Sequence membership

Given two sorted sequences, this method returns the intersection, a-b, and b-a, using a single iteration over both sequences. The return type is an IEnumerable<KeyValuePair<T, int>>, where:

• only in A = -1


• in both = 0


• only in B = 1

/// <summary>
/// Return an int for every element in sortedSetA and sortedSetB specifying objects
/// that belong to A but not to B (-1), objects which are both in A and in B (0), and objects
/// that belong to B but not A (1).
/// </summary>
/// <remarks>This method is an O(n+m) operation when the two sets have different members, where n 
/// is the count of <paramref name="sortedSetA"/> and m is the count of <paramref name="sortedSetB"/>.
/// Otherwise the operation approaches O(n+m-n) where m is the count of the larger set and n is the
/// smaller set.
/// </remarks>
/// <typeparam name="T">Type of element in each set</typeparam>
/// <param name="setA">A set where each element is of type <typeparamref name="T"/></param>
/// <param name="setB">A set where each element is of type <typeparamref name="T"/></param>
/// <returns>Returns A \ B (-1), the intersection of A and B (0), and B \ A (1)</returns>
public static IEnumerable<KeyValuePair<T, int>> Membership<T> (IEnumerable<T> sortedSetA, IEnumerable<T> sortedSetB) {
    return Membership<T> (sortedSetA, sortedSetB, Comparer<T>.Default);
}
/// <summary>
/// Return a KeyValuePair<int, T> for every element in sortedSetA and sortedSetB where the int
/// specifies membership and T is the element. The int specifies objects that belong to A but
/// not to B (-1), objects which are both in A and in B (0), and objects that belong to B but
/// not A (1).
/// </summary>
/// <remarks>This method is an O(n+m) operation when the two sets have different members, where n 
/// is the count of <paramref name="sortedSetA"/> and m is the count of <paramref name="sortedSetB"/>.
/// Otherwise the operation approaches O(n+m-n) where m is the count of the larger set and n is the
/// smaller set.
/// </remarks>
/// <typeparam name="T">Type of element in each set</typeparam>
/// <param name="setA">A set where each element is of type <typeparamref name="T"/></param>
/// <param name="setB">A set where each element is of type <typeparamref name="T"/></param>
/// <param name="comparer"><see cref="IComparer"/> used to sort the sets</param>
/// <returns>Returns A \ B (-1), the intersection of A and B (0), and B \ A (1)</returns>
public static IEnumerable<KeyValuePair<T, int>> Membership<T> (IEnumerable<T> sortedSetA, IEnumerable<T> sortedSetB, IComparer<T> comparer) {
    const int onlyA = -1;
    const int both = 0;
    const int onlyB = 1;

    if (sortedSetA == null)
        throw new ArgumentNullException ("sortedSetA");
    if (sortedSetB == null)
        throw new ArgumentNullException ("sortedSetB");
    if (comparer == null)
        throw new ArgumentNullException ("comparer");

    IEnumerator<T> enumeratorA = sortedSetA.GetEnumerator ();
    IEnumerator<T> enumeratorB = sortedSetB.GetEnumerator ();

    bool nextA = enumeratorA.MoveNext ();
    bool nextB = enumeratorB.MoveNext ();

    // default value for type T
    T a = default (T);
    // default value for type T
    T b = default (T);

    // if both collections have a value
    if (nextA & nextB) {
        // get current value
        a = enumeratorA.Current;
        // get current value
        b = enumeratorB.Current;

        do {
            // Compare a to b: is a < b, a == b, or a > b ?
            int val = comparer.Compare (a, b);
            // a == b
            if (val == 0) {
                // return both collections have the value a
                yield return new KeyValuePair<T, int> (a, both);
                // if collection a can move next
                if (nextA = enumeratorA.MoveNext ())
                    // get the next a
                    a = enumeratorA.Current;
                // if collection b can move next
                if (nextB = enumeratorB.MoveNext ())
                    // get the next b
                    b = enumeratorB.Current;
            }
            // a < b
            else if (val < 0) {
                // return only collection a has the value a
                yield return new KeyValuePair<T, int> (a, onlyA);
                // if collection a can move next
                if (nextA = enumeratorA.MoveNext ())
                    // get the next a
                    a = enumeratorA.Current;
            }
            // a > b
            else {
                // return only collection b has the value b
                yield return new KeyValuePair<T, int> (b, onlyB);
                // if collection b can move next
                if (nextB = enumeratorB.MoveNext ())
                    // get the next b
                    b = enumeratorB.Current;
            }
            // loop while there are values for both collections
        } while (nextA & nextB);
    }
    // if collection a has more values
    if (nextA) {
        // return only collection a has the value a
        yield return new KeyValuePair<T, int> (a, onlyA);
        // if collection a can move next
        while (enumeratorA.MoveNext ()) {
            // return only collection a has the value a
            yield return new KeyValuePair<T, int> (enumeratorA.Current, onlyA);
        }
    }
    // if collection b has more values
    else if (nextB) {
        // return only collection b has the value b
        yield return new KeyValuePair<T, int> (b, onlyB);
        // if collection b can move next
        while (enumeratorB.MoveNext ()) {
            // return only collection b has the value b
            yield return new KeyValuePair<T, int> (enumeratorB.Current, onlyB);
        }
    }
}

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