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/*++
Copyright (c) 2025 Microsoft Corporation
Module Name:
search_tree.h
Abstract:
A binary search tree for managing the search space of a DPLL(T) solver.
It supports splitting on atoms, backtracking on conflicts, and activating nodes.
Nodes can be in one of three states: open, closed, or active.
- Closed nodes are fully explored (both children are closed).
- Active nodes have no children and are currently being explored.
- Open nodes either have children that are open or are leaves.
A node can be split if it is active. After splitting, it becomes open and has two open children.
Backtracking on a conflict closes all nodes below the last node whose atom is in the conflict set.
Activation searches an open node closest to a seed node.
Author:
Ilana Shapiro 2025-9-06
--*/
#include "util/util.h"
#include "util/vector.h"
#pragma once
namespace search_tree {
enum class status { open, closed, active };
template<typename Config>
class node {
typedef typename Config::literal literal;
literal m_literal;
node* m_left = nullptr, * m_right = nullptr, * m_parent = nullptr;
status m_status;
public:
node(literal const& l, node* parent) :
m_literal(l), m_parent(parent), m_status(status::open) {}
~node() {
dealloc(m_left);
dealloc(m_right);
}
status get_status() const { return m_status; }
void set_status(status s) { m_status = s; }
literal const& get_literal() const { return m_literal; }
bool literal_is_null() const { return Config::is_null(m_literal); }
void split(literal const& a, literal const& b) {
SASSERT(!Config::literal_is_null(a));
SASSERT(!Config::literal_is_null(b));
if (m_status != status::active)
return;
SASSERT(!m_left);
SASSERT(!m_right);
m_left = alloc(node<Config>, a, this);
m_right = alloc(node<Config>, b, this);
m_status = status::open;
}
node* left() const { return m_left; }
node* right() const { return m_right; }
node* parent() const { return m_parent; }
node* find_active_node() {
if (m_status == status::active)
return this;
if (m_status != status::open)
return nullptr;
node* nodes[2] = { m_left, m_right };
for (unsigned i = 0; i < 2; ++i) {
auto res = nodes[i] ? nodes[i]->find_active_node() : nullptr;
if (res)
return res;
}
if (m_left->get_status() == status::closed && m_right->get_status() == status::closed)
m_status = status::closed;
return nullptr;
}
void display(std::ostream& out, unsigned indent) const {
for (unsigned i = 0; i < indent; ++i)
out << " ";
Config::display_literal(out, m_literal);
out << (get_status() == status::open ? " (o)" : get_status() == status::closed ? " (c)" : " (a)");
out << "\n";
if (m_left)
m_left->display(out, indent + 2);
if (m_right)
m_right->display(out, indent + 2);
}
};
template<typename Config>
class tree {
typedef typename Config::literal literal;
scoped_ptr<node<Config>> m_root = nullptr;
literal m_null_literal;
random_gen m_rand;
// return an active node in the subtree rooted at n, or nullptr if there is none
// close nodes that are fully explored (whose children are all closed)
node<Config>* activate_from_root(node<Config>* n) {
if (!n)
return nullptr;
if (n->get_status() != status::open)
return nullptr;
auto left = n->left();
auto right = n->right();
if (!left && !right) {
n->set_status(status::active);
return n;
}
node<Config>* nodes[2] = { left, right };
unsigned index = m_rand(2);
auto child = activate_from_root(nodes[index]);
if (child)
return child;
child = activate_from_root(nodes[1 - index]);
if (child)
return child;
if (left && right && left->get_status() == status::closed && right->get_status() == status::closed)
n->set_status(status::closed);
return nullptr;
}
void close_node(node<Config>* n) {
if (!n)
return;
if (n->get_status() == status::closed)
return;
n->set_status(status::closed);
close_node(n->left());
close_node(n->right());
while (n) {
auto p = n->parent();
if (!p)
return;
if (p->get_status() != status::open)
return;
if (p->left()->get_status() != status::closed)
return;
if (p->right()->get_status() != status::closed)
return;
p->set_status(status::closed);
n = p;
}
}
public:
tree(literal const& null_literal) : m_null_literal(null_literal) {
reset();
}
void set_seed(unsigned seed) {
m_rand.set_seed(seed);
}
void reset() {
m_root = alloc(node<Config>, m_null_literal, nullptr);
m_root->set_status(status::active);
}
// Split current node if it is active.
// After the call, n is open and has two children.
void split(node<Config>* n, literal const& a, literal const& b) {
n->split(a, b);
}
// conflict is given by a set of literals.
// they are a subset of literals on the path from root to n
void backtrack(node<Config>* n, vector<literal> const& conflict) {
if (conflict.empty()) {
close_node(m_root.get());
m_root->set_status(status::closed);
return;
}
SASSERT(n != m_root.get());
// all literals in conflict are on the path from root to n
// remove assumptions from conflict to ensure this.
DEBUG_CODE(
auto on_path = [&](literal const& a) {
node<Config>* p = n;
while (p) {
if (p->get_literal() == a)
return true;
p = p->parent();
}
return false;
};
SASSERT(all_of(conflict, [&](auto const& a) { return on_path(a); }));
);
while (n) {
if (any_of(conflict, [&](auto const& a) { return a == n->get_literal(); })) {
close_node(n);
return;
}
n = n->parent();
}
UNREACHABLE();
}
// return an active node in the tree, or nullptr if there is none
// first check if there is a node to activate under n,
// if not, go up the tree and try to activate a sibling subtree
node<Config>* activate_node(node<Config>* n) {
if (!n) {
if (m_root->get_status() == status::active)
return m_root.get();
n = m_root.get();
}
auto res = activate_from_root(n);
if (res)
return res;
auto p = n->parent();
while (p) {
if (p->left() && p->left()->get_status() == status::closed &&
p->right() && p->right()->get_status() == status::closed) {
p->set_status(status::closed);
n = p;
p = n->parent();
continue;
}
if (n == p->left()) {
res = activate_from_root(p->right());
if (res)
return res;
}
else {
VERIFY(n == p->right());
res = activate_from_root(p->left());
if (res)
return res;
}
n = p;
p = n->parent();
}
return nullptr;
}
node<Config>* find_active_node() {
return m_root->find_active_node();
}
bool is_closed() const {
return m_root->get_status() == status::closed;
}
std::ostream& display(std::ostream& out) const {
m_root->display(out, 0);
return out;
}
};
}