从给定的数字对中查找未配对的数字

Question

是否有任何算法可从给定的成对数字列表中查找未成对数字。例如，在{（1,2），（2,3），（3,4）}中，成对（1,3）和（2,4 ）从未配对过。

Answer 1

You could do this as follows:

1. Iterate over all the pairs and build up a set of all the numbers that appear in the set.
2. Construct all possible pairs of numbers, storing the result in a different set.
3. Iterate over all the pairs from the original list, and remove each one that you find from the set of all pairs.
4. You are now left with all pairs that did not appear in the original set.

Of course, this assumes that you only care about pairs of values from the original set. For example, the pair (1, 5) wasn't in your example either. Neither was (cat, dog).

This runs in time O(n ² ), where n is the number of numbers represented in the original set of pairs.

Hope this helps!

Answer 2

Using LINQ and a symmetry trick taking advantage of the fact that (1,3) and (3,1) are identical, so ignoring cases where the second number is bigger than the first:

public static IEnumerable<Tuple<int, int>> GetUnpairedNumbers(IEnumerable<Tuple<int, int>> existingPairs ) {
    var uniqueNumbers = existingPairs.SelectMany(p => new[] {p.Item1, p.Item2}).Distinct().ToList();
    var isUsed = uniqueNumbers.ToDictionary(n => n, n => uniqueNumbers.Where(inner => n < inner).ToDictionary(inner => inner, inner => false));

    foreach(var currentPair in existingPairs) {
        isUsed[currentPair.Item1][currentPair.Item2] = true;
    }

    return isUsed.Keys.SelectMany(n => isUsed[n].Where(kvp => !kvp.Value).Select(kvp => Tuple.Create(n, kvp.Key)));
}
public static void Main(string[] args) {
    var unpairedNumbers = GetUnpairedNumbers(new[] { P(1, 2), P(2, 3), P(3, 4) });
}

private static Tuple<int, int> P(int a, int b) {
    return Tuple.Create(a, b);
}