BitSet

public class BitSet implements Cloneable, java.io.Serializable {
    private static final int ADDRESS_BITS_PER_WORD = 6;
    private static final int BITS_PER_WORD = 1 << ADDRESS_BITS_PER_WORD;
    private static final int BIT_INDEX_MASK = BITS_PER_WORD - 1;

    private static final long WORD_MASK = 0xffffffffffffffffL;

    private static final ObjectStreamField[] serialPersistentFields = {
        new ObjectStreamField("bits", long[].class),
    };

    private long[] words;

    private transient int wordsInUse = 0;

    private transient boolean sizeIsSticky = false;

    private static int wordIndex(int bitIndex) {
        return bitIndex >> ADDRESS_BITS_PER_WORD;
    }

    private void checkInvariants() {
        assert(wordsInUse == 0 || words[wordsInUse - 1] != 0);
        assert(wordsInUse >= 0 && wordsInUse <= words.length);
        assert(wordsInUse == words.length || words[wordsInUse] == 0);
    }

    private void recalculateWordsInUse() {
        int i;
        for (i = wordsInUse-1; i >= 0; i--)
            if (words[i] != 0)
                break;

        wordsInUse = i+1; // The new logical size
    }

    public BitSet() {
		//默认64位
        initWords(BITS_PER_WORD);
        sizeIsSticky = false;
    }

    public BitSet(int nbits) {
        // nbits can't be negative; size 0 is OK
        if (nbits < 0)
            throw new NegativeArraySizeException("nbits < 0: " + nbits);

        initWords(nbits);
        sizeIsSticky = true;
    }

    private void initWords(int nbits) {
        words = new long[wordIndex(nbits-1) + 1];
    }

    private BitSet(long[] words) {
        this.words = words;
        this.wordsInUse = words.length;
        checkInvariants();
    }

    public static BitSet valueOf(long[] longs) {
        int n;
        for (n = longs.length; n > 0 && longs[n - 1] == 0; n--)
            ;
        return new BitSet(Arrays.copyOf(longs, n));
    }

    
    public static BitSet valueOf(LongBuffer lb) {
		//返回副本 
        lb = lb.slice();
        int n;
        for (n = lb.remaining(); n > 0 && lb.get(n - 1) == 0; n--)
            ;
        long[] words = new long[n];
        lb.get(words);
        return new BitSet(words);
    }

    public static BitSet valueOf(byte[] bytes) {
        return BitSet.valueOf(ByteBuffer.wrap(bytes));
    }

  
    public static BitSet valueOf(ByteBuffer bb) {
        bb = bb.slice().order(ByteOrder.LITTLE_ENDIAN);
        int n;
		//首个不为0的index
        for (n = bb.remaining(); n > 0 && bb.get(n - 1) == 0; n--)
            ;
        long[] words = new long[(n + 7) / 8];
        bb.limit(n);
        int i = 0;
        while (bb.remaining() >= 8)
            words[i++] = bb.getLong();    
        for (int remaining = bb.remaining(), j = 0; j < remaining; j++)
            words[i] |= (bb.get() & 0xffL) << (8 * j);
        return new BitSet(words);
    }

    public byte[] toByteArray() {
        int n = wordsInUse;
        if (n == 0)
            return new byte[0];
        int len = 8 * (n-1);
		//直到最后一个不为0的字节
        for (long x = words[n - 1]; x != 0; x >>>= 8)
            len++;
        byte[] bytes = new byte[len];
        ByteBuffer bb = ByteBuffer.wrap(bytes).order(ByteOrder.LITTLE_ENDIAN);
        for (int i = 0; i < n - 1; i++)
            bb.putLong(words[i]);
        for (long x = words[n - 1]; x != 0; x >>>= 8)
            bb.put((byte) (x & 0xff));
        return bytes;
    }

    public long[] toLongArray() {
        return Arrays.copyOf(words, wordsInUse);
    }

    private void ensureCapacity(int wordsRequired) {
        if (words.length < wordsRequired) {
            // Allocate larger of doubled size or required size
            int request = Math.max(2 * words.length, wordsRequired);
            words = Arrays.copyOf(words, request);
            sizeIsSticky = false;
        }
    }

    /**
     * Ensures that the BitSet can accommodate a given wordIndex,
     * temporarily violating the invariants.  The caller must
     * restore the invariants before returning to the user,
     * possibly using recalculateWordsInUse().
     * @param wordIndex the index to be accommodated.
     */
    private void expandTo(int wordIndex) {
        int wordsRequired = wordIndex+1;
        if (wordsInUse < wordsRequired) {
			//Math.max(2 * words.length, wordsRequired);
            ensureCapacity(wordsRequired);
            wordsInUse = wordsRequired;
        }
    }

    private static void checkRange(int fromIndex, int toIndex) {
        if (fromIndex < 0)
            throw new IndexOutOfBoundsException("fromIndex < 0: " + fromIndex);
        if (toIndex < 0)
            throw new IndexOutOfBoundsException("toIndex < 0: " + toIndex);
        if (fromIndex > toIndex)
            throw new IndexOutOfBoundsException("fromIndex: " + fromIndex +
                                                " > toIndex: " + toIndex);
    }

	//index的补码
    public void flip(int bitIndex) {
        if (bitIndex < 0)
            throw new IndexOutOfBoundsException("bitIndex < 0: " + bitIndex);

        int wordIndex = wordIndex(bitIndex);
        expandTo(wordIndex);

        words[wordIndex] ^= (1L << bitIndex);

        recalculateWordsInUse();
        checkInvariants();
    }

    public void flip(int fromIndex, int toIndex) {
        checkRange(fromIndex, toIndex);

        if (fromIndex == toIndex)
            return;

        int startWordIndex = wordIndex(fromIndex);
        int endWordIndex   = wordIndex(toIndex - 1);
        expandTo(endWordIndex);

        long firstWordMask = WORD_MASK << fromIndex;
		//移位操作符左边如果是int类型，则操作符右边的数只有低5位有效（右边的数会首先与0x1f做AND运算），如果操作符左边是long类型，右边的数就只取低6位为有效位。
        //假设-5L,-5在内存中的表示为0xfffffffb，取低6位有效，那么实际有效值是0x3b，换成十进制就是59，也就是把-1L右移59位，可见，表达式的结果正好是低5位全1，高位全0。 
		long lastWordMask  = WORD_MASK >>> -toIndex;
        if (startWordIndex == endWordIndex) {
            // Case 1: One word
            words[startWordIndex] ^= (firstWordMask & lastWordMask);
        } else {
            // Case 2: Multiple words
            // Handle first word
            words[startWordIndex] ^= firstWordMask;

            // Handle intermediate words, if any
            for (int i = startWordIndex+1; i < endWordIndex; i++)
                words[i] ^= WORD_MASK;

            // Handle last word
            words[endWordIndex] ^= lastWordMask;
        }

        recalculateWordsInUse();
        checkInvariants();
    }

    public void set(int bitIndex) {
        if (bitIndex < 0)
            throw new IndexOutOfBoundsException("bitIndex < 0: " + bitIndex);

        int wordIndex = wordIndex(bitIndex);
        expandTo(wordIndex);

        words[wordIndex] |= (1L << bitIndex); // Restores invariants

        checkInvariants();
    }

    public void set(int bitIndex, boolean value) {
        if (value)
            set(bitIndex);
        else
            clear(bitIndex);
    }

    public void set(int fromIndex, int toIndex) {
        checkRange(fromIndex, toIndex);

        if (fromIndex == toIndex)
            return;

        // Increase capacity if necessary
        int startWordIndex = wordIndex(fromIndex);
        int endWordIndex   = wordIndex(toIndex - 1);
        expandTo(endWordIndex);

        long firstWordMask = WORD_MASK << fromIndex;
        long lastWordMask  = WORD_MASK >>> -toIndex;
        if (startWordIndex == endWordIndex) {
            // Case 1: One word
            words[startWordIndex] |= (firstWordMask & lastWordMask);
        } else {
            // Case 2: Multiple words
            // Handle first word
            words[startWordIndex] |= firstWordMask;

            // Handle intermediate words, if any
            for (int i = startWordIndex+1; i < endWordIndex; i++)
                words[i] = WORD_MASK;

            // Handle last word (restores invariants)
            words[endWordIndex] |= lastWordMask;
        }

        checkInvariants();
    }

    public void set(int fromIndex, int toIndex, boolean value) {
        if (value)
            set(fromIndex, toIndex);
        else
            clear(fromIndex, toIndex);
    }

    public void clear(int bitIndex) {
        if (bitIndex < 0)
            throw new IndexOutOfBoundsException("bitIndex < 0: " + bitIndex);

        int wordIndex = wordIndex(bitIndex);
        if (wordIndex >= wordsInUse)
            return;

        words[wordIndex] &= ~(1L << bitIndex);

        recalculateWordsInUse();
        checkInvariants();
    }

    public void clear(int fromIndex, int toIndex) {
        checkRange(fromIndex, toIndex);

        if (fromIndex == toIndex)
            return;

        int startWordIndex = wordIndex(fromIndex);
        if (startWordIndex >= wordsInUse)
            return;

        int endWordIndex = wordIndex(toIndex - 1);
        if (endWordIndex >= wordsInUse) {
            toIndex = length();
            endWordIndex = wordsInUse - 1;
        }

        long firstWordMask = WORD_MASK << fromIndex;
        long lastWordMask  = WORD_MASK >>> -toIndex;
        if (startWordIndex == endWordIndex) {
            // Case 1: One word
            words[startWordIndex] &= ~(firstWordMask & lastWordMask);
        } else {
            // Case 2: Multiple words
            // Handle first word
            words[startWordIndex] &= ~firstWordMask;

            // Handle intermediate words, if any
            for (int i = startWordIndex+1; i < endWordIndex; i++)
                words[i] = 0;

            // Handle last word
            words[endWordIndex] &= ~lastWordMask;
        }

        recalculateWordsInUse();
        checkInvariants();
    }

    public void clear() {
        while (wordsInUse > 0)
            words[--wordsInUse] = 0;
    }

    public boolean get(int bitIndex) {
        if (bitIndex < 0)
            throw new IndexOutOfBoundsException("bitIndex < 0: " + bitIndex);

        checkInvariants();

        int wordIndex = wordIndex(bitIndex);
        return (wordIndex < wordsInUse)
            && ((words[wordIndex] & (1L << bitIndex)) != 0);
    }

    public BitSet get(int fromIndex, int toIndex) {
        checkRange(fromIndex, toIndex);

        checkInvariants();

        int len = length();

        // If no set bits in range return empty bitset
        if (len <= fromIndex || fromIndex == toIndex)
            return new BitSet(0);

        // An optimization
        if (toIndex > len)
            toIndex = len;

        BitSet result = new BitSet(toIndex - fromIndex);
        int targetWords = wordIndex(toIndex - fromIndex - 1) + 1;
        int sourceIndex = wordIndex(fromIndex);
		//是否对齐
        boolean wordAligned = ((fromIndex & BIT_INDEX_MASK) == 0);

        // Process all words but the last word
        for (int i = 0; i < targetWords - 1; i++, sourceIndex++)
            result.words[i] = wordAligned ? words[sourceIndex] :
                (words[sourceIndex] >>> fromIndex) |
                (words[sourceIndex+1] << -fromIndex);

        // Process the last word
        long lastWordMask = WORD_MASK >>> -toIndex;
        result.words[targetWords - 1] =
            ((toIndex-1) & BIT_INDEX_MASK) < (fromIndex & BIT_INDEX_MASK)
            ? /* straddles source words */
            ((words[sourceIndex] >>> fromIndex) |
             (words[sourceIndex+1] & lastWordMask) << -fromIndex)
            :
            ((words[sourceIndex] & lastWordMask) >>> fromIndex);

        // Set wordsInUse correctly
        result.wordsInUse = targetWords;
        result.recalculateWordsInUse();
        result.checkInvariants();

        return result;
    }

    public int nextSetBit(int fromIndex) {
        if (fromIndex < 0)
            throw new IndexOutOfBoundsException("fromIndex < 0: " + fromIndex);

        checkInvariants();

        int u = wordIndex(fromIndex);
        if (u >= wordsInUse)
            return -1;

        long word = words[u] & (WORD_MASK << fromIndex);

        while (true) {
            if (word != 0)
                return (u * BITS_PER_WORD) + Long.numberOfTrailingZeros(word);
            if (++u == wordsInUse)
                return -1;
            word = words[u];
        }
    }

    public int nextClearBit(int fromIndex) {
        // Neither spec nor implementation handle bitsets of maximal length.
        // See 4816253.
        if (fromIndex < 0)
            throw new IndexOutOfBoundsException("fromIndex < 0: " + fromIndex);

        checkInvariants();

        int u = wordIndex(fromIndex);
        if (u >= wordsInUse)
            return fromIndex;

        long word = ~words[u] & (WORD_MASK << fromIndex);

        while (true) {
            if (word != 0)
                return (u * BITS_PER_WORD) + Long.numberOfTrailingZeros(word);
            if (++u == wordsInUse)
                return wordsInUse * BITS_PER_WORD;
            word = ~words[u];
        }
    }

    public int previousSetBit(int fromIndex) {
        if (fromIndex < 0) {
            if (fromIndex == -1)
                return -1;
            throw new IndexOutOfBoundsException(
                "fromIndex < -1: " + fromIndex);
        }

        checkInvariants();

        int u = wordIndex(fromIndex);
        if (u >= wordsInUse)
            return length() - 1;

        long word = words[u] & (WORD_MASK >>> -(fromIndex+1));

        while (true) {
            if (word != 0)
                return (u+1) * BITS_PER_WORD - 1 - Long.numberOfLeadingZeros(word);
            if (u-- == 0)
                return -1;
            word = words[u];
        }
    }

    public int previousClearBit(int fromIndex) {
        if (fromIndex < 0) {
            if (fromIndex == -1)
                return -1;
            throw new IndexOutOfBoundsException(
                "fromIndex < -1: " + fromIndex);
        }

        checkInvariants();

        int u = wordIndex(fromIndex);
        if (u >= wordsInUse)
            return fromIndex;

        long word = ~words[u] & (WORD_MASK >>> -(fromIndex+1));

        while (true) {
            if (word != 0)
                return (u+1) * BITS_PER_WORD -1 - Long.numberOfLeadingZeros(word);
            if (u-- == 0) 
                return -1;
            word = ~words[u];
        }
    }

    public int length() {
        if (wordsInUse == 0)
            return 0;

        return BITS_PER_WORD * (wordsInUse - 1) +
            (BITS_PER_WORD - Long.numberOfLeadingZeros(words[wordsInUse - 1]));
    }

    public boolean isEmpty() {
        return wordsInUse == 0;
    }

    public boolean intersects(BitSet set) {
        for (int i = Math.min(wordsInUse, set.wordsInUse) - 1; i >= 0; i--)
            if ((words[i] & set.words[i]) != 0)
                return true;
        return false;
    }

    public int cardinality() {
        int sum = 0;
        for (int i = 0; i < wordsInUse; i++)
            sum += Long.bitCount(words[i]);
        return sum;
    }

    public void and(BitSet set) {
        if (this == set)
            return;

        while (wordsInUse > set.wordsInUse)
            words[--wordsInUse] = 0;

        // Perform logical AND on words in common
        for (int i = 0; i < wordsInUse; i++)
            words[i] &= set.words[i];

        recalculateWordsInUse();
        checkInvariants();
    }
	
    public void or(BitSet set) {
        if (this == set)
            return;

        int wordsInCommon = Math.min(wordsInUse, set.wordsInUse);

        if (wordsInUse < set.wordsInUse) {
            ensureCapacity(set.wordsInUse);
            wordsInUse = set.wordsInUse;
        }

        // Perform logical OR on words in common
        for (int i = 0; i < wordsInCommon; i++)
            words[i] |= set.words[i];

        // Copy any remaining words
        if (wordsInCommon < set.wordsInUse)
            System.arraycopy(set.words, wordsInCommon,
                             words, wordsInCommon,
                             wordsInUse - wordsInCommon);

        // recalculateWordsInUse() is unnecessary
        checkInvariants();
    }

    public void xor(BitSet set) {
        int wordsInCommon = Math.min(wordsInUse, set.wordsInUse);

        if (wordsInUse < set.wordsInUse) {
            ensureCapacity(set.wordsInUse);
            wordsInUse = set.wordsInUse;
        }

        // Perform logical XOR on words in common
        for (int i = 0; i < wordsInCommon; i++)
            words[i] ^= set.words[i];

        // Copy any remaining words
        if (wordsInCommon < set.wordsInUse)
            System.arraycopy(set.words, wordsInCommon,
                             words, wordsInCommon,
                             set.wordsInUse - wordsInCommon);

        recalculateWordsInUse();
        checkInvariants();
    }

    public void andNot(BitSet set) {
        // Perform logical (a & !b) on words in common
        for (int i = Math.min(wordsInUse, set.wordsInUse) - 1; i >= 0; i--)
            words[i] &= ~set.words[i];

        recalculateWordsInUse();
        checkInvariants();
    }

    public int hashCode() {
        long h = 1234;
        for (int i = wordsInUse; --i >= 0; )
            h ^= words[i] * (i + 1);

        return (int)((h >> 32) ^ h);
    }

    public int size() {
        return words.length * BITS_PER_WORD;
    }

    public boolean equals(Object obj) {
        if (!(obj instanceof BitSet))
            return false;
        if (this == obj)
            return true;

        BitSet set = (BitSet) obj;

        checkInvariants();
        set.checkInvariants();

        if (wordsInUse != set.wordsInUse)
            return false;

        // Check words in use by both BitSets
        for (int i = 0; i < wordsInUse; i++)
            if (words[i] != set.words[i])
                return false;

        return true;
    }

    public Object clone() {
        if (! sizeIsSticky)
            trimToSize();

        try {
            BitSet result = (BitSet) super.clone();
            result.words = words.clone();
            result.checkInvariants();
            return result;
        } catch (CloneNotSupportedException e) {
            throw new InternalError(e);
        }
    }

    private void trimToSize() {
        if (wordsInUse != words.length) {
            words = Arrays.copyOf(words, wordsInUse);
            checkInvariants();
        }
    }

    private void writeObject(ObjectOutputStream s)
        throws IOException {

        checkInvariants();

        if (! sizeIsSticky)
            trimToSize();

        ObjectOutputStream.PutField fields = s.putFields();
        fields.put("bits", words);
        s.writeFields();
    }

    private void readObject(ObjectInputStream s)
        throws IOException, ClassNotFoundException {

        ObjectInputStream.GetField fields = s.readFields();
        words = (long[]) fields.get("bits", null);

        // Assume maximum length then find real length
        // because recalculateWordsInUse assumes maintenance
        // or reduction in logical size
        wordsInUse = words.length;
        recalculateWordsInUse();
        sizeIsSticky = (words.length > 0 && words[words.length-1] == 0L); // heuristic
        checkInvariants();
    }

    public String toString() {
        checkInvariants();

        int numBits = (wordsInUse > 128) ?
            cardinality() : wordsInUse * BITS_PER_WORD;
        StringBuilder b = new StringBuilder(6*numBits + 2);
        b.append('{');

        int i = nextSetBit(0);
        if (i != -1) {
            b.append(i);
            while (true) {
                if (++i < 0) break;
                if ((i = nextSetBit(i)) < 0) break;
                int endOfRun = nextClearBit(i);
                do { b.append(", ").append(i); }
                while (++i != endOfRun);
            }
        }

        b.append('}');
        return b.toString();
    }

	//待补
    /**
     * Returns a stream of indices for which this {@code BitSet}
     * contains a bit in the set state. The indices are returned
     * in order, from lowest to highest. The size of the stream
     * is the number of bits in the set state, equal to the value
     * returned by the {@link #cardinality()} method.
     *
     * <p>The stream binds to this bit set when the terminal stream operation
     * commences (specifically, the spliterator for the stream is
     * <a href="Spliterator.html#binding"><em>late-binding</em></a>).  If the
     * bit set is modified during that operation then the result is undefined.
     *
     * @return a stream of integers representing set indices
     * @since 1.8
     */
    public IntStream stream() {
        class BitSetSpliterator implements Spliterator.OfInt {
            private int index; // current bit index for a set bit
            private int fence; // -1 until used; then one past last bit index
            private int est;   // size estimate
            private boolean root; // true if root and not split
            // root == true then size estimate is accurate
            // index == -1 or index >= fence if fully traversed
            // Special case when the max bit set is Integer.MAX_VALUE

            BitSetSpliterator(int origin, int fence, int est, boolean root) {
                this.index = origin;
                this.fence = fence;
                this.est = est;
                this.root = root;
            }

            private int getFence() {
                int hi;
                if ((hi = fence) < 0) {
                    // Round up fence to maximum cardinality for allocated words
                    // This is sufficient and cheap for sequential access
                    // When splitting this value is lowered
                    hi = fence = (wordsInUse >= wordIndex(Integer.MAX_VALUE))
                                 ? Integer.MAX_VALUE
                                 : wordsInUse << ADDRESS_BITS_PER_WORD;
                    est = cardinality();
                    index = nextSetBit(0);
                }
                return hi;
            }

            @Override
            public boolean tryAdvance(IntConsumer action) {
                Objects.requireNonNull(action);

                int hi = getFence();
                int i = index;
                if (i < 0 || i >= hi) {
                    // Check if there is a final bit set for Integer.MAX_VALUE
                    if (i == Integer.MAX_VALUE && hi == Integer.MAX_VALUE) {
                        index = -1;
                        action.accept(Integer.MAX_VALUE);
                        return true;
                    }
                    return false;
                }

                index = nextSetBit(i + 1, wordIndex(hi - 1));
                action.accept(i);
                return true;
            }

            @Override
            public void forEachRemaining(IntConsumer action) {
                Objects.requireNonNull(action);

                int hi = getFence();
                int i = index;
                int v = wordIndex(hi - 1);
                index = -1;
                while (i >= 0 && i < hi) {
                    action.accept(i);
                    i = nextSetBit(i + 1, v);
                }
                // Check if there is a final bit set for Integer.MAX_VALUE
                if (i == Integer.MAX_VALUE && hi == Integer.MAX_VALUE) {
                    action.accept(Integer.MAX_VALUE);
                }
            }

            @Override
            public OfInt trySplit() {
                int hi = getFence();
                int lo = index;
                if (lo < 0) {
                    return null;
                }

                // Lower the fence to be the upper bound of last bit set
                // The index is the first bit set, thus this spliterator
                // covers one bit and cannot be split, or two or more
                // bits
                hi = fence = (hi < Integer.MAX_VALUE || !get(Integer.MAX_VALUE))
                        ? previousSetBit(hi - 1) + 1
                        : Integer.MAX_VALUE;

                // Find the mid point
                int mid = (lo + hi) >>> 1;
                if (lo >= mid) {
                    return null;
                }

                // Raise the index of this spliterator to be the next set bit
                // from the mid point
                index = nextSetBit(mid, wordIndex(hi - 1));
                root = false;

                // Don't lower the fence (mid point) of the returned spliterator,
                // traversal or further splitting will do that work
                return new BitSetSpliterator(lo, mid, est >>>= 1, false);
            }

            @Override
            public long estimateSize() {
                getFence(); // force init
                return est;
            }

            @Override
            public int characteristics() {
                // Only sized when root and not split
                return (root ? Spliterator.SIZED : 0) |
                    Spliterator.ORDERED | Spliterator.DISTINCT | Spliterator.SORTED;
            }

            @Override
            public Comparator<? super Integer> getComparator() {
                return null;
            }
        }
        return StreamSupport.intStream(new BitSetSpliterator(0, -1, 0, true), false);
    }

    private int nextSetBit(int fromIndex, int toWordIndex) {
        int u = wordIndex(fromIndex);
        // Check if out of bounds
        if (u > toWordIndex)
            return -1;

        long word = words[u] & (WORD_MASK << fromIndex);

        while (true) {
            if (word != 0)
                return (u * BITS_PER_WORD) + Long.numberOfTrailingZeros(word);
            // Check if out of bounds
            if (++u > toWordIndex)
                return -1;
            word = words[u];
        }
    }

}