From 35e87d63ea072294e79304db363b727683d2a523 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Ondra=20Mi=C4=8Dka=20=40=20miles-teg?=
<mitch.ondra@gmail.com>
Date: Fri, 8 Oct 2021 11:25:26 +0200
Subject: [PATCH] Splay operation
---
02-splay_operation/cpp/Makefile | 12 ++
02-splay_operation/cpp/splay_operation.h | 158 ++++++++++++++
.../cpp/splay_operation_test.cpp | 192 ++++++++++++++++++
02-splay_operation/cpp/splay_tests.txt | 62 ++++++
02-splay_operation/cpp/test_main.cpp | 43 ++++
02-splay_operation/python/splay_operation.py | 118 +++++++++++
.../python/splay_operation_test.py | 145 +++++++++++++
02-splay_operation/python/splay_tests.txt | 62 ++++++
02-splay_operation/task.md | 9 +
9 files changed, 801 insertions(+)
create mode 100644 02-splay_operation/cpp/Makefile
create mode 100644 02-splay_operation/cpp/splay_operation.h
create mode 100644 02-splay_operation/cpp/splay_operation_test.cpp
create mode 100644 02-splay_operation/cpp/splay_tests.txt
create mode 100644 02-splay_operation/cpp/test_main.cpp
create mode 100644 02-splay_operation/python/splay_operation.py
create mode 100644 02-splay_operation/python/splay_operation_test.py
create mode 100644 02-splay_operation/python/splay_tests.txt
create mode 100644 02-splay_operation/task.md
diff --git a/02-splay_operation/cpp/Makefile b/02-splay_operation/cpp/Makefile
new file mode 100644
index 0000000..4ca8274
--- /dev/null
+++ b/02-splay_operation/cpp/Makefile
@@ -0,0 +1,12 @@
+test: splay_operation_test
+ ./$<
+
+CXXFLAGS=-std=c++11 -O2 -Wall -Wextra -g -Wno-sign-compare
+
+splay_operation_test: splay_operation.h splay_operation_test.cpp test_main.cpp
+ $(CXX) $(CXXFLAGS) $^ -o $@
+
+clean::
+ rm -f splay_operation_test
+
+.PHONY: clean test
diff --git a/02-splay_operation/cpp/splay_operation.h b/02-splay_operation/cpp/splay_operation.h
new file mode 100644
index 0000000..249f3dd
--- /dev/null
+++ b/02-splay_operation/cpp/splay_operation.h
@@ -0,0 +1,158 @@
+// A node of the tree
+class Node {
+ public:
+ int key;
+ Node* left;
+ Node* right;
+ Node* parent;
+
+ // Constructor
+ Node(int key, Node* parent=nullptr, Node* left=nullptr, Node* right=nullptr) {
+ this->key = key;
+ this->parent = parent;
+ this->left = left;
+ this->right = right;
+ if (left) left->parent = this;
+ if (right) right->parent = this;
+ }
+};
+
+// Binary tree
+class Tree {
+ public:
+ // Pointer to root of the tree; nullptr if the tree is empty.
+ Node* root;
+
+ Tree(Node* root=nullptr) {
+ this->root = root;
+ }
+
+ // Rotate the given `node` up. Perform a single rotation of the edge
+ // between the node and its parent, choosing left or right rotation
+ // appropriately.
+ virtual void rotate(Node* node) {
+ if (node->parent) {
+ if (node->parent->left == node) {
+ if (node->right) node->right->parent = node->parent;
+ node->parent->left = node->right;
+ node->right = node->parent;
+ } else {
+ if (node->left) node->left->parent = node->parent;
+ node->parent->right = node->left;
+ node->left = node->parent;
+ }
+ if (node->parent->parent) {
+ if (node->parent->parent->left == node->parent)
+ node->parent->parent->left = node;
+ else
+ node->parent->parent->right = node;
+ } else {
+ root = node;
+ }
+
+ Node* original_parent = node->parent;
+ node->parent = node->parent->parent;
+ original_parent->parent = node;
+ }
+ }
+
+ // Look up the given key in the tree, returning the
+ // the node with the requested key or nullptr.
+ Node* lookup(int key) {
+ // TODO: Utilize splay suitably.
+ Node* node = root;
+ while (node) {
+ if (node->key == key) {
+ return node;
+ }
+ if (key < node->key)
+ node = node->left;
+ else
+ node = node->right;
+ }
+ return nullptr;
+ }
+
+ // Insert a key into the tree.
+ // If the key is already present, nothing happens.
+ void insert(int key) {
+ // TODO: Utilize splay suitably.
+ if (!root) {
+ root = new Node(key);
+ return;
+ }
+
+ Node* node = root;
+ while (node->key != key) {
+ if (key < node->key) {
+ if (!node->left)
+ node->left = new Node(key, node);
+ node = node->left;
+ } else {
+ if (!node->right)
+ node->right = new Node(key, node);
+ node = node->right;
+ }
+ }
+ }
+
+ // Delete given key from the tree.
+ // It the key is not present, nothing happens.
+ void remove(int key) {
+ // TODO: Utilize splay suitably.
+ Node* node = root;
+ while (node && node->key != key) {
+ if (key < node->key)
+ node = node->left;
+ else
+ node = node->right;
+ }
+
+ if (node) {
+ if (node->left && node->right) {
+ Node* replacement = node->right;
+ while (replacement->left)
+ replacement = replacement->left;
+ node->key = replacement->key;
+ node = replacement;
+ }
+
+ Node* replacement = node->left ? node->left : node->right;
+ if (node->parent) {
+ if (node->parent->left == node) node->parent->left = replacement;
+ else node->parent->right = replacement;
+ } else {
+ root = replacement;
+ }
+ if (replacement)
+ replacement->parent = node->parent;
+ delete node;
+ }
+ }
+
+ // Splay the given node.
+ // If a single rotation needs to be performed, perform it as the last rotation
+ // (i.e., to move the splayed node to the root of the tree).
+ virtual void splay(Node* node) {
+ // TODO: Implement
+ }
+
+ // Destructor to free all allocated memory.
+ ~Tree() {
+ Node* node = root;
+ while (node) {
+ Node* next;
+ if (node->left) {
+ next = node->left;
+ node->left = nullptr;
+ } else if (node->right) {
+ next = node->right;
+ node->right = nullptr;
+ } else {
+ next = node->parent;
+ delete node;
+ }
+ node = next;
+ }
+ }
+};
diff --git a/02-splay_operation/cpp/splay_operation_test.cpp b/02-splay_operation/cpp/splay_operation_test.cpp
new file mode 100644
index 0000000..d1e6c99
--- /dev/null
+++ b/02-splay_operation/cpp/splay_operation_test.cpp
@@ -0,0 +1,192 @@
+#include <algorithm>
+#include <cassert>
+#include <fstream>
+#include <functional>
+#include <string>
+#include <utility>
+#include <vector>
+
+#include "splay_operation.h"
+
+using namespace std;
+
+// If the condition is not true, report an error and halt.
+#define EXPECT(condition, message) do { if (!(condition)) expect_failed(message); } while (0)
+void expect_failed(const string& message);
+
+// Flatten the tree: return a sorted list of all keys in the tree.
+vector<int> flatten(const Tree& tree) {
+ constexpr int L = 0, R = 1, F = 2;
+
+ Node* node = tree.root;
+ vector<int> flattened, stack = {L};
+ while (!stack.empty()) {
+ if (stack.back() == L) {
+ stack.back() = R;
+ if (node->left) {
+ node = node->left;
+ stack.push_back(L);
+ }
+ } else if (stack.back() == R) {
+ flattened.push_back(node->key);
+ stack.back() = F;
+ if (node->right) {
+ node = node->right;
+ stack.push_back(L);
+ }
+ } else {
+ node = node->parent;
+ stack.pop_back();
+ }
+ }
+ return flattened;
+}
+
+// Test for splay operation with required helpers
+class TestSplay {
+ public:
+ static Node* deserialize_node(const string& text, int& index) {
+ EXPECT(text[index++] == '(', "Internal error during example deserialization");
+ if (text[index] == ')') {
+ index++;
+ return nullptr;
+ } else {
+ int comma = text.find(',', index);
+ int key = stoi(text.substr(index, comma - index));
+ Node* left = deserialize_node(text, (index=comma + 1));
+ Node* right = deserialize_node(text, ++index);
+ EXPECT(text[index++] == ')', "Internal error during example deserialization");
+ return new Node(key, nullptr, left, right);
+ }
+ }
+
+ static Node* deserialize_root(const string& text) {
+ int index = 0;
+ Node* root = deserialize_node(text, index);
+ assert(index == text.size());
+ return root;
+ }
+
+ static string compare(Node* system, Node* gold) {
+ if (!system && gold) {
+ return "expected node with key " + to_string(gold->key) + ", found None";
+ } else if (system && !gold) {
+ return "expected None, found node with key " + to_string(system->key);
+ } else if (system && gold) {
+ if (system->key != gold->key)
+ return "expected node with key " + to_string(gold->key) + ", found " + to_string(system->key);
+ auto result = compare(system->left, gold->left);
+ if (!result.empty()) return result;
+ return compare(system->right, gold->right);
+ }
+ return string();
+ }
+
+ static void test() {
+ ifstream splay_tests_file("splay_tests.txt");
+ EXPECT(splay_tests_file.is_open(), "Cannot open splay_tests.txt file with the tests");
+
+ string original, splayed;
+ int target;
+ while (splay_tests_file >> original >> target >> splayed) {
+ Tree original_tree(deserialize_root(original));
+ Tree splayed_tree(deserialize_root(splayed));
+
+ Node* target_node = original_tree.root;
+ while (target_node && target_node->key != target)
+ if (target < target_node->key)
+ target_node = target_node->left;
+ else
+ target_node = target_node->right;
+ EXPECT(target_node, "Internal error during finding the target node in the tree to splay");
+
+ original_tree.splay(target_node);
+ auto error = compare(original_tree.root, splayed_tree.root);
+ EXPECT(error.empty(), "Error running splay on key " + to_string(target) + " of " + original + ": " + error);
+ }
+ }
+};
+
+void test_lookup() {
+ // Insert even numbers
+ Tree tree;
+ for (int i = 0; i < 5000000; i += 2)
+ tree.insert(i);
+
+ // Find non-existing
+ for (int i = 1; i < 5000000; i += 2)
+ for (int j = 0; j < 10; j++)
+ EXPECT(!tree.lookup(i), "Non-existing element was found");
+
+ // Find existing
+ for (int i = 0; i < 5000000; i += 2)
+ for (int j = 0; j < 10; j++)
+ EXPECT(tree.lookup(i), "Existing element was not found");
+}
+
+void test_insert() {
+ // Test validity first
+ {
+ Tree tree;
+ vector<int> sequence = {997};
+ for (int i = 2; i < 1999; i++)
+ sequence.push_back((sequence.back() * sequence.front()) % 1999);
+ for (const auto& i : sequence)
+ tree.insert(i);
+
+ vector<int> flattened = flatten(tree);
+ sort(sequence.begin(), sequence.end());
+ EXPECT(flattened == sequence, "Incorrect tree after a sequence of inserts");
+ }
+
+ // Test speed
+ {
+ Tree tree;
+ for (int i = 0; i < 5000000; i++)
+ for (int j = 0; j < 10; j++)
+ tree.insert(i);
+ }
+}
+
+void test_remove() {
+ // Test validity first
+ {
+ Tree tree;
+ for (int i = 2; i < 1999 * 2; i++)
+ tree.insert(i);
+
+ vector<int> sequence = {2 * 997};
+ for (int i = 2; i < 1999; i++)
+ sequence.push_back(2 * ((sequence.back() * sequence.front() / 4) % 1999));
+ for (const auto& i : sequence)
+ tree.remove(i + 1);
+
+ vector<int> flattened = flatten(tree);
+ sort(sequence.begin(), sequence.end());
+ EXPECT(flattened == sequence, "Correct tree after a sequence of removes");
+ }
+
+ // Test speed
+ {
+ Tree tree;
+ for (int i = 0; i < 5000000; i++)
+ tree.insert(i);
+
+ // Non-existing elements
+ for (int i = 1; i < 5000000; i += 2)
+ for (int j = 0; j < 10; j++)
+ tree.remove(i);
+
+ // Existing elements
+ for (int i = 2; i < 5000000; i += 2)
+ for (int j = 0; j < 10; j++)
+ tree.remove(i);
+ }
+}
+
+vector<pair<string, function<void()>>> tests = {
+ { "splay", TestSplay::test },
+ { "lookup", test_lookup },
+ { "insert", test_insert },
+ { "remove", test_remove },
+};
diff --git a/02-splay_operation/cpp/splay_tests.txt b/02-splay_operation/cpp/splay_tests.txt
new file mode 100644
index 0000000..7f3259e
--- /dev/null
+++ b/02-splay_operation/cpp/splay_tests.txt
@@ -0,0 +1,62 @@
+(3,(1,(0,(),()),(2,(),())),(4,(),())) 4 (4,(3,(1,(0,(),()),(2,(),())),()),())
+(6,(5,(),()),(8,(7,(),()),(9,(),()))) 5 (5,(),(6,(),(8,(7,(),()),(9,(),()))))
+(3,(1,(0,(),()),(2,(),())),(7,(5,(4,(),()),(6,(),())),(8,(),()))) 8 (8,(7,(3,(1,(0,(),()),(2,(),())),(5,(4,(),()),(6,(),()))),()),())
+(11,(9,(7,(6,(),()),(8,(),())),(10,(),())),(13,(12,(),()),(14,(),()))) 10 (10,(9,(7,(6,(),()),(8,(),())),()),(11,(),(13,(12,(),()),(14,(),()))))
+(8,(6,(5,(),()),(7,(),())),(10,(9,(),()),(12,(11,(),()),(13,(),())))) 9 (9,(8,(6,(5,(),()),(7,(),())),()),(10,(),(12,(11,(),()),(13,(),()))))
+(16,(12,(11,(),()),(14,(13,(),()),(15,(),()))),(18,(17,(),()),(19,(),()))) 11 (11,(),(12,(),(16,(14,(13,(),()),(15,(),())),(18,(17,(),()),(19,(),())))))
+(3,(1,(0,(),()),(2,(),())),(7,(5,(4,(),()),(6,(),())),(11,(9,(8,(),()),(10,(),())),(12,(),())))) 12 (12,(3,(1,(0,(),()),(2,(),())),(11,(7,(5,(4,(),()),(6,(),())),(9,(8,(),()),(10,(),()))),())),())
+(17,(11,(9,(8,(),()),(10,(),())),(15,(13,(12,(),()),(14,(),())),(16,(),()))),(19,(18,(),()),(20,(),()))) 16 (16,(15,(11,(9,(8,(),()),(10,(),())),(13,(12,(),()),(14,(),()))),()),(17,(),(19,(18,(),()),(20,(),()))))
+(9,(7,(6,(),()),(8,(),())),(15,(13,(11,(10,(),()),(12,(),())),(14,(),())),(17,(16,(),()),(18,(),())))) 14 (14,(9,(7,(6,(),()),(8,(),())),(13,(11,(10,(),()),(12,(),())),())),(15,(),(17,(16,(),()),(18,(),()))))
+(23,(19,(17,(15,(14,(),()),(16,(),())),(18,(),())),(21,(20,(),()),(22,(),()))),(25,(24,(),()),(26,(),()))) 18 (18,(17,(15,(14,(),()),(16,(),())),()),(23,(19,(),(21,(20,(),()),(22,(),()))),(25,(24,(),()),(26,(),()))))
+(8,(6,(5,(),()),(7,(),())),(12,(10,(9,(),()),(11,(),())),(14,(13,(),()),(16,(15,(),()),(17,(),()))))) 13 (13,(8,(6,(5,(),()),(7,(),())),(12,(10,(9,(),()),(11,(),())),())),(14,(),(16,(15,(),()),(17,(),()))))
+(22,(16,(14,(13,(),()),(15,(),())),(18,(17,(),()),(20,(19,(),()),(21,(),())))),(24,(23,(),()),(25,(),()))) 17 (17,(16,(14,(13,(),()),(15,(),())),()),(22,(18,(),(20,(19,(),()),(21,(),()))),(24,(23,(),()),(25,(),()))))
+(14,(12,(11,(),()),(13,(),())),(20,(16,(15,(),()),(18,(17,(),()),(19,(),()))),(22,(21,(),()),(23,(),())))) 15 (15,(14,(12,(11,(),()),(13,(),())),()),(16,(),(20,(18,(17,(),()),(19,(),())),(22,(21,(),()),(23,(),())))))
+(28,(24,(20,(19,(),()),(22,(21,(),()),(23,(),()))),(26,(25,(),()),(27,(),()))),(30,(29,(),()),(31,(),()))) 19 (19,(),(28,(20,(),(24,(22,(21,(),()),(23,(),())),(26,(25,(),()),(27,(),())))),(30,(29,(),()),(31,(),()))))
+(3,(1,(0,(),()),(2,(),())),(7,(5,(4,(),()),(6,(),())),(11,(9,(8,(),()),(10,(),())),(15,(13,(12,(),()),(14,(),())),(16,(),()))))) 16 (16,(7,(3,(1,(0,(),()),(2,(),())),(5,(4,(),()),(6,(),()))),(15,(11,(9,(8,(),()),(10,(),())),(13,(12,(),()),(14,(),()))),())),())
+(25,(15,(13,(12,(),()),(14,(),())),(19,(17,(16,(),()),(18,(),())),(23,(21,(20,(),()),(22,(),())),(24,(),())))),(27,(26,(),()),(28,(),()))) 24 (24,(15,(13,(12,(),()),(14,(),())),(23,(19,(17,(16,(),()),(18,(),())),(21,(20,(),()),(22,(),()))),())),(25,(),(27,(26,(),()),(28,(),()))))
+(11,(9,(8,(),()),(10,(),())),(21,(15,(13,(12,(),()),(14,(),())),(19,(17,(16,(),()),(18,(),())),(20,(),()))),(23,(22,(),()),(24,(),())))) 20 (20,(11,(9,(8,(),()),(10,(),())),(19,(15,(13,(12,(),()),(14,(),())),(17,(16,(),()),(18,(),()))),())),(21,(),(23,(22,(),()),(24,(),()))))
+(33,(29,(23,(21,(20,(),()),(22,(),())),(27,(25,(24,(),()),(26,(),())),(28,(),()))),(31,(30,(),()),(32,(),()))),(35,(34,(),()),(36,(),()))) 28 (28,(27,(23,(21,(20,(),()),(22,(),())),(25,(24,(),()),(26,(),()))),()),(29,(),(33,(31,(30,(),()),(32,(),())),(35,(34,(),()),(36,(),())))))
+(9,(7,(6,(),()),(8,(),())),(13,(11,(10,(),()),(12,(),())),(19,(17,(15,(14,(),()),(16,(),())),(18,(),())),(21,(20,(),()),(22,(),()))))) 18 (18,(13,(9,(7,(6,(),()),(8,(),())),(11,(10,(),()),(12,(),()))),(17,(15,(14,(),()),(16,(),())),())),(19,(),(21,(20,(),()),(22,(),()))))
+(31,(21,(19,(18,(),()),(20,(),())),(27,(25,(23,(22,(),()),(24,(),())),(26,(),())),(29,(28,(),()),(30,(),())))),(33,(32,(),()),(34,(),()))) 26 (26,(21,(19,(18,(),()),(20,(),())),(25,(23,(22,(),()),(24,(),())),())),(31,(27,(),(29,(28,(),()),(30,(),()))),(33,(32,(),()),(34,(),()))))
+(17,(15,(14,(),()),(16,(),())),(27,(23,(21,(19,(18,(),()),(20,(),())),(22,(),())),(25,(24,(),()),(26,(),()))),(29,(28,(),()),(30,(),())))) 22 (22,(17,(15,(14,(),()),(16,(),())),(21,(19,(18,(),()),(20,(),())),())),(27,(23,(),(25,(24,(),()),(26,(),()))),(29,(28,(),()),(30,(),()))))
+(39,(35,(31,(29,(27,(26,(),()),(28,(),())),(30,(),())),(33,(32,(),()),(34,(),()))),(37,(36,(),()),(38,(),()))),(41,(40,(),()),(42,(),()))) 30 (30,(29,(27,(26,(),()),(28,(),())),()),(35,(31,(),(33,(32,(),()),(34,(),()))),(39,(37,(36,(),()),(38,(),())),(41,(40,(),()),(42,(),())))))
+(8,(6,(5,(),()),(7,(),())),(12,(10,(9,(),()),(11,(),())),(16,(14,(13,(),()),(15,(),())),(18,(17,(),()),(20,(19,(),()),(21,(),())))))) 17 (17,(12,(8,(6,(5,(),()),(7,(),())),(10,(9,(),()),(11,(),()))),(16,(14,(13,(),()),(15,(),())),())),(18,(),(20,(19,(),()),(21,(),()))))
+(30,(20,(18,(17,(),()),(19,(),())),(24,(22,(21,(),()),(23,(),())),(26,(25,(),()),(28,(27,(),()),(29,(),()))))),(32,(31,(),()),(33,(),()))) 25 (25,(20,(18,(17,(),()),(19,(),())),(24,(22,(21,(),()),(23,(),())),())),(30,(26,(),(28,(27,(),()),(29,(),()))),(32,(31,(),()),(33,(),()))))
+(16,(14,(13,(),()),(15,(),())),(26,(20,(18,(17,(),()),(19,(),())),(22,(21,(),()),(24,(23,(),()),(25,(),())))),(28,(27,(),()),(29,(),())))) 21 (21,(16,(14,(13,(),()),(15,(),())),(20,(18,(17,(),()),(19,(),())),())),(26,(22,(),(24,(23,(),()),(25,(),()))),(28,(27,(),()),(29,(),()))))
+(38,(34,(28,(26,(25,(),()),(27,(),())),(30,(29,(),()),(32,(31,(),()),(33,(),())))),(36,(35,(),()),(37,(),()))),(40,(39,(),()),(41,(),()))) 29 (29,(28,(26,(25,(),()),(27,(),())),()),(34,(30,(),(32,(31,(),()),(33,(),()))),(38,(36,(35,(),()),(37,(),())),(40,(39,(),()),(41,(),())))))
+(14,(12,(11,(),()),(13,(),())),(18,(16,(15,(),()),(17,(),())),(24,(20,(19,(),()),(22,(21,(),()),(23,(),()))),(26,(25,(),()),(27,(),()))))) 19 (19,(18,(14,(12,(11,(),()),(13,(),())),(16,(15,(),()),(17,(),()))),()),(20,(),(24,(22,(21,(),()),(23,(),())),(26,(25,(),()),(27,(),())))))
+(36,(26,(24,(23,(),()),(25,(),())),(32,(28,(27,(),()),(30,(29,(),()),(31,(),()))),(34,(33,(),()),(35,(),())))),(38,(37,(),()),(39,(),()))) 27 (27,(26,(24,(23,(),()),(25,(),())),()),(36,(28,(),(32,(30,(29,(),()),(31,(),())),(34,(33,(),()),(35,(),())))),(38,(37,(),()),(39,(),()))))
+(22,(20,(19,(),()),(21,(),())),(32,(28,(24,(23,(),()),(26,(25,(),()),(27,(),()))),(30,(29,(),()),(31,(),()))),(34,(33,(),()),(35,(),())))) 23 (23,(22,(20,(19,(),()),(21,(),())),()),(32,(24,(),(28,(26,(25,(),()),(27,(),())),(30,(29,(),()),(31,(),())))),(34,(33,(),()),(35,(),()))))
+(44,(40,(36,(32,(31,(),()),(34,(33,(),()),(35,(),()))),(38,(37,(),()),(39,(),()))),(42,(41,(),()),(43,(),()))),(46,(45,(),()),(47,(),()))) 31 (31,(),(40,(32,(),(36,(34,(33,(),()),(35,(),())),(38,(37,(),()),(39,(),())))),(44,(42,(41,(),()),(43,(),())),(46,(45,(),()),(47,(),())))))
+(3,(1,(0,(),()),(2,(),())),(7,(5,(4,(),()),(6,(),())),(11,(9,(8,(),()),(10,(),())),(15,(13,(12,(),()),(14,(),())),(19,(17,(16,(),()),(18,(),())),(20,(),())))))) 20 (20,(3,(1,(0,(),()),(2,(),())),(11,(7,(5,(4,(),()),(6,(),())),(9,(8,(),()),(10,(),()))),(19,(15,(13,(12,(),()),(14,(),())),(17,(16,(),()),(18,(),()))),()))),())
+(37,(23,(21,(20,(),()),(22,(),())),(27,(25,(24,(),()),(26,(),())),(31,(29,(28,(),()),(30,(),())),(35,(33,(32,(),()),(34,(),())),(36,(),()))))),(39,(38,(),()),(40,(),()))) 36 (36,(27,(23,(21,(20,(),()),(22,(),())),(25,(24,(),()),(26,(),()))),(35,(31,(29,(28,(),()),(30,(),())),(33,(32,(),()),(34,(),()))),())),(37,(),(39,(38,(),()),(40,(),()))))
+(15,(13,(12,(),()),(14,(),())),(29,(19,(17,(16,(),()),(18,(),())),(23,(21,(20,(),()),(22,(),())),(27,(25,(24,(),()),(26,(),())),(28,(),())))),(31,(30,(),()),(32,(),())))) 28 (28,(15,(13,(12,(),()),(14,(),())),(19,(17,(16,(),()),(18,(),())),(27,(23,(21,(20,(),()),(22,(),())),(25,(24,(),()),(26,(),()))),()))),(29,(),(31,(30,(),()),(32,(),()))))
+(49,(45,(35,(33,(32,(),()),(34,(),())),(39,(37,(36,(),()),(38,(),())),(43,(41,(40,(),()),(42,(),())),(44,(),())))),(47,(46,(),()),(48,(),()))),(51,(50,(),()),(52,(),()))) 44 (44,(35,(33,(32,(),()),(34,(),())),(43,(39,(37,(36,(),()),(38,(),())),(41,(40,(),()),(42,(),()))),())),(49,(45,(),(47,(46,(),()),(48,(),()))),(51,(50,(),()),(52,(),()))))
+(11,(9,(8,(),()),(10,(),())),(15,(13,(12,(),()),(14,(),())),(25,(19,(17,(16,(),()),(18,(),())),(23,(21,(20,(),()),(22,(),())),(24,(),()))),(27,(26,(),()),(28,(),()))))) 24 (24,(11,(9,(8,(),()),(10,(),())),(15,(13,(12,(),()),(14,(),())),(23,(19,(17,(16,(),()),(18,(),())),(21,(20,(),()),(22,(),()))),()))),(25,(),(27,(26,(),()),(28,(),()))))
+(45,(31,(29,(28,(),()),(30,(),())),(41,(35,(33,(32,(),()),(34,(),())),(39,(37,(36,(),()),(38,(),())),(40,(),()))),(43,(42,(),()),(44,(),())))),(47,(46,(),()),(48,(),()))) 40 (40,(31,(29,(28,(),()),(30,(),())),(39,(35,(33,(32,(),()),(34,(),())),(37,(36,(),()),(38,(),()))),())),(45,(41,(),(43,(42,(),()),(44,(),()))),(47,(46,(),()),(48,(),()))))
+(23,(21,(20,(),()),(22,(),())),(37,(33,(27,(25,(24,(),()),(26,(),())),(31,(29,(28,(),()),(30,(),())),(32,(),()))),(35,(34,(),()),(36,(),()))),(39,(38,(),()),(40,(),())))) 32 (32,(23,(21,(20,(),()),(22,(),())),(31,(27,(25,(24,(),()),(26,(),())),(29,(28,(),()),(30,(),()))),())),(33,(),(37,(35,(34,(),()),(36,(),())),(39,(38,(),()),(40,(),())))))
+(57,(53,(49,(43,(41,(40,(),()),(42,(),())),(47,(45,(44,(),()),(46,(),())),(48,(),()))),(51,(50,(),()),(52,(),()))),(55,(54,(),()),(56,(),()))),(59,(58,(),()),(60,(),()))) 48 (48,(47,(43,(41,(40,(),()),(42,(),())),(45,(44,(),()),(46,(),()))),()),(57,(49,(),(53,(51,(50,(),()),(52,(),())),(55,(54,(),()),(56,(),())))),(59,(58,(),()),(60,(),()))))
+(9,(7,(6,(),()),(8,(),())),(13,(11,(10,(),()),(12,(),())),(17,(15,(14,(),()),(16,(),())),(23,(21,(19,(18,(),()),(20,(),())),(22,(),())),(25,(24,(),()),(26,(),())))))) 22 (22,(9,(7,(6,(),()),(8,(),())),(17,(13,(11,(10,(),()),(12,(),())),(15,(14,(),()),(16,(),()))),(21,(19,(18,(),()),(20,(),())),()))),(23,(),(25,(24,(),()),(26,(),()))))
+(43,(29,(27,(26,(),()),(28,(),())),(33,(31,(30,(),()),(32,(),())),(39,(37,(35,(34,(),()),(36,(),())),(38,(),())),(41,(40,(),()),(42,(),()))))),(45,(44,(),()),(46,(),()))) 38 (38,(33,(29,(27,(26,(),()),(28,(),())),(31,(30,(),()),(32,(),()))),(37,(35,(34,(),()),(36,(),())),())),(43,(39,(),(41,(40,(),()),(42,(),()))),(45,(44,(),()),(46,(),()))))
+(21,(19,(18,(),()),(20,(),())),(35,(25,(23,(22,(),()),(24,(),())),(31,(29,(27,(26,(),()),(28,(),())),(30,(),())),(33,(32,(),()),(34,(),())))),(37,(36,(),()),(38,(),())))) 30 (30,(21,(19,(18,(),()),(20,(),())),(25,(23,(22,(),()),(24,(),())),(29,(27,(26,(),()),(28,(),())),()))),(35,(31,(),(33,(32,(),()),(34,(),()))),(37,(36,(),()),(38,(),()))))
+(55,(51,(41,(39,(38,(),()),(40,(),())),(47,(45,(43,(42,(),()),(44,(),())),(46,(),())),(49,(48,(),()),(50,(),())))),(53,(52,(),()),(54,(),()))),(57,(56,(),()),(58,(),()))) 46 (46,(41,(39,(38,(),()),(40,(),())),(45,(43,(42,(),()),(44,(),())),())),(55,(51,(47,(),(49,(48,(),()),(50,(),()))),(53,(52,(),()),(54,(),()))),(57,(56,(),()),(58,(),()))))
+(17,(15,(14,(),()),(16,(),())),(21,(19,(18,(),()),(20,(),())),(31,(27,(25,(23,(22,(),()),(24,(),())),(26,(),())),(29,(28,(),()),(30,(),()))),(33,(32,(),()),(34,(),()))))) 26 (26,(17,(15,(14,(),()),(16,(),())),(21,(19,(18,(),()),(20,(),())),(25,(23,(22,(),()),(24,(),())),()))),(31,(27,(),(29,(28,(),()),(30,(),()))),(33,(32,(),()),(34,(),()))))
+(51,(37,(35,(34,(),()),(36,(),())),(47,(43,(41,(39,(38,(),()),(40,(),())),(42,(),())),(45,(44,(),()),(46,(),()))),(49,(48,(),()),(50,(),())))),(53,(52,(),()),(54,(),()))) 42 (42,(37,(35,(34,(),()),(36,(),())),(41,(39,(38,(),()),(40,(),())),())),(51,(47,(43,(),(45,(44,(),()),(46,(),()))),(49,(48,(),()),(50,(),()))),(53,(52,(),()),(54,(),()))))
+(29,(27,(26,(),()),(28,(),())),(43,(39,(35,(33,(31,(30,(),()),(32,(),())),(34,(),())),(37,(36,(),()),(38,(),()))),(41,(40,(),()),(42,(),()))),(45,(44,(),()),(46,(),())))) 34 (34,(29,(27,(26,(),()),(28,(),())),(33,(31,(30,(),()),(32,(),())),())),(39,(35,(),(37,(36,(),()),(38,(),()))),(43,(41,(40,(),()),(42,(),())),(45,(44,(),()),(46,(),())))))
+(63,(59,(55,(51,(49,(47,(46,(),()),(48,(),())),(50,(),())),(53,(52,(),()),(54,(),()))),(57,(56,(),()),(58,(),()))),(61,(60,(),()),(62,(),()))),(65,(64,(),()),(66,(),()))) 50 (50,(49,(47,(46,(),()),(48,(),())),()),(63,(55,(51,(),(53,(52,(),()),(54,(),()))),(59,(57,(56,(),()),(58,(),())),(61,(60,(),()),(62,(),())))),(65,(64,(),()),(66,(),()))))
+(8,(6,(5,(),()),(7,(),())),(12,(10,(9,(),()),(11,(),())),(16,(14,(13,(),()),(15,(),())),(20,(18,(17,(),()),(19,(),())),(22,(21,(),()),(24,(23,(),()),(25,(),()))))))) 21 (21,(8,(6,(5,(),()),(7,(),())),(16,(12,(10,(9,(),()),(11,(),())),(14,(13,(),()),(15,(),()))),(20,(18,(17,(),()),(19,(),())),()))),(22,(),(24,(23,(),()),(25,(),()))))
+(42,(28,(26,(25,(),()),(27,(),())),(32,(30,(29,(),()),(31,(),())),(36,(34,(33,(),()),(35,(),())),(38,(37,(),()),(40,(39,(),()),(41,(),())))))),(44,(43,(),()),(45,(),()))) 37 (37,(32,(28,(26,(25,(),()),(27,(),())),(30,(29,(),()),(31,(),()))),(36,(34,(33,(),()),(35,(),())),())),(42,(38,(),(40,(39,(),()),(41,(),()))),(44,(43,(),()),(45,(),()))))
+(20,(18,(17,(),()),(19,(),())),(34,(24,(22,(21,(),()),(23,(),())),(28,(26,(25,(),()),(27,(),())),(30,(29,(),()),(32,(31,(),()),(33,(),()))))),(36,(35,(),()),(37,(),())))) 29 (29,(20,(18,(17,(),()),(19,(),())),(24,(22,(21,(),()),(23,(),())),(28,(26,(25,(),()),(27,(),())),()))),(34,(30,(),(32,(31,(),()),(33,(),()))),(36,(35,(),()),(37,(),()))))
+(54,(50,(40,(38,(37,(),()),(39,(),())),(44,(42,(41,(),()),(43,(),())),(46,(45,(),()),(48,(47,(),()),(49,(),()))))),(52,(51,(),()),(53,(),()))),(56,(55,(),()),(57,(),()))) 45 (45,(40,(38,(37,(),()),(39,(),())),(44,(42,(41,(),()),(43,(),())),())),(54,(50,(46,(),(48,(47,(),()),(49,(),()))),(52,(51,(),()),(53,(),()))),(56,(55,(),()),(57,(),()))))
+(16,(14,(13,(),()),(15,(),())),(20,(18,(17,(),()),(19,(),())),(30,(24,(22,(21,(),()),(23,(),())),(26,(25,(),()),(28,(27,(),()),(29,(),())))),(32,(31,(),()),(33,(),()))))) 25 (25,(16,(14,(13,(),()),(15,(),())),(20,(18,(17,(),()),(19,(),())),(24,(22,(21,(),()),(23,(),())),()))),(30,(26,(),(28,(27,(),()),(29,(),()))),(32,(31,(),()),(33,(),()))))
+(50,(36,(34,(33,(),()),(35,(),())),(46,(40,(38,(37,(),()),(39,(),())),(42,(41,(),()),(44,(43,(),()),(45,(),())))),(48,(47,(),()),(49,(),())))),(52,(51,(),()),(53,(),()))) 41 (41,(36,(34,(33,(),()),(35,(),())),(40,(38,(37,(),()),(39,(),())),())),(50,(46,(42,(),(44,(43,(),()),(45,(),()))),(48,(47,(),()),(49,(),()))),(52,(51,(),()),(53,(),()))))
+(28,(26,(25,(),()),(27,(),())),(42,(38,(32,(30,(29,(),()),(31,(),())),(34,(33,(),()),(36,(35,(),()),(37,(),())))),(40,(39,(),()),(41,(),()))),(44,(43,(),()),(45,(),())))) 33 (33,(28,(26,(25,(),()),(27,(),())),(32,(30,(29,(),()),(31,(),())),())),(38,(34,(),(36,(35,(),()),(37,(),()))),(42,(40,(39,(),()),(41,(),())),(44,(43,(),()),(45,(),())))))
+(62,(58,(54,(48,(46,(45,(),()),(47,(),())),(50,(49,(),()),(52,(51,(),()),(53,(),())))),(56,(55,(),()),(57,(),()))),(60,(59,(),()),(61,(),()))),(64,(63,(),()),(65,(),()))) 49 (49,(48,(46,(45,(),()),(47,(),())),()),(62,(54,(50,(),(52,(51,(),()),(53,(),()))),(58,(56,(55,(),()),(57,(),())),(60,(59,(),()),(61,(),())))),(64,(63,(),()),(65,(),()))))
+(14,(12,(11,(),()),(13,(),())),(18,(16,(15,(),()),(17,(),())),(22,(20,(19,(),()),(21,(),())),(28,(24,(23,(),()),(26,(25,(),()),(27,(),()))),(30,(29,(),()),(31,(),())))))) 23 (23,(14,(12,(11,(),()),(13,(),())),(22,(18,(16,(15,(),()),(17,(),())),(20,(19,(),()),(21,(),()))),())),(24,(),(28,(26,(25,(),()),(27,(),())),(30,(29,(),()),(31,(),())))))
+(48,(34,(32,(31,(),()),(33,(),())),(38,(36,(35,(),()),(37,(),())),(44,(40,(39,(),()),(42,(41,(),()),(43,(),()))),(46,(45,(),()),(47,(),()))))),(50,(49,(),()),(51,(),()))) 39 (39,(38,(34,(32,(31,(),()),(33,(),())),(36,(35,(),()),(37,(),()))),()),(48,(40,(),(44,(42,(41,(),()),(43,(),())),(46,(45,(),()),(47,(),())))),(50,(49,(),()),(51,(),()))))
+(26,(24,(23,(),()),(25,(),())),(40,(30,(28,(27,(),()),(29,(),())),(36,(32,(31,(),()),(34,(33,(),()),(35,(),()))),(38,(37,(),()),(39,(),())))),(42,(41,(),()),(43,(),())))) 31 (31,(26,(24,(23,(),()),(25,(),())),(30,(28,(27,(),()),(29,(),())),())),(40,(32,(),(36,(34,(33,(),()),(35,(),())),(38,(37,(),()),(39,(),())))),(42,(41,(),()),(43,(),()))))
+(60,(56,(46,(44,(43,(),()),(45,(),())),(52,(48,(47,(),()),(50,(49,(),()),(51,(),()))),(54,(53,(),()),(55,(),())))),(58,(57,(),()),(59,(),()))),(62,(61,(),()),(63,(),()))) 47 (47,(46,(44,(43,(),()),(45,(),())),()),(60,(56,(48,(),(52,(50,(49,(),()),(51,(),())),(54,(53,(),()),(55,(),())))),(58,(57,(),()),(59,(),()))),(62,(61,(),()),(63,(),()))))
+(22,(20,(19,(),()),(21,(),())),(26,(24,(23,(),()),(25,(),())),(36,(32,(28,(27,(),()),(30,(29,(),()),(31,(),()))),(34,(33,(),()),(35,(),()))),(38,(37,(),()),(39,(),()))))) 27 (27,(22,(20,(19,(),()),(21,(),())),(26,(24,(23,(),()),(25,(),())),())),(36,(28,(),(32,(30,(29,(),()),(31,(),())),(34,(33,(),()),(35,(),())))),(38,(37,(),()),(39,(),()))))
+(56,(42,(40,(39,(),()),(41,(),())),(52,(48,(44,(43,(),()),(46,(45,(),()),(47,(),()))),(50,(49,(),()),(51,(),()))),(54,(53,(),()),(55,(),())))),(58,(57,(),()),(59,(),()))) 43 (43,(42,(40,(39,(),()),(41,(),())),()),(56,(52,(44,(),(48,(46,(45,(),()),(47,(),())),(50,(49,(),()),(51,(),())))),(54,(53,(),()),(55,(),()))),(58,(57,(),()),(59,(),()))))
+(34,(32,(31,(),()),(33,(),())),(48,(44,(40,(36,(35,(),()),(38,(37,(),()),(39,(),()))),(42,(41,(),()),(43,(),()))),(46,(45,(),()),(47,(),()))),(50,(49,(),()),(51,(),())))) 35 (35,(34,(32,(31,(),()),(33,(),())),()),(44,(36,(),(40,(38,(37,(),()),(39,(),())),(42,(41,(),()),(43,(),())))),(48,(46,(45,(),()),(47,(),())),(50,(49,(),()),(51,(),())))))
+(68,(64,(60,(56,(52,(51,(),()),(54,(53,(),()),(55,(),()))),(58,(57,(),()),(59,(),()))),(62,(61,(),()),(63,(),()))),(66,(65,(),()),(67,(),()))),(70,(69,(),()),(71,(),()))) 51 (51,(),(68,(60,(52,(),(56,(54,(53,(),()),(55,(),())),(58,(57,(),()),(59,(),())))),(64,(62,(61,(),()),(63,(),())),(66,(65,(),()),(67,(),())))),(70,(69,(),()),(71,(),()))))
diff --git a/02-splay_operation/cpp/test_main.cpp b/02-splay_operation/cpp/test_main.cpp
new file mode 100644
index 0000000..3f4aff0
--- /dev/null
+++ b/02-splay_operation/cpp/test_main.cpp
@@ -0,0 +1,43 @@
+#include <cstdlib>
+#include <functional>
+#include <iostream>
+#include <string>
+#include <utility>
+#include <vector>
+
+using namespace std;
+
+extern vector<pair<string, function<void()>>> tests;
+
+void expect_failed(const string& message) {
+ cerr << "Test error: " << message << endl;
+ exit(1);
+}
+
+int main(int argc, char* argv[]) {
+ vector<string> required_tests;
+
+ if (argc > 1) {
+ required_tests.assign(argv + 1, argv + argc);
+ } else {
+ for (const auto& test : tests)
+ required_tests.push_back(test.first);
+ }
+
+ for (const auto& required_test : required_tests) {
+ bool found = false;
+ for (const auto& test : tests)
+ if (required_test == test.first) {
+ cerr << "Running test " << required_test << endl;
+ test.second();
+ found = true;
+ break;
+ }
+ if (!found) {
+ cerr << "Unknown test " << required_test << endl;
+ return 1;
+ }
+ }
+
+ return 0;
+}
diff --git a/02-splay_operation/python/splay_operation.py b/02-splay_operation/python/splay_operation.py
new file mode 100644
index 0000000..4e40e04
--- /dev/null
+++ b/02-splay_operation/python/splay_operation.py
@@ -0,0 +1,118 @@
+#!/usr/bin/env python3
+
+class Node:
+ """Node in a binary tree `Tree`"""
+
+ def __init__(self, key, left=None, right=None, parent=None):
+ self.key = key
+ self.parent = parent
+ self.left = left
+ self.right = right
+ if left is not None: left.parent = self
+ if right is not None: right.parent = self
+
+class Tree:
+ """A simple binary search tree"""
+
+ def __init__(self, root=None):
+ self.root = root
+
+ def rotate(self, node):
+ """ Rotate the given `node` up.
+
+ Performs a single rotation of the edge between the given node
+ and its parent, choosing left or right rotation appropriately.
+ """
+ if node.parent is not None:
+ if node.parent.left == node:
+ if node.right is not None: node.right.parent = node.parent
+ node.parent.left = node.right
+ node.right = node.parent
+ else:
+ if node.left is not None: node.left.parent = node.parent
+ node.parent.right = node.left
+ node.left = node.parent
+ if node.parent.parent is not None:
+ if node.parent.parent.left == node.parent:
+ node.parent.parent.left = node
+ else:
+ node.parent.parent.right = node
+ else:
+ self.root = node
+ node.parent.parent, node.parent = node, node.parent.parent
+
+ def lookup(self, key):
+ """Look up the given key in the tree.
+
+ Returns the node with the requested key or `None`.
+ """
+ # TODO: Utilize splay suitably.
+ node = self.root
+ while node is not None:
+ if node.key == key:
+ return node
+ if key < node.key:
+ node = node.left
+ else:
+ node = node.right
+ return None
+
+ def insert(self, key):
+ """Insert key into the tree.
+
+ If the key is already present, nothing happens.
+ """
+ # TODO: Utilize splay suitably.
+ if self.root is None:
+ self.root = Node(key)
+ return
+
+ node = self.root
+ while node.key != key:
+ if key < node.key:
+ if node.left is None:
+ node.left = Node(key, parent=node)
+ node = node.left
+ else:
+ if node.right is None:
+ node.right = Node(key, parent=node)
+ node = node.right
+
+ def remove(self, key):
+ """Remove given key from the tree.
+
+ It the key is not present, nothing happens.
+ """
+ # TODO: Utilize splay suitably.
+ node = self.root
+ while node is not None and node.key != key:
+ if key < node.key:
+ node = node.left
+ else:
+ node = node.right
+
+ if node is not None:
+ if node.left is not None and node.right is not None:
+ replacement = node.right
+ while replacement.left is not None:
+ replacement = replacement.left
+ node.key = replacement.key
+ node = replacement
+
+ replacement = node.left if node.left is not None else node.right
+ if node.parent is not None:
+ if node.parent.left == node: node.parent.left = replacement
+ else: node.parent.right = replacement
+ else:
+ self.root = replacement
+ if replacement is not None:
+ replacement.parent = node.parent
+
+ def splay(self, node):
+ """Splay the given node.
+
+ If a single rotation needs to be performed, perform it as the last rotation
+ (i.e., to move the splayed node to the root of the tree).
+ """
+ # TODO: Implement
+ raise NotImplementedError
diff --git a/02-splay_operation/python/splay_operation_test.py b/02-splay_operation/python/splay_operation_test.py
new file mode 100644
index 0000000..b342520
--- /dev/null
+++ b/02-splay_operation/python/splay_operation_test.py
@@ -0,0 +1,145 @@
+#!/usr/bin/env python3
+import itertools
+import math
+import sys
+
+from splay_operation import Tree, Node
+
+def flatten(tree):
+ """Flatten given tree in ascending order."""
+ L, R, F = 0, 1, 2
+
+ node, stack, flattened = tree.root, [L], []
+ while node is not None:
+ if stack[-1] == L:
+ stack[-1] = R
+ if node.left is not None:
+ node = node.left
+ stack.append(L)
+ elif stack[-1] == R:
+ flattened.append(node.key)
+ stack[-1] = F
+ if node.right is not None:
+ node = node.right
+ stack.append(L)
+ else:
+ node = node.parent
+ stack.pop()
+
+ return flattened
+
+def test_splay():
+ def deserialize_tree(string):
+ def deserialize_node(i):
+ assert string[i] == "("
+ i += 1
+ if string[i] == ")":
+ return i + 1, None
+ else:
+ comma = string.find(",", i)
+ comma2, left = deserialize_node(comma + 1)
+ rparen, right = deserialize_node(comma2 + 1)
+ assert string[rparen] == ")"
+ return rparen + 1, Node(int(string[i : comma]), left=left, right=right)
+
+ index, root = deserialize_node(0)
+ assert index == len(string)
+ return Tree(root)
+
+ def compare(system, gold):
+ if system is None and gold is not None:
+ return "expected node with key {}, found None".format(gold.key)
+ elif system is not None and gold is None:
+ return "expected None, found node with key {}".format(system.key)
+ elif system is not None and gold is not None:
+ if system.key != gold.key:
+ return "expected node with key {}, found {}".format(gold.key, system.key)
+ return compare(system.left, gold.left) or compare(system.right, gold.right)
+
+ with open("splay_tests.txt", "r") as splay_tests_file:
+ for line in splay_tests_file:
+ original_serialized, target_serialized, splayed_serialized = line.rstrip("\n").split()
+ original = deserialize_tree(original_serialized)
+ splayed = deserialize_tree(splayed_serialized)
+ target = int(target_serialized)
+
+ node = original.root
+ while node is not None and node.key != target:
+ if target < node.key: node = node.left
+ else: node = node.right
+ assert node is not None
+
+ original.splay(node)
+ error = compare(original.root, splayed.root)
+ assert not error, "Error running splay on key {} of {}: {}".format(node.key, original_serialized, error)
+
+def test_lookup():
+ tree = Tree()
+ for elem in range(0, 100000, 2):
+ tree.insert(elem)
+
+ # Find non-existing
+ for elem in range(1, 100000, 2):
+ for _ in range(10):
+ assert tree.lookup(elem) is None, "Non-existing element was found"
+
+ # Find existing
+ for elem in range(0, 100000, 2):
+ for _ in range(10):
+ assert tree.lookup(elem) is not None, "Existing element was not found"
+
+def test_insert():
+ # Test validity first
+ tree = Tree()
+ sequence = [pow(997, i, 1999) for i in range(1, 1999)]
+ for elem in sequence:
+ tree.insert(elem)
+ assert flatten(tree) == sorted(sequence), "Incorrect tree after a sequence of inserts"
+
+ # Test speed
+ tree = Tree()
+ for elem in range(200000):
+ for _ in range(10):
+ tree.insert(elem)
+
+def test_remove():
+ # Test validity first
+ tree = Tree()
+ for elem in range(2, 1999 * 2):
+ tree.insert(elem)
+
+ sequence = [2 * pow(997, i, 1999) for i in range(1, 1999)]
+ for elem in sequence:
+ tree.remove(elem + 1)
+ assert flatten(tree) == sorted(sequence), "Incorrect tree after a sequence of removes"
+
+ # Test speed
+ tree = Tree()
+ for elem in range(0, 100000, 2):
+ tree.insert(elem)
+
+ # Non-existing elements
+ for elem in range(1, 100000, 2):
+ for _ in range(10):
+ tree.remove(elem)
+
+ # Existing elements
+ for elem in range(2, 100000, 2):
+ tree.remove(elem)
+
+tests = [
+ ("splay", test_splay),
+ ("lookup", test_lookup),
+ ("insert", test_insert),
+ ("remove", test_remove),
+]
+
+if __name__ == "__main__":
+ for required_test in sys.argv[1:] or [name for name, _ in tests]:
+ for name, test in tests:
+ if name == required_test:
+ print("Running test {}".format(name), file=sys.stderr)
+ test()
+ break
+ else:
+ raise ValueError("Unknown test {}".format(name))
diff --git a/02-splay_operation/python/splay_tests.txt b/02-splay_operation/python/splay_tests.txt
new file mode 100644
index 0000000..7f3259e
--- /dev/null
+++ b/02-splay_operation/python/splay_tests.txt
@@ -0,0 +1,62 @@
+(3,(1,(0,(),()),(2,(),())),(4,(),())) 4 (4,(3,(1,(0,(),()),(2,(),())),()),())
+(6,(5,(),()),(8,(7,(),()),(9,(),()))) 5 (5,(),(6,(),(8,(7,(),()),(9,(),()))))
+(3,(1,(0,(),()),(2,(),())),(7,(5,(4,(),()),(6,(),())),(8,(),()))) 8 (8,(7,(3,(1,(0,(),()),(2,(),())),(5,(4,(),()),(6,(),()))),()),())
+(11,(9,(7,(6,(),()),(8,(),())),(10,(),())),(13,(12,(),()),(14,(),()))) 10 (10,(9,(7,(6,(),()),(8,(),())),()),(11,(),(13,(12,(),()),(14,(),()))))
+(8,(6,(5,(),()),(7,(),())),(10,(9,(),()),(12,(11,(),()),(13,(),())))) 9 (9,(8,(6,(5,(),()),(7,(),())),()),(10,(),(12,(11,(),()),(13,(),()))))
+(16,(12,(11,(),()),(14,(13,(),()),(15,(),()))),(18,(17,(),()),(19,(),()))) 11 (11,(),(12,(),(16,(14,(13,(),()),(15,(),())),(18,(17,(),()),(19,(),())))))
+(3,(1,(0,(),()),(2,(),())),(7,(5,(4,(),()),(6,(),())),(11,(9,(8,(),()),(10,(),())),(12,(),())))) 12 (12,(3,(1,(0,(),()),(2,(),())),(11,(7,(5,(4,(),()),(6,(),())),(9,(8,(),()),(10,(),()))),())),())
+(17,(11,(9,(8,(),()),(10,(),())),(15,(13,(12,(),()),(14,(),())),(16,(),()))),(19,(18,(),()),(20,(),()))) 16 (16,(15,(11,(9,(8,(),()),(10,(),())),(13,(12,(),()),(14,(),()))),()),(17,(),(19,(18,(),()),(20,(),()))))
+(9,(7,(6,(),()),(8,(),())),(15,(13,(11,(10,(),()),(12,(),())),(14,(),())),(17,(16,(),()),(18,(),())))) 14 (14,(9,(7,(6,(),()),(8,(),())),(13,(11,(10,(),()),(12,(),())),())),(15,(),(17,(16,(),()),(18,(),()))))
+(23,(19,(17,(15,(14,(),()),(16,(),())),(18,(),())),(21,(20,(),()),(22,(),()))),(25,(24,(),()),(26,(),()))) 18 (18,(17,(15,(14,(),()),(16,(),())),()),(23,(19,(),(21,(20,(),()),(22,(),()))),(25,(24,(),()),(26,(),()))))
+(8,(6,(5,(),()),(7,(),())),(12,(10,(9,(),()),(11,(),())),(14,(13,(),()),(16,(15,(),()),(17,(),()))))) 13 (13,(8,(6,(5,(),()),(7,(),())),(12,(10,(9,(),()),(11,(),())),())),(14,(),(16,(15,(),()),(17,(),()))))
+(22,(16,(14,(13,(),()),(15,(),())),(18,(17,(),()),(20,(19,(),()),(21,(),())))),(24,(23,(),()),(25,(),()))) 17 (17,(16,(14,(13,(),()),(15,(),())),()),(22,(18,(),(20,(19,(),()),(21,(),()))),(24,(23,(),()),(25,(),()))))
+(14,(12,(11,(),()),(13,(),())),(20,(16,(15,(),()),(18,(17,(),()),(19,(),()))),(22,(21,(),()),(23,(),())))) 15 (15,(14,(12,(11,(),()),(13,(),())),()),(16,(),(20,(18,(17,(),()),(19,(),())),(22,(21,(),()),(23,(),())))))
+(28,(24,(20,(19,(),()),(22,(21,(),()),(23,(),()))),(26,(25,(),()),(27,(),()))),(30,(29,(),()),(31,(),()))) 19 (19,(),(28,(20,(),(24,(22,(21,(),()),(23,(),())),(26,(25,(),()),(27,(),())))),(30,(29,(),()),(31,(),()))))
+(3,(1,(0,(),()),(2,(),())),(7,(5,(4,(),()),(6,(),())),(11,(9,(8,(),()),(10,(),())),(15,(13,(12,(),()),(14,(),())),(16,(),()))))) 16 (16,(7,(3,(1,(0,(),()),(2,(),())),(5,(4,(),()),(6,(),()))),(15,(11,(9,(8,(),()),(10,(),())),(13,(12,(),()),(14,(),()))),())),())
+(25,(15,(13,(12,(),()),(14,(),())),(19,(17,(16,(),()),(18,(),())),(23,(21,(20,(),()),(22,(),())),(24,(),())))),(27,(26,(),()),(28,(),()))) 24 (24,(15,(13,(12,(),()),(14,(),())),(23,(19,(17,(16,(),()),(18,(),())),(21,(20,(),()),(22,(),()))),())),(25,(),(27,(26,(),()),(28,(),()))))
+(11,(9,(8,(),()),(10,(),())),(21,(15,(13,(12,(),()),(14,(),())),(19,(17,(16,(),()),(18,(),())),(20,(),()))),(23,(22,(),()),(24,(),())))) 20 (20,(11,(9,(8,(),()),(10,(),())),(19,(15,(13,(12,(),()),(14,(),())),(17,(16,(),()),(18,(),()))),())),(21,(),(23,(22,(),()),(24,(),()))))
+(33,(29,(23,(21,(20,(),()),(22,(),())),(27,(25,(24,(),()),(26,(),())),(28,(),()))),(31,(30,(),()),(32,(),()))),(35,(34,(),()),(36,(),()))) 28 (28,(27,(23,(21,(20,(),()),(22,(),())),(25,(24,(),()),(26,(),()))),()),(29,(),(33,(31,(30,(),()),(32,(),())),(35,(34,(),()),(36,(),())))))
+(9,(7,(6,(),()),(8,(),())),(13,(11,(10,(),()),(12,(),())),(19,(17,(15,(14,(),()),(16,(),())),(18,(),())),(21,(20,(),()),(22,(),()))))) 18 (18,(13,(9,(7,(6,(),()),(8,(),())),(11,(10,(),()),(12,(),()))),(17,(15,(14,(),()),(16,(),())),())),(19,(),(21,(20,(),()),(22,(),()))))
+(31,(21,(19,(18,(),()),(20,(),())),(27,(25,(23,(22,(),()),(24,(),())),(26,(),())),(29,(28,(),()),(30,(),())))),(33,(32,(),()),(34,(),()))) 26 (26,(21,(19,(18,(),()),(20,(),())),(25,(23,(22,(),()),(24,(),())),())),(31,(27,(),(29,(28,(),()),(30,(),()))),(33,(32,(),()),(34,(),()))))
+(17,(15,(14,(),()),(16,(),())),(27,(23,(21,(19,(18,(),()),(20,(),())),(22,(),())),(25,(24,(),()),(26,(),()))),(29,(28,(),()),(30,(),())))) 22 (22,(17,(15,(14,(),()),(16,(),())),(21,(19,(18,(),()),(20,(),())),())),(27,(23,(),(25,(24,(),()),(26,(),()))),(29,(28,(),()),(30,(),()))))
+(39,(35,(31,(29,(27,(26,(),()),(28,(),())),(30,(),())),(33,(32,(),()),(34,(),()))),(37,(36,(),()),(38,(),()))),(41,(40,(),()),(42,(),()))) 30 (30,(29,(27,(26,(),()),(28,(),())),()),(35,(31,(),(33,(32,(),()),(34,(),()))),(39,(37,(36,(),()),(38,(),())),(41,(40,(),()),(42,(),())))))
+(8,(6,(5,(),()),(7,(),())),(12,(10,(9,(),()),(11,(),())),(16,(14,(13,(),()),(15,(),())),(18,(17,(),()),(20,(19,(),()),(21,(),())))))) 17 (17,(12,(8,(6,(5,(),()),(7,(),())),(10,(9,(),()),(11,(),()))),(16,(14,(13,(),()),(15,(),())),())),(18,(),(20,(19,(),()),(21,(),()))))
+(30,(20,(18,(17,(),()),(19,(),())),(24,(22,(21,(),()),(23,(),())),(26,(25,(),()),(28,(27,(),()),(29,(),()))))),(32,(31,(),()),(33,(),()))) 25 (25,(20,(18,(17,(),()),(19,(),())),(24,(22,(21,(),()),(23,(),())),())),(30,(26,(),(28,(27,(),()),(29,(),()))),(32,(31,(),()),(33,(),()))))
+(16,(14,(13,(),()),(15,(),())),(26,(20,(18,(17,(),()),(19,(),())),(22,(21,(),()),(24,(23,(),()),(25,(),())))),(28,(27,(),()),(29,(),())))) 21 (21,(16,(14,(13,(),()),(15,(),())),(20,(18,(17,(),()),(19,(),())),())),(26,(22,(),(24,(23,(),()),(25,(),()))),(28,(27,(),()),(29,(),()))))
+(38,(34,(28,(26,(25,(),()),(27,(),())),(30,(29,(),()),(32,(31,(),()),(33,(),())))),(36,(35,(),()),(37,(),()))),(40,(39,(),()),(41,(),()))) 29 (29,(28,(26,(25,(),()),(27,(),())),()),(34,(30,(),(32,(31,(),()),(33,(),()))),(38,(36,(35,(),()),(37,(),())),(40,(39,(),()),(41,(),())))))
+(14,(12,(11,(),()),(13,(),())),(18,(16,(15,(),()),(17,(),())),(24,(20,(19,(),()),(22,(21,(),()),(23,(),()))),(26,(25,(),()),(27,(),()))))) 19 (19,(18,(14,(12,(11,(),()),(13,(),())),(16,(15,(),()),(17,(),()))),()),(20,(),(24,(22,(21,(),()),(23,(),())),(26,(25,(),()),(27,(),())))))
+(36,(26,(24,(23,(),()),(25,(),())),(32,(28,(27,(),()),(30,(29,(),()),(31,(),()))),(34,(33,(),()),(35,(),())))),(38,(37,(),()),(39,(),()))) 27 (27,(26,(24,(23,(),()),(25,(),())),()),(36,(28,(),(32,(30,(29,(),()),(31,(),())),(34,(33,(),()),(35,(),())))),(38,(37,(),()),(39,(),()))))
+(22,(20,(19,(),()),(21,(),())),(32,(28,(24,(23,(),()),(26,(25,(),()),(27,(),()))),(30,(29,(),()),(31,(),()))),(34,(33,(),()),(35,(),())))) 23 (23,(22,(20,(19,(),()),(21,(),())),()),(32,(24,(),(28,(26,(25,(),()),(27,(),())),(30,(29,(),()),(31,(),())))),(34,(33,(),()),(35,(),()))))
+(44,(40,(36,(32,(31,(),()),(34,(33,(),()),(35,(),()))),(38,(37,(),()),(39,(),()))),(42,(41,(),()),(43,(),()))),(46,(45,(),()),(47,(),()))) 31 (31,(),(40,(32,(),(36,(34,(33,(),()),(35,(),())),(38,(37,(),()),(39,(),())))),(44,(42,(41,(),()),(43,(),())),(46,(45,(),()),(47,(),())))))
+(3,(1,(0,(),()),(2,(),())),(7,(5,(4,(),()),(6,(),())),(11,(9,(8,(),()),(10,(),())),(15,(13,(12,(),()),(14,(),())),(19,(17,(16,(),()),(18,(),())),(20,(),())))))) 20 (20,(3,(1,(0,(),()),(2,(),())),(11,(7,(5,(4,(),()),(6,(),())),(9,(8,(),()),(10,(),()))),(19,(15,(13,(12,(),()),(14,(),())),(17,(16,(),()),(18,(),()))),()))),())
+(37,(23,(21,(20,(),()),(22,(),())),(27,(25,(24,(),()),(26,(),())),(31,(29,(28,(),()),(30,(),())),(35,(33,(32,(),()),(34,(),())),(36,(),()))))),(39,(38,(),()),(40,(),()))) 36 (36,(27,(23,(21,(20,(),()),(22,(),())),(25,(24,(),()),(26,(),()))),(35,(31,(29,(28,(),()),(30,(),())),(33,(32,(),()),(34,(),()))),())),(37,(),(39,(38,(),()),(40,(),()))))
+(15,(13,(12,(),()),(14,(),())),(29,(19,(17,(16,(),()),(18,(),())),(23,(21,(20,(),()),(22,(),())),(27,(25,(24,(),()),(26,(),())),(28,(),())))),(31,(30,(),()),(32,(),())))) 28 (28,(15,(13,(12,(),()),(14,(),())),(19,(17,(16,(),()),(18,(),())),(27,(23,(21,(20,(),()),(22,(),())),(25,(24,(),()),(26,(),()))),()))),(29,(),(31,(30,(),()),(32,(),()))))
+(49,(45,(35,(33,(32,(),()),(34,(),())),(39,(37,(36,(),()),(38,(),())),(43,(41,(40,(),()),(42,(),())),(44,(),())))),(47,(46,(),()),(48,(),()))),(51,(50,(),()),(52,(),()))) 44 (44,(35,(33,(32,(),()),(34,(),())),(43,(39,(37,(36,(),()),(38,(),())),(41,(40,(),()),(42,(),()))),())),(49,(45,(),(47,(46,(),()),(48,(),()))),(51,(50,(),()),(52,(),()))))
+(11,(9,(8,(),()),(10,(),())),(15,(13,(12,(),()),(14,(),())),(25,(19,(17,(16,(),()),(18,(),())),(23,(21,(20,(),()),(22,(),())),(24,(),()))),(27,(26,(),()),(28,(),()))))) 24 (24,(11,(9,(8,(),()),(10,(),())),(15,(13,(12,(),()),(14,(),())),(23,(19,(17,(16,(),()),(18,(),())),(21,(20,(),()),(22,(),()))),()))),(25,(),(27,(26,(),()),(28,(),()))))
+(45,(31,(29,(28,(),()),(30,(),())),(41,(35,(33,(32,(),()),(34,(),())),(39,(37,(36,(),()),(38,(),())),(40,(),()))),(43,(42,(),()),(44,(),())))),(47,(46,(),()),(48,(),()))) 40 (40,(31,(29,(28,(),()),(30,(),())),(39,(35,(33,(32,(),()),(34,(),())),(37,(36,(),()),(38,(),()))),())),(45,(41,(),(43,(42,(),()),(44,(),()))),(47,(46,(),()),(48,(),()))))
+(23,(21,(20,(),()),(22,(),())),(37,(33,(27,(25,(24,(),()),(26,(),())),(31,(29,(28,(),()),(30,(),())),(32,(),()))),(35,(34,(),()),(36,(),()))),(39,(38,(),()),(40,(),())))) 32 (32,(23,(21,(20,(),()),(22,(),())),(31,(27,(25,(24,(),()),(26,(),())),(29,(28,(),()),(30,(),()))),())),(33,(),(37,(35,(34,(),()),(36,(),())),(39,(38,(),()),(40,(),())))))
+(57,(53,(49,(43,(41,(40,(),()),(42,(),())),(47,(45,(44,(),()),(46,(),())),(48,(),()))),(51,(50,(),()),(52,(),()))),(55,(54,(),()),(56,(),()))),(59,(58,(),()),(60,(),()))) 48 (48,(47,(43,(41,(40,(),()),(42,(),())),(45,(44,(),()),(46,(),()))),()),(57,(49,(),(53,(51,(50,(),()),(52,(),())),(55,(54,(),()),(56,(),())))),(59,(58,(),()),(60,(),()))))
+(9,(7,(6,(),()),(8,(),())),(13,(11,(10,(),()),(12,(),())),(17,(15,(14,(),()),(16,(),())),(23,(21,(19,(18,(),()),(20,(),())),(22,(),())),(25,(24,(),()),(26,(),())))))) 22 (22,(9,(7,(6,(),()),(8,(),())),(17,(13,(11,(10,(),()),(12,(),())),(15,(14,(),()),(16,(),()))),(21,(19,(18,(),()),(20,(),())),()))),(23,(),(25,(24,(),()),(26,(),()))))
+(43,(29,(27,(26,(),()),(28,(),())),(33,(31,(30,(),()),(32,(),())),(39,(37,(35,(34,(),()),(36,(),())),(38,(),())),(41,(40,(),()),(42,(),()))))),(45,(44,(),()),(46,(),()))) 38 (38,(33,(29,(27,(26,(),()),(28,(),())),(31,(30,(),()),(32,(),()))),(37,(35,(34,(),()),(36,(),())),())),(43,(39,(),(41,(40,(),()),(42,(),()))),(45,(44,(),()),(46,(),()))))
+(21,(19,(18,(),()),(20,(),())),(35,(25,(23,(22,(),()),(24,(),())),(31,(29,(27,(26,(),()),(28,(),())),(30,(),())),(33,(32,(),()),(34,(),())))),(37,(36,(),()),(38,(),())))) 30 (30,(21,(19,(18,(),()),(20,(),())),(25,(23,(22,(),()),(24,(),())),(29,(27,(26,(),()),(28,(),())),()))),(35,(31,(),(33,(32,(),()),(34,(),()))),(37,(36,(),()),(38,(),()))))
+(55,(51,(41,(39,(38,(),()),(40,(),())),(47,(45,(43,(42,(),()),(44,(),())),(46,(),())),(49,(48,(),()),(50,(),())))),(53,(52,(),()),(54,(),()))),(57,(56,(),()),(58,(),()))) 46 (46,(41,(39,(38,(),()),(40,(),())),(45,(43,(42,(),()),(44,(),())),())),(55,(51,(47,(),(49,(48,(),()),(50,(),()))),(53,(52,(),()),(54,(),()))),(57,(56,(),()),(58,(),()))))
+(17,(15,(14,(),()),(16,(),())),(21,(19,(18,(),()),(20,(),())),(31,(27,(25,(23,(22,(),()),(24,(),())),(26,(),())),(29,(28,(),()),(30,(),()))),(33,(32,(),()),(34,(),()))))) 26 (26,(17,(15,(14,(),()),(16,(),())),(21,(19,(18,(),()),(20,(),())),(25,(23,(22,(),()),(24,(),())),()))),(31,(27,(),(29,(28,(),()),(30,(),()))),(33,(32,(),()),(34,(),()))))
+(51,(37,(35,(34,(),()),(36,(),())),(47,(43,(41,(39,(38,(),()),(40,(),())),(42,(),())),(45,(44,(),()),(46,(),()))),(49,(48,(),()),(50,(),())))),(53,(52,(),()),(54,(),()))) 42 (42,(37,(35,(34,(),()),(36,(),())),(41,(39,(38,(),()),(40,(),())),())),(51,(47,(43,(),(45,(44,(),()),(46,(),()))),(49,(48,(),()),(50,(),()))),(53,(52,(),()),(54,(),()))))
+(29,(27,(26,(),()),(28,(),())),(43,(39,(35,(33,(31,(30,(),()),(32,(),())),(34,(),())),(37,(36,(),()),(38,(),()))),(41,(40,(),()),(42,(),()))),(45,(44,(),()),(46,(),())))) 34 (34,(29,(27,(26,(),()),(28,(),())),(33,(31,(30,(),()),(32,(),())),())),(39,(35,(),(37,(36,(),()),(38,(),()))),(43,(41,(40,(),()),(42,(),())),(45,(44,(),()),(46,(),())))))
+(63,(59,(55,(51,(49,(47,(46,(),()),(48,(),())),(50,(),())),(53,(52,(),()),(54,(),()))),(57,(56,(),()),(58,(),()))),(61,(60,(),()),(62,(),()))),(65,(64,(),()),(66,(),()))) 50 (50,(49,(47,(46,(),()),(48,(),())),()),(63,(55,(51,(),(53,(52,(),()),(54,(),()))),(59,(57,(56,(),()),(58,(),())),(61,(60,(),()),(62,(),())))),(65,(64,(),()),(66,(),()))))
+(8,(6,(5,(),()),(7,(),())),(12,(10,(9,(),()),(11,(),())),(16,(14,(13,(),()),(15,(),())),(20,(18,(17,(),()),(19,(),())),(22,(21,(),()),(24,(23,(),()),(25,(),()))))))) 21 (21,(8,(6,(5,(),()),(7,(),())),(16,(12,(10,(9,(),()),(11,(),())),(14,(13,(),()),(15,(),()))),(20,(18,(17,(),()),(19,(),())),()))),(22,(),(24,(23,(),()),(25,(),()))))
+(42,(28,(26,(25,(),()),(27,(),())),(32,(30,(29,(),()),(31,(),())),(36,(34,(33,(),()),(35,(),())),(38,(37,(),()),(40,(39,(),()),(41,(),())))))),(44,(43,(),()),(45,(),()))) 37 (37,(32,(28,(26,(25,(),()),(27,(),())),(30,(29,(),()),(31,(),()))),(36,(34,(33,(),()),(35,(),())),())),(42,(38,(),(40,(39,(),()),(41,(),()))),(44,(43,(),()),(45,(),()))))
+(20,(18,(17,(),()),(19,(),())),(34,(24,(22,(21,(),()),(23,(),())),(28,(26,(25,(),()),(27,(),())),(30,(29,(),()),(32,(31,(),()),(33,(),()))))),(36,(35,(),()),(37,(),())))) 29 (29,(20,(18,(17,(),()),(19,(),())),(24,(22,(21,(),()),(23,(),())),(28,(26,(25,(),()),(27,(),())),()))),(34,(30,(),(32,(31,(),()),(33,(),()))),(36,(35,(),()),(37,(),()))))
+(54,(50,(40,(38,(37,(),()),(39,(),())),(44,(42,(41,(),()),(43,(),())),(46,(45,(),()),(48,(47,(),()),(49,(),()))))),(52,(51,(),()),(53,(),()))),(56,(55,(),()),(57,(),()))) 45 (45,(40,(38,(37,(),()),(39,(),())),(44,(42,(41,(),()),(43,(),())),())),(54,(50,(46,(),(48,(47,(),()),(49,(),()))),(52,(51,(),()),(53,(),()))),(56,(55,(),()),(57,(),()))))
+(16,(14,(13,(),()),(15,(),())),(20,(18,(17,(),()),(19,(),())),(30,(24,(22,(21,(),()),(23,(),())),(26,(25,(),()),(28,(27,(),()),(29,(),())))),(32,(31,(),()),(33,(),()))))) 25 (25,(16,(14,(13,(),()),(15,(),())),(20,(18,(17,(),()),(19,(),())),(24,(22,(21,(),()),(23,(),())),()))),(30,(26,(),(28,(27,(),()),(29,(),()))),(32,(31,(),()),(33,(),()))))
+(50,(36,(34,(33,(),()),(35,(),())),(46,(40,(38,(37,(),()),(39,(),())),(42,(41,(),()),(44,(43,(),()),(45,(),())))),(48,(47,(),()),(49,(),())))),(52,(51,(),()),(53,(),()))) 41 (41,(36,(34,(33,(),()),(35,(),())),(40,(38,(37,(),()),(39,(),())),())),(50,(46,(42,(),(44,(43,(),()),(45,(),()))),(48,(47,(),()),(49,(),()))),(52,(51,(),()),(53,(),()))))
+(28,(26,(25,(),()),(27,(),())),(42,(38,(32,(30,(29,(),()),(31,(),())),(34,(33,(),()),(36,(35,(),()),(37,(),())))),(40,(39,(),()),(41,(),()))),(44,(43,(),()),(45,(),())))) 33 (33,(28,(26,(25,(),()),(27,(),())),(32,(30,(29,(),()),(31,(),())),())),(38,(34,(),(36,(35,(),()),(37,(),()))),(42,(40,(39,(),()),(41,(),())),(44,(43,(),()),(45,(),())))))
+(62,(58,(54,(48,(46,(45,(),()),(47,(),())),(50,(49,(),()),(52,(51,(),()),(53,(),())))),(56,(55,(),()),(57,(),()))),(60,(59,(),()),(61,(),()))),(64,(63,(),()),(65,(),()))) 49 (49,(48,(46,(45,(),()),(47,(),())),()),(62,(54,(50,(),(52,(51,(),()),(53,(),()))),(58,(56,(55,(),()),(57,(),())),(60,(59,(),()),(61,(),())))),(64,(63,(),()),(65,(),()))))
+(14,(12,(11,(),()),(13,(),())),(18,(16,(15,(),()),(17,(),())),(22,(20,(19,(),()),(21,(),())),(28,(24,(23,(),()),(26,(25,(),()),(27,(),()))),(30,(29,(),()),(31,(),())))))) 23 (23,(14,(12,(11,(),()),(13,(),())),(22,(18,(16,(15,(),()),(17,(),())),(20,(19,(),()),(21,(),()))),())),(24,(),(28,(26,(25,(),()),(27,(),())),(30,(29,(),()),(31,(),())))))
+(48,(34,(32,(31,(),()),(33,(),())),(38,(36,(35,(),()),(37,(),())),(44,(40,(39,(),()),(42,(41,(),()),(43,(),()))),(46,(45,(),()),(47,(),()))))),(50,(49,(),()),(51,(),()))) 39 (39,(38,(34,(32,(31,(),()),(33,(),())),(36,(35,(),()),(37,(),()))),()),(48,(40,(),(44,(42,(41,(),()),(43,(),())),(46,(45,(),()),(47,(),())))),(50,(49,(),()),(51,(),()))))
+(26,(24,(23,(),()),(25,(),())),(40,(30,(28,(27,(),()),(29,(),())),(36,(32,(31,(),()),(34,(33,(),()),(35,(),()))),(38,(37,(),()),(39,(),())))),(42,(41,(),()),(43,(),())))) 31 (31,(26,(24,(23,(),()),(25,(),())),(30,(28,(27,(),()),(29,(),())),())),(40,(32,(),(36,(34,(33,(),()),(35,(),())),(38,(37,(),()),(39,(),())))),(42,(41,(),()),(43,(),()))))
+(60,(56,(46,(44,(43,(),()),(45,(),())),(52,(48,(47,(),()),(50,(49,(),()),(51,(),()))),(54,(53,(),()),(55,(),())))),(58,(57,(),()),(59,(),()))),(62,(61,(),()),(63,(),()))) 47 (47,(46,(44,(43,(),()),(45,(),())),()),(60,(56,(48,(),(52,(50,(49,(),()),(51,(),())),(54,(53,(),()),(55,(),())))),(58,(57,(),()),(59,(),()))),(62,(61,(),()),(63,(),()))))
+(22,(20,(19,(),()),(21,(),())),(26,(24,(23,(),()),(25,(),())),(36,(32,(28,(27,(),()),(30,(29,(),()),(31,(),()))),(34,(33,(),()),(35,(),()))),(38,(37,(),()),(39,(),()))))) 27 (27,(22,(20,(19,(),()),(21,(),())),(26,(24,(23,(),()),(25,(),())),())),(36,(28,(),(32,(30,(29,(),()),(31,(),())),(34,(33,(),()),(35,(),())))),(38,(37,(),()),(39,(),()))))
+(56,(42,(40,(39,(),()),(41,(),())),(52,(48,(44,(43,(),()),(46,(45,(),()),(47,(),()))),(50,(49,(),()),(51,(),()))),(54,(53,(),()),(55,(),())))),(58,(57,(),()),(59,(),()))) 43 (43,(42,(40,(39,(),()),(41,(),())),()),(56,(52,(44,(),(48,(46,(45,(),()),(47,(),())),(50,(49,(),()),(51,(),())))),(54,(53,(),()),(55,(),()))),(58,(57,(),()),(59,(),()))))
+(34,(32,(31,(),()),(33,(),())),(48,(44,(40,(36,(35,(),()),(38,(37,(),()),(39,(),()))),(42,(41,(),()),(43,(),()))),(46,(45,(),()),(47,(),()))),(50,(49,(),()),(51,(),())))) 35 (35,(34,(32,(31,(),()),(33,(),())),()),(44,(36,(),(40,(38,(37,(),()),(39,(),())),(42,(41,(),()),(43,(),())))),(48,(46,(45,(),()),(47,(),())),(50,(49,(),()),(51,(),())))))
+(68,(64,(60,(56,(52,(51,(),()),(54,(53,(),()),(55,(),()))),(58,(57,(),()),(59,(),()))),(62,(61,(),()),(63,(),()))),(66,(65,(),()),(67,(),()))),(70,(69,(),()),(71,(),()))) 51 (51,(),(68,(60,(52,(),(56,(54,(53,(),()),(55,(),())),(58,(57,(),()),(59,(),())))),(64,(62,(61,(),()),(63,(),())),(66,(65,(),()),(67,(),())))),(70,(69,(),()),(71,(),()))))
diff --git a/02-splay_operation/task.md b/02-splay_operation/task.md
new file mode 100644
index 0000000..1967c79
--- /dev/null
+++ b/02-splay_operation/task.md
@@ -0,0 +1,9 @@
+Given an implementation of a binary search tree including parent pointers:
+- implement `splay` method, preferably utilizing the provided `rotate` operation
+ performing a single rotation;
+- update `lookup`, `insert` and `remove` methods to utilize it correctly.
+
+You should submit the `splay_operation.*` file (but not the
+`splay_operation_test.*`).
+
+Source code templates can be found in [git](https://gitlab.kam.mff.cuni.cz/datovky/assignments/-/tree/master).
--
GitLab