Question

I have a string like “0189”, for which I need to generate all subsequences, but the ordering of the individual characters must be kept, i.e, here 9 should not come before 0, 1 or 8. Ex: 0, 018, 01, 09, 0189, 18, 19, 019, etc.

Another example is “10292” for which subsequences would be: 1, 10, 02, 02, 09, 29, 92, etc. As you might have noticed ’02’ two times, since ‘2’ comes twice in the given string. But again things like: 21, 01, 91 are invalid as order is to be maintained.

Any algorithm or psuedo code, which could be implemented in C/C++ would be appreciated!

Answer 1

I’d recommend using the natural correspondence between the power set of a sequence and the set of binary numbers from 0 to 2^n - 1, where n is the length of the sequence.

In your case, n is 4, so consider 0 = 0000 .. 15 = 1111; where there is a 1 in the binary expression include the corresponding item from the sequence. To implement this you’ll need bitshift and binary operations:

for (int i = 0; i < (1 << n); ++i) {
    std::string item;
    for (j = 0; j < n; ++j) {
        if (i & (1 << j)) {
            item += sequence[j];
        }
    }
    result.push_back(item);
}

Also consider how you’d handle sequences longer than can be covered by an int (hint: consider overflow and arithmetic carry).