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https://github.com/Z3Prover/z3
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adding review notes to code
Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner
commit
9903c722af
7 changed files with 215 additions and 103 deletions
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@ -24,6 +24,12 @@ Notes:
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namespace smt {
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template<typename Ext>
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network_flow<Ext>::network_flow(graph & g, vector<fin_numeral> const& costs) :
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m_graph(g),
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m_costs(costs) {
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}
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template<typename Ext>
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void network_flow<Ext>::initialize() {
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// TODO: construct an initial spanning tree i.e. inializing m_pred, m_depth and m_thread.
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@ -36,54 +42,73 @@ namespace smt {
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SASSERT(!m_potentials.empty());
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SASSERT(!m_thread.empty());
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SASSERT(m_thread.size() == m_pred.size());
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array<rational, m_potentials.size()> potentials;
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std::copy(m_potentials.begin(), m_potentials.end(), potentials);
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rational zero(0);
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potentials[0] = zero;
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node next = m_thread[0];
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while (next != 0) {
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node current = m_pred[next];
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edge e;
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if (m_graph.get_edge(current, next, e)) {
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potentials[next] = potentials[current] - e.get_weight();
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m_potentials.set(0, numeral::zero());
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node target = m_thread[0];
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while (target != 0) {
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node source = m_pred[target];
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edge_id e_id;
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if (m_graph.get_edge_id(source, target, e_id)) {
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m_potentials.set(target, m_potentials[source] - m_graph.get_weight(e_id));
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}
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if (m_graph.get_edge(next, current, e)) {
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potentials[next] = potentials[current] + e.get_weight();
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if (m_graph.get_edge_id(target, source, e_id)) {
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m_potentials.set(target, m_potentials[source] + m_graph.get_weight(e_id));
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}
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next = m_thread[next];
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target = m_thread[target];
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}
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std::copy(potentials.begin(), potentials.end(), m_potentials);
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}
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template<typename Ext>
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void network_flow<Ext>::compute_flows() {
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vector<numeral> balances(m_balances);
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numeral zero;
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m_flows.fill(zero);
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vector<edge> basics(m_basics);
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// TODO: need a way to find a leaf node of a spanning tree
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// OPTIMIZE: Need a set data structure for efficiently removing elements
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vector<edge_id> basics;
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while (!basics.empty()) {
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return;
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// Find a leaf node of a spanning tree
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node target;
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for (unsigned int i = 0; i < m_thread.size(); ++i) {
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if (m_depth[i] <= m_depth[m_thread[i]]) {
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target = i;
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break;
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}
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}
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node source = m_pred[target];
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edge_id e_id;
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if (m_graph.get_edge_id(source, target, e_id)) {
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m_flows.set(e_id, -m_graph.get_weight(basics[target]));
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basics[source] += basics[target];
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basics.erase(e_id);
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}
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else if (m_graph.get_edge_id(target, source, e_id)) {
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m_flows.set(e_id, m_graph.get_weight(basics[target]));
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basics[source] += basics[target];
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basics.erase(e_id);
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}
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}
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}
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template<typename Ext>
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bool network_flow<Ext>::is_optimal(edge & violating_edge) {
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typename vector<edge>::iterator it = m_nonbasics.begin();
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typename vector<edge>::iterator end = m_nonbasics.end();
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bool network_flow<Ext>::is_optimal(edge_id & violating_edge) {
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// TODO: how to get nonbasics vector?
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vector<edge> nonbasics;
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typename vector<edge>::iterator it = nonbasics.begin();
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typename vector<edge>::iterator end = nonbasics.end();
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bool found = false;
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for (unsigned int i = 0; i < m_nonbasics.size(); ++i) {
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edge & e = m_nonbasics[i];
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for (unsigned int i = 0; i < nonbasics.size(); ++i) {
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edge & e = nonbasics[i];
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if (e.is_enabled()) {
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node source = e.get_source();
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node target = e.get_target();
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numeral cost = e.get_weight() - m_potentials[source] + m_potentials[target];
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// Choose the first negative-cost edge to be the violating edge
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// TODO: add multiple pivoting strategies
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if (cost < 0) {
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violating_edge = e;
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numeral zero(0);
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if (cost < zero) {
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edge_id e_id;
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m_graph.get_edge_id(source, target, e_id);
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violating_edge = e_id;
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found = true;
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break;
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}
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@ -93,9 +118,9 @@ namespace smt {
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}
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template<typename Ext>
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dl_edge<typename network_flow<Ext>::GExt> network_flow<Ext>::choose_leaving_edge(const edge & entering_edge) {
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node source = entering_edge.get_source();
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node target = entering_edge.get_target();
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edge_id network_flow<Ext>::choose_leaving_edge(edge_id entering_edge) {
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node source = m_graph.get_source(entering_edge);
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node target = m_graph.get_target(entering_edge);
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while (source != target) {
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if (m_depth[source] > m_depth[target])
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source = m_pred[source];
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@ -106,14 +131,28 @@ namespace smt {
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target = m_pred[target];
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}
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}
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edge e;
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m_graph.get_edge(source, target, e);
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return e;
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edge_id e_id;
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m_graph.get_edge_id(source, target, e_id);
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return e_id;
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}
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template<typename Ext>
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void network_flow<Ext>::update_basics(const edge & entering_edge, const edge & leaving_edge) {
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void network_flow<Ext>::update_spanning_tree(edge_id entering_edge, edge_id leaving_edge) {
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// Need special handling in case two edges are identical
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SASSERT(entering_edge != leaving_edge);
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// Update potentials
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node target = m_upwards[leaving_edge] ? m_graph.get_source(leaving_edge) : m_graph.get_target(leaving_edge);
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numeral src_pot = m_potentials[m_graph.get_source(entering_edge)];
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numeral tgt_pot = m_potentials[m_graph.get_target(entering_edge)];
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numeral weight = m_graph.get_weight(entering_edge);
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numeral change = m_upwards[entering_edge] ? (weight - src_pot + tgt_pot) : (-weight + src_pot - tgt_pot);
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m_potentials[target] += change;
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node start = m_thread[target];
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while (m_depth[start] > m_depth[target]) {
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m_potentials[start] += change;
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start = m_thread[start];
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}
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}
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template<typename Ext>
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@ -124,24 +163,34 @@ namespace smt {
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// Get the optimal solution
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template<typename Ext>
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void network_flow<Ext>::get_optimal_solution(numeral & objective, vector<numeral> & flows) {
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SASSERT(m_is_optimal);
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flows.reset();
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flows.append(m_flows);
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// TODO: calculate objective value
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numeral cost(0);
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for (unsigned int i = 0; i < m_flows.size(); ++i) {
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// FIXME: this * operator is not supported
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cost += m_costs[i] * m_flows[i];
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}
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objective = cost;
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}
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// Minimize cost flows
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// Return true if found an optimal solution, and return false if unbounded
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template<typename Ext>
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bool network_flow<Ext>::min_cost() {
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SASSERT(!m_graph.get_all_edges().empty());
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initialize();
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edge & entering_edge;
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edge_id entering_edge;
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while (!is_optimal(entering_edge)) {
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edge & leaving_edge = choose_leaving_edge();
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update_tree(entering_edge, leaving_edge);
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if (is_unbounded())
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return false;
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edge_id leaving_edge = choose_leaving_edge(entering_edge);
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update_spanning_tree(entering_edge, leaving_edge);
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if (is_unbounded()) {
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m_is_optimal = false;
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return m_is_optimal;
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}
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}
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return true;
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m_is_optimal = true;
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return m_is_optimal;
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}
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}
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