printing all binary trees from inorder traversal

Question

Came across this question in an interview. Given inorder traversal of a binary tree. Print all the possible binary trees from it.

Initial thought:

If say we

Answer 1

I'd write one function for constructing the trees and another for printing them.

The construction of the trees goes like this:

#include 
#include 
#include 

struct Tree {
    int value;
    Tree* left;
    Tree* right;

    Tree(int value, Tree* left, Tree* right) :
        value(value), left(left), right(right) {}
};

typedef std::vector Seq;

Seq all_trees(const std::vector& xs, int from, int to)
{
    Seq result;
    if (from >= to) result.push_back(0);
    else {
        for (int i = from; i < to; i++) {
            const Seq left = all_trees(xs, from, i);
            const Seq right = all_trees(xs, i + 1, to);
            BOOST_FOREACH(Tree* tl, left) {
                BOOST_FOREACH(Tree* tr, right) {
                    result.push_back(new Tree(xs[i], tl,  tr));
                }
            }
        }
    }
    return result;
}

Seq all_trees(const std::vector& xs)
{
    return all_trees(xs, 0, (int)xs.size());
}

Observe that for root value there are multiple trees that be constructed from the values to the left and the right of the root value. All combinations of these left and right trees are included.

Writing the pretty-printer is left as an exercise (a boring one), but we can test that the function indeed constructs the expected number of trees:

int main()
{
    const std::vector xs(3, 0); // 3 values gives 5 trees.
    const Seq result = all_trees(xs);
    std::cout << "Number of trees: " << result.size() << "\n";
}