Question

Thanks @Scotty, @paddy. FYI, the optimal solution is this:

void RecSubsets(string soFar, string rest) {
    if (rest == "") {
        cout << soFar << end;
    }
    else {
      RecSubsets(soFar + rest[0], rest.substr(1));
      RecSubsets(soFar, rest.substr(1));
    }
 }

void CanMakeSum(string set) {
    RecSubsets("", set);
 }

---

I’m writing a simple program to calculate all possible combinations in a set by splitting the data into 2 sets (C(n-1, k-1) & C(n-1, k)) and calling the function recursively.
Below is what I’ve written:

void RecSubsets(string soFar, string rest) {
    if (rest == "") cout << soFar << end;
    }
    else {
        for (int i = 0; i < rest.length(); i++) {
            string next = soFar + rest[i];
            string remaining = rest.substr(i+1);
            RecSubsets(next, remaining);
        }
    }
}

void CanMakeSum(string set) {
    RecSubsets("", set);
    RecSubsets("", set.substr(1));
}

int main() {    
    string set = "abcd";
    CanMakeSum(set);
    return 0;
}

So for an input string of ‘abcd’, it’d split into 2 groups (abcd and abc) and then print out the combinations by calling the function recursively. Under this logic, the output ought to be: abcd, abc, abd, ab, acd, ac, ad, a…
However, using the program above, the output is abcd, abd, acd, ad…
I understand conceptually what I’m trying to achieve, but am having difficulty translating it into codes. Can someone pls point out where I’m going wrong? Thanks

Answer 1

It’s a good attempt. There are just two small problems:

1. You should not be “splitting the data into two sets (C(n-1, k-1) & C(n-1, k))”. That’s what your recursive function is for!

2. RecSubsets() should always print out soFar. Remove the if (rest == "").

For example:

void RecSubsets(string soFar, string rest) {
    // First print out "a" or wherever we are up to
    // This ensures we correctly get "ab" and "ac" without trailing characters etc
    cout << soFar << end;

    // Now print out the other combinations that begin with soFar
    // This part of your algorithm was already correct :)
    for (int i = 0; i < rest.length(); i++) {
        string next = soFar + rest[i];
        string remaining = rest.substr(i+1);
        RecSubsets(next, remaining);
    }
}

void CanMakeSum(string set)
{
    RecSubsets("", set);
    // Don't call it a second time here
}