#include <vector>
#include <iostream>

struct node {
    node * root = nullptr;
    node * left = nullptr;
    node * right = nullptr;
    double data = 0;

    node( double d, node * r = nullptr )
    : root(r)
    , data(d)
    {}
};

node * prefix_to_tree( const std::vector<double>& v ){
    
    if ( !v.size() ){
        return nullptr;
    }

    node * root = new node(v[0]);
    node * current = root;
    node * max_node = nullptr;

    for ( int i = 1; i < v.size(); ) {
        if ( v[i] < current->data ){
            max_node = current;
            current = new node(v[i++],current);
            current->root->left = current;
        } else if ( !max_node
                    || v[i] < max_node->data ){
            current = new node(v[i++],current);
            current->root->right = current;
        } else if ( current->root ){
            current = current->root;
            while ( max_node  
                    && max_node->data <= current->data ) {
                node * tmp = max_node;
                max_node = max_node->root;
                if ( max_node && tmp == max_node->left ){
                    break;                    
                }
            }
        } else {
            std::cout << "error" << std::endl;
            break;
        }

        if ( !current || !root ) {
            std::cout << "errrrrrror" << std::endl;
        }
    }

    std::cout << root << std::endl;
    return root;
}

void print( node * root, const std::string& level = "" ){
    if ( root ) {
        print( root->left, level + "   ");
        std::cout << level << "- " << root->data << std::endl;
        print( root->right, level + "   ");
    }
}

void traverse( node * root, std::vector<double>& v ){
    if ( root ) {
        v.push_back(root->data);
        traverse(root->left, v);
        traverse(root->right, v);
    }
}

void test( const std::vector<double>& v ){
    auto r = prefix_to_tree( v );
    //print( r );
    std::vector<double> w;
    traverse( r, w );
    if ( v.size() != w.size() ) {
        std::cout << "v.size() != w.size() => " << v.size() << " != " << w.size() << std::endl;
    }
    for (int i = 0; i < v.size(); ++i ){
        if (v[i]!=w[i]){
            std::cout << "error at index " << i << " -> "<< v[i] << " != " << w[i] << std::endl;
        }
    }
}

int main( void ) {

    test( {1} );
    test( {2, 1, 3} );
    test( {4, 2, 1, 3, 6, 5, 7} );
    test( {8, 4, 2, 1, 3, 6, 5, 7, 12, 10, 9, 11, 14, 13, 15} );
    test( {8, 4, 2,    3, 6, 5, 7, 12, 10, 9, 11, 14, 13, 15} );
    test( {8, 4,          6, 5, 7, 12, 10, 9,     14, 13, 15} );
    test( {8,                      12, 10, 9, 11, 14, 13,   } );
    test( {8, 4, 2, 1,    6,       12, 10,    11, 14,     15} );

    return 0;
}