Pasted

package ch.claude_martin;
 
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Set;
import java.util.TreeSet;
 
class SomeClass {
 
    static boolean test(int a, int b) {
        return a + 2 == b;
    }
 
    public static void main(final String... args) {
        // Take the data from the arguments or use the example list:
        final var data = args.length > 0 ? Arrays.stream(args).mapToInt(Integer::parseInt).sorted().toArray()
                : new int[] { 1, 2, 5, 7, 8, 9, 11, 12, 14 };
        System.out.println(Arrays.toString(data));// [5, 7, 9, 11, 12, 14]
        final var size = data.length;
        // three pointers are needed for this. Initially we look at the first two
        // elements of the data.
        // When third is used below to find longer progressions and add each sublist to
        // the result set.
        var p0 = 0;
        var p1 = 1;
        // The result set is a collection of sets. Each of those sets is a progression.
        var resultSet = new ArrayList<Set<Integer>>();
        // This loops through all possible pairs, but p1 is always < p1:
        while (p0 < size && p1 < size) {
            // The set contains at least 2 elements if it is part of the result set:
            var set = new TreeSet<Integer>();
            var a = data[p0];
            var b = data[p1];
            if (test(a, b)) {
                set.add(a);
                set.add(b);
                resultSet.add(new TreeSet<>(set));
                // Now we look for longer progressions that start with the one we just found:
                for (var p2 = p1 + 1; p2 < size; p2++) {
                    var c = data[p2];
                    if (test(b, c)) {
                        set.add(b = c);
                        resultSet.add(new TreeSet<>(set));
                    }
                }
            }
            p1++; // increment pointer for "b":
            // But it we go out of bounds we instead increment p0:
            if (p1 == size) { 
                // And p1 points to the one next to the new p0:
                p1 = ++p0 + 1;
            }
        }
        // Show the result set:
        System.out.println(resultSet);
    }
}