449 lines
15 KiB
C++
449 lines
15 KiB
C++
/*
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Copyright (c) 2013 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Author: Leonardo de Moura
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*/
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#pragma once
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#include <iostream>
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#include <algorithm>
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#include <utility>
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#include "util/rc.h"
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#include "util/pair.h"
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#include "util/debug.h"
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#include "util/buffer.h"
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#include "util/thread.h"
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namespace lean {
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/**
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\brief Splay trees (see http://en.wikipedia.org/wiki/Splay_tree)
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It uses a O(1) copy operation. Different tree can share nodes.
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The sharing is thread-safe.
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\c CMP is a functional object for comparing values of type T.
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It must have a method
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<code>
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int operator()(T const & v1, T const & v2) const;
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</code>
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The method must return
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- -1 if <tt>v1 < v2</tt>,
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- 0 if <tt>v1 == v2</tt>,
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- 1 if <tt>v1 > v2</tt>
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*/
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template<typename T, typename CMP>
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class splay_tree : public CMP {
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struct node {
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node * m_left;
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node * m_right;
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T m_value;
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MK_LEAN_RC();
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static void inc_ref(node * n) { if (n) n->inc_ref(); }
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static void dec_ref(node * n) { if (n) n->dec_ref(); }
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explicit node(T const & v, node * left = nullptr, node * right = nullptr):
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m_left(left), m_right(right), m_value(v), m_rc(0) {
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// the return type of CMP()(t1, 2) should be int
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static_assert(std::is_same<typename std::result_of<decltype(std::declval<CMP>())(T const &, T const &)>::type,
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int>::value,
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"The return type of CMP()(t1, t2) is not int.");
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inc_ref(m_left);
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inc_ref(m_right);
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}
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node(node const & n):node(n.m_value, n.m_left, n.m_right) {}
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~node() {
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dec_ref(m_left);
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dec_ref(m_right);
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}
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void dealloc() {
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delete this;
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}
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bool is_shared() const { return m_rc > 1; }
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static void display(std::ostream & out, node const * n) {
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if (n) {
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if (n->m_left == nullptr && n->m_right == nullptr) {
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out << n->m_value << ":" << n->m_rc;
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} else {
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out << "(" << n->m_value << ":" << n->m_rc << " ";
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display(out, n->m_left);
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out << " ";
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display(out, n->m_right);
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out << ")";
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}
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} else {
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out << "()";
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}
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}
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};
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node * m_ptr;
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int cmp(T const & v1, T const & v2) const {
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return CMP::operator()(v1, v2);
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}
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void update(node * n, node * l, node * r) {
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lean_assert(!n->is_shared());
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n->m_left = l;
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n->m_right = r;
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}
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struct entry {
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bool m_right;
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node * m_node;
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entry(bool r, node * n):m_right(r), m_node(n) {}
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};
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void splay_to_top(buffer<entry, 32> & path, node * n) {
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lean_assert(!n->is_shared());
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while (path.size() > 1) {
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auto p_entry = path.back(); path.pop_back();
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auto g_entry = path.back(); path.pop_back();
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bool g_right = g_entry.m_right;
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bool p_right = p_entry.m_right;
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node * g = g_entry.m_node;
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node * p = p_entry.m_node;
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lean_assert(!g->is_shared());
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lean_assert(!p->is_shared());
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if (!g_right && !p_right) {
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// zig-zig left
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// (g (p (n A B) C) D) ==> (n A (p B (g C D)))
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lean_assert(g->m_left == p);
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node * A = n->m_left;
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node * B = n->m_right;
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node * C = p->m_right;
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node * D = g->m_right;
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update(g, C, D);
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update(p, B, g);
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update(n, A, p);
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} else if (!g_right && p_right) {
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// zig-zag left-right
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// (g (p A (n B C)) D) ==> (n (p A B) (g C D))
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lean_assert(g->m_left == p);
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node * A = p->m_left;
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node * B = n->m_left;
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node * C = n->m_right;
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node * D = g->m_right;
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update(p, A, B);
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update(g, C, D);
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update(n, p, g);
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} else if (g_right && !p_right) {
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// zig-zag right-left
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// (g A (p (n B C) D)) ==> (n (g A B) (p C D))
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lean_assert(g->m_right == p);
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node * A = g->m_left;
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node * B = n->m_left;
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node * C = n->m_right;
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node * D = p->m_right;
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update(g, A, B);
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update(p, C, D);
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update(n, g, p);
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} else {
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lean_assert(g_right && p_right);
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lean_assert(g->m_right == p);
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// zig-zig right
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// (g A (p B (n C D))) ==> (n (p (g A B) C) D)
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node * A = g->m_left;
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node * B = p->m_left;
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node * C = n->m_left;
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node * D = n->m_right;
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update(g, A, B);
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update(p, g, C);
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update(n, p, D);
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}
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}
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lean_assert(!n->is_shared());
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if (path.size() == 1) {
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auto p_entry = path.back(); path.pop_back();
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bool p_right = p_entry.m_right;
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node * p = p_entry.m_node;
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if (!p_right) {
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// zig left
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// (p (n A B) C) ==> (n A (p B C))
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node * A = n->m_left;
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node * B = n->m_right;
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node * C = p->m_right;
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update(p, B, C);
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update(n, A, p);
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} else {
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// zig right
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// (p A (n B C)) ==> (n (p A B) C)
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node * A = p->m_left;
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node * B = n->m_left;
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node * C = n->m_right;
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update(p, A, B);
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update(n, p, C);
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}
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}
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lean_assert(path.empty());
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lean_assert(!n->is_shared());
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}
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bool check_invariant(node const * n) const {
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if (n) {
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if (n->m_left) {
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check_invariant(n->m_left);
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lean_assert_lt(cmp(n->m_left->m_value, n->m_value), 0);
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}
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if (n->m_right) {
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check_invariant(n->m_right);
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lean_assert_lt(cmp(n->m_value, n->m_right->m_value), 0);
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}
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}
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return true;
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}
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void update_parent(buffer<entry, 32> const & path, node * child) {
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lean_assert(child);
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if (path.empty()) {
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child->inc_ref();
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node::dec_ref(m_ptr);
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m_ptr = child;
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} else {
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child->inc_ref();
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entry const & last = path.back();
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node * parent = last.m_node;
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lean_assert(!parent->is_shared());
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if (last.m_right) {
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node::dec_ref(parent->m_right);
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parent->m_right = child;
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} else {
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node::dec_ref(parent->m_left);
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parent->m_left = child;
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}
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}
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}
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static void to_buffer(node const * n, buffer<T> & r) {
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if (n) {
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to_buffer(n->m_left, r);
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r.push_back(n->m_value);
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to_buffer(n->m_right, r);
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}
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}
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bool insert_pull(T const & v, bool is_insert) {
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buffer<entry, 32> path;
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node * n = m_ptr;
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bool found = false;
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while (true) {
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if (n == nullptr) {
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if (is_insert) {
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n = new node(v);
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update_parent(path, n);
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} else {
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if (path.empty())
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return false;
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n = path.back().m_node;
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path.pop_back();
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}
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break;
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} else {
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if (n->is_shared()) {
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n = new node(*n);
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update_parent(path, n);
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}
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lean_assert(!n->is_shared());
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int c = cmp(v, n->m_value);
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if (c < 0) {
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path.emplace_back(false, n);
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n = n->m_left;
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} else if (c > 0) {
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path.emplace_back(true, n);
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n = n->m_right;
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} else {
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if (is_insert)
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n->m_value = v;
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found = true;
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break;
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}
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}
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}
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splay_to_top(path, n);
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m_ptr = n;
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lean_assert(check_invariant());
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return found;
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}
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bool pull(T const & v) {
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return insert_pull(v, false);
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}
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void pull_max() {
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if (!m_ptr) return;
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buffer<entry, 32> path;
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node * n = m_ptr;
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while (true) {
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lean_assert(n);
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if (n->is_shared()) {
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n = new node(*n);
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update_parent(path, n);
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}
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if (n->m_right) {
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path.emplace_back(true, n);
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n = n->m_right;
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} else {
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splay_to_top(path, n);
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m_ptr = n;
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lean_assert(check_invariant());
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return;
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}
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}
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}
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template<typename F, typename R>
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static R fold(node const * n, F && f, R r) {
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static_assert(std::is_same<typename std::result_of<F(T const &, R)>::type, R>::value,
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"fold: return type of f(t : T, r : R) is not R");
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if (n) {
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r = fold(n->m_left, f, r);
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r = f(n->m_value, r);
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return fold(n->m_right, f, r);
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} else {
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return r;
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}
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}
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template<typename F>
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static void for_each(node const * n, F && f) {
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static_assert(std::is_same<typename std::result_of<F(T const &)>::type, void>::value,
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"for_each: return type of f is not void");
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if (n) {
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for_each(n->m_left, f);
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f(n->m_value);
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for_each(n->m_right, f);
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}
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}
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splay_tree(splay_tree const & s, node * new_root):CMP(s), m_ptr(new_root) { node::inc_ref(m_ptr); }
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public:
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splay_tree(CMP const & cmp = CMP()):CMP(cmp), m_ptr(nullptr) {}
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splay_tree(splay_tree const & s):CMP(s), m_ptr(s.m_ptr) { node::inc_ref(m_ptr); }
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splay_tree(splay_tree && s):CMP(s), m_ptr(s.m_ptr) { s.m_ptr = nullptr; }
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~splay_tree() { node::dec_ref(m_ptr); }
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/** \brief O(1) copy */
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splay_tree & operator=(splay_tree const & s) { LEAN_COPY_REF(s); }
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/** \brief O(1) move */
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splay_tree & operator=(splay_tree && s) { LEAN_MOVE_REF(s); }
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friend void swap(splay_tree & t1, splay_tree & t2) { std::swap(t1.m_ptr, t2.m_ptr); }
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/** \brief Return true iff this splay tree is empty. */
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bool empty() const { return m_ptr == nullptr; }
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/** \brief Remove all elements from the splay tree. */
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void clear() { node::dec_ref(m_ptr); m_ptr = nullptr; }
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/** \brief Return true iff this splay tree and \c t point to the same node */
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bool is_eqp(splay_tree const & t) const { return m_ptr == t.m_ptr; }
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/** \brief Return the size of the splay tree */
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unsigned size() const { return fold([](T const &, unsigned a) { return a + 1; }, 0u); }
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/** \brief Insert \c v in this splay tree. */
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void insert(T const & v) {
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insert_pull(v, true);
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}
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/**
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\brief Return a pointer to a value equal to \c v that is stored in this splay tree.
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If the splay tree does not contain any value equal to \c v, then return \c nullptr.
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\remark <tt>find(v) != nullptr</tt> iff <tt>contains(v)</tt>
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\warning The content of the tree is not modified, but it is "reorganized".
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*/
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T const * find(T const & v) const {
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if (const_cast<splay_tree*>(this)->pull(v)) {
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lean_assert(cmp(m_ptr->m_value, v) == 0);
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return &(m_ptr->m_value);
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} else {
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return nullptr;
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}
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}
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/** \brief Return true iff the splay tree contains an element equal to \c v. */
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bool contains(T const & v) const {
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return find(v);
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}
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/** \brief Remove \c v from this splay tree. Actually, it removes an element that is equal to \c v. */
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void erase(T const & v) {
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if (pull(v)) {
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lean_assert(cmp(m_ptr->m_value, v) == 0);
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splay_tree left(*this, m_ptr->m_left);
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splay_tree right(*this, m_ptr->m_right);
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if (left.empty()) {
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swap(*this, right);
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} else if (right.empty()) {
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swap(*this, left);
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} else {
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clear();
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left.pull_max();
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lean_assert(left.m_ptr->m_right == nullptr);
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right.m_ptr->inc_ref();
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left.m_ptr->m_right = right.m_ptr;
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swap(*this, left);
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}
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}
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}
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/** \brief (For debugging) Check whether this splay tree is well formed. */
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bool check_invariant() const {
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return check_invariant(m_ptr);
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}
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/**
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\brief Copy the contents of this splay tree to the given buffer.
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The elements will be stored in increasing order.
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*/
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void to_buffer(buffer<T> & r) const {
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to_buffer(m_ptr, r);
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}
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/** \brief (For debugging) Display the content of this splay tree. */
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friend std::ostream & operator<<(std::ostream & out, splay_tree const & t) {
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node::display(out, t.m_ptr);
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return out;
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}
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/**
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\brief Return <tt>f(a_k, ..., f(a_1, f(a_0, r)) ...)</tt>, where
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<tt>a_0, a_1, ... a_k</tt> are the elements is stored in the splay tree.
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*/
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template<typename F, typename R>
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R fold(F && f, R r) const {
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static_assert(std::is_same<typename std::result_of<F(T const &, R)>::type, R>::value,
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"fold: return type of f(t : T, r : R) is not R");
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return fold(m_ptr, std::forward<F>(f), r);
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}
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/**
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\brief Apply \c f to each value stored in the splay tree.
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*/
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template<typename F>
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void for_each(F && f) const {
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static_assert(std::is_same<typename std::result_of<F(T const &)>::type, void>::value,
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"for_each: return type of f is not void");
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for_each(m_ptr, std::forward<F>(f));
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}
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};
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template<typename T, typename CMP>
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splay_tree<T, CMP> insert(splay_tree<T, CMP> & t, T const & v) { splay_tree<T, CMP> r(t); r.insert(v); return r; }
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template<typename T, typename CMP>
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splay_tree<T, CMP> erase(splay_tree<T, CMP> & t, T const & v) { splay_tree<T, CMP> r(t); r.erase(v); return r; }
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template<typename T, typename CMP, typename F, typename R>
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R fold(splay_tree<T, CMP> const & t, F && f, R r) {
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static_assert(std::is_same<typename std::result_of<F(T const &, R)>::type, R>::value,
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"fold: return type of f(t : T, r : R) is not R");
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return t.fold(std::forward<F>(f), r);
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}
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template<typename T, typename CMP, typename F>
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void for_each(splay_tree<T, CMP> const & t, F && f) {
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static_assert(std::is_same<typename std::result_of<F(T const &)>::type, void>::value,
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"for_each: return type of f is not void");
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return t.for_each(std::forward<F>(f));
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}
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}
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