
}
return ((a.fields [last] & a.highMask) | fields [last]) == fields [last];
}
public QMColumn (int size, int colCount) : base (size)
{
Flags = new BitField (colCount);
}
public QMColumn (TruthTableColumn ttc, int colCount) : base (ttc)
{
Result = ttc.Result;
Flags = new BitField (colCount);
}
// 長さが違うとエラー（特にエラー処理はしない）
public static BitField operator | (BitField a, BitField b){
var c = new BitField (a.length);
for (int i = 0; i < a.fields.Length; i ++) {
c.fields [i] = a.fields [i] | b.fields [i];
}
return c;
}