diff --git a/02-splay_operation/cpp/Makefile b/02-splay_operation/cpp/Makefile
new file mode 100644
index 0000000000000000000000000000000000000000..4ca82749b82280d73f3eb750ae3167fa1fbafd4f
--- /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 0000000000000000000000000000000000000000..249f3dd7222ad3e3ce3870f478f91a9bf85bcab4
--- /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 0000000000000000000000000000000000000000..d1e6c996b56b28dd37db3d85ddd7d817c82269b9
--- /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 0000000000000000000000000000000000000000..7f3259e5d6a4689f8e7cc608e450905b82647b7b
--- /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 0000000000000000000000000000000000000000..3f4aff0785f636b7fd0ea1a15aa69dafe06f290f
--- /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 0000000000000000000000000000000000000000..4e40e04ca2ad5a6423a3ca189faabb933d3d498e
--- /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 0000000000000000000000000000000000000000..b342520d608ef65eec87adce7f927187defc6205
--- /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 0000000000000000000000000000000000000000..7f3259e5d6a4689f8e7cc608e450905b82647b7b
--- /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 0000000000000000000000000000000000000000..86157d290268c1cfb5005c8c3f26bf2873b9a5b0
--- /dev/null
+++ b/02-splay_operation/task.md
@@ -0,0 +1,7 @@
+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.*`).
diff --git a/03-splay_experiment/cpp/Makefile b/03-splay_experiment/cpp/Makefile
new file mode 100644
index 0000000000000000000000000000000000000000..aa0b7d534cd4240f8073fbbb4896685105db0ac9
--- /dev/null
+++ b/03-splay_experiment/cpp/Makefile
@@ -0,0 +1,22 @@
+STUDENT_ID ?= PLEASE_SET_STUDENT_ID
+
+.PHONY: test
+test: splay_experiment
+ @rm -rf out && mkdir out
+ @for test in sequential random subset ; do \
+ for mode in std naive ; do \
+ echo t-$$test-$$mode ; \
+ ./splay_experiment $$test $(STUDENT_ID) $$mode >out/t-$$test-$$mode ; \
+ done ; \
+ done
+
+INCLUDE ?= .
+CXXFLAGS=-std=c++11 -O2 -Wall -Wextra -g -Wno-sign-compare -I$(INCLUDE)
+
+splay_experiment: splay_operation.h splay_experiment.cpp $(INCLUDE)/random.h
+ $(CXX) $(CPPFLAGS) $(CXXFLAGS) $^ -o $@
+
+.PHONY: clean
+clean:
+ rm -f splay_experiment
+ rm -rf out
diff --git a/03-splay_experiment/cpp/random.h b/03-splay_experiment/cpp/random.h
new file mode 100644
index 0000000000000000000000000000000000000000..5ef10aeb1fe7e58a48277fb3565169ec267d43d9
--- /dev/null
+++ b/03-splay_experiment/cpp/random.h
@@ -0,0 +1,61 @@
+#ifndef DS1_RANDOM_H
+#define DS1_RANDOM_H
+
+#include <cstdint>
+
+/*
+ * This is the xoroshiro128+ random generator, designed in 2016 by David Blackman
+ * and Sebastiano Vigna, distributed under the CC-0 license. For more details,
+ * see http://vigna.di.unimi.it/xorshift/.
+ *
+ * Rewritten to C++ by Martin Mares, also placed under CC-0.
+ */
+
+class RandomGen {
+ uint64_t state[2];
+
+ uint64_t rotl(uint64_t x, int k)
+ {
+ return (x << k) | (x >> (64 - k));
+ }
+
+ public:
+ // Initialize the generator, set its seed and warm it up.
+ RandomGen(unsigned int seed)
+ {
+ state[0] = seed * 0xdeadbeef;
+ state[1] = seed ^ 0xc0de1234;
+ for (int i=0; i<100; i++)
+ next_u64();
+ }
+
+ // Generate a random 64-bit number.
+ uint64_t next_u64(void)
+ {
+ uint64_t s0 = state[0], s1 = state[1];
+ uint64_t result = s0 + s1;
+ s1 ^= s0;
+ state[0] = rotl(s0, 55) ^ s1 ^ (s1 << 14);
+ state[1] = rotl(s1, 36);
+ return result;
+ }
+
+ // Generate a random 32-bit number.
+ uint32_t next_u32(void)
+ {
+ return next_u64() >> 11;
+ }
+
+ // Generate a number between 0 and range-1.
+ unsigned int next_range(unsigned int range)
+ {
+ /*
+ * This is not perfectly uniform, unless the range is a power of two.
+ * However, for 64-bit random values and 32-bit ranges, the bias is
+ * insignificant.
+ */
+ return next_u64() % range;
+ }
+};
+
+#endif
diff --git a/03-splay_experiment/cpp/splay_experiment.cpp b/03-splay_experiment/cpp/splay_experiment.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..a47da8b11bcff20db58805a330f8b05d0a6c15b5
--- /dev/null
+++ b/03-splay_experiment/cpp/splay_experiment.cpp
@@ -0,0 +1,208 @@
+#include <algorithm>
+#include <functional>
+#include <string>
+#include <utility>
+#include <vector>
+#include <iostream>
+#include <cmath>
+
+#include "splay_operation.h"
+#include "random.h"
+
+using namespace std;
+
+/*
+ * A modified Splay tree for benchmarking.
+ *
+ * We inherit the implementation of operations from the Tree class
+ * and extend it by keeping statistics on the number of splay operations
+ * and the total number of rotations. Also, if naive is turned on,
+ * splay uses only single rotations.
+ *
+ * Please make sure that your Tree class defines the rotate() and splay()
+ * methods as virtual.
+ */
+
+class BenchmarkingTree : public Tree {
+public:
+ int num_operations;
+ int num_rotations;
+ bool do_naive;
+
+ BenchmarkingTree(bool naive=false)
+ {
+ do_naive = naive;
+ reset();
+ }
+
+ void reset()
+ {
+ num_operations = 0;
+ num_rotations = 0;
+ }
+
+ void rotate(Node *node) override
+ {
+ num_rotations++;
+ Tree::rotate(node);
+ }
+
+ void splay(Node *node) override
+ {
+ num_operations++;
+ if (do_naive) {
+ while (node->parent)
+ rotate(node);
+ } else {
+ Tree::splay(node);
+ }
+ }
+
+ // Return the average number of rotations per operation.
+ double rot_per_op()
+ {
+ if (num_operations > 0)
+ return (double) num_rotations / num_operations;
+ else
+ return 0;
+ }
+};
+
+bool naive; // Use of naive rotations requested
+RandomGen *rng; // Random generator object
+
+void test_sequential()
+{
+ for (int n=100; n<=3000; n+=100) {
+ BenchmarkingTree tree = BenchmarkingTree(naive);
+
+ for (int x=0; x<n; x++)
+ tree.insert(x);
+
+ for (int i=0; i<5; i++)
+ for (int x=0; x<n; x++)
+ tree.lookup(x);
+
+ cout << n << " " << tree.rot_per_op() << endl;
+ }
+}
+
+// An auxiliary function for generating a random permutation.
+vector<int> random_permutation(int n)
+{
+ vector<int> perm;
+ for (int i=0; i<n; i++)
+ perm.push_back(i);
+ for (int i=0; i<n-1; i++)
+ swap(perm[i], perm[i + rng->next_range(n-i)]);
+ return perm;
+}
+
+void test_random()
+{
+ for (int e=32; e<=64; e++) {
+ int n = (int) pow(2, e/4.);
+ BenchmarkingTree tree = BenchmarkingTree(naive);
+
+ vector<int> perm = random_permutation(n);
+ for (int x : perm)
+ tree.insert(x);
+
+ for (int i=0; i<5*n; i++)
+ tree.lookup(rng->next_range(n));
+
+ cout << n << " " << tree.rot_per_op() << endl;
+ }
+}
+
+/*
+ * An auxiliary function for constructing arithmetic progressions.
+ * The vector seq will be modified to contain an arithmetic progression
+ * of elements in interval [A,B] starting from position s with step inc.
+ */
+void make_progression(vector<int> &seq, int A, int B, int s, int inc)
+{
+ for (int i=0; i<seq.size(); i++)
+ while (seq[i] >= A && seq[i] <= B && s + inc*(seq[i]-A) != i)
+ swap(seq[i], seq[s + inc*(seq[i] - A)]);
+}
+
+void test_subset_s(int sub)
+{
+ for (int e=32; e<=64; e++) {
+ int n = (int) pow(2, e/4.);
+ if (n < sub)
+ continue;
+
+ // We will insert elements in order, which contain several
+ // arithmetic progressions interspersed with random elements.
+ vector<int> seq = random_permutation(n);
+ make_progression(seq, n/4, n/4 + n/20, n/10, 1);
+ make_progression(seq, n/2, n/2 + n/20, n/10, -1);
+ make_progression(seq, 3*n/4, 3*n/4 + n/20, n/2, -4);
+ make_progression(seq, 17*n/20, 17*n/20 + n/20, 2*n/5, 5);
+
+ BenchmarkingTree tree = BenchmarkingTree(naive);
+ for (int x : seq)
+ tree.insert(x);
+ tree.reset();
+
+ for (int i=0; i<10000; i++)
+ tree.lookup(seq[rng->next_range(sub)]);
+
+ cout << sub << " " << n << " " << tree.rot_per_op() << endl;
+ }
+}
+
+void test_subset()
+{
+ test_subset_s(10);
+ test_subset_s(100);
+ test_subset_s(1000);
+}
+
+vector<pair<string, function<void()>>> tests = {
+ { "sequential", test_sequential },
+ { "random", test_random },
+ { "subset", test_subset },
+};
+
+int main(int argc, char **argv)
+{
+ if (argc != 4) {
+ cerr << "Usage: " << argv[0] << " <test> <student-id> (std|naive)" << endl;
+ return 1;
+ }
+
+ string which_test = argv[1];
+ string id_str = argv[2];
+ string mode = argv[3];
+
+ try {
+ rng = new RandomGen(stoi(id_str));
+ } catch (...) {
+ cerr << "Invalid student ID" << endl;
+ return 1;
+ }
+
+ if (mode == "std")
+ naive = false;
+ else if (mode == "naive")
+ naive = true;
+ else
+ {
+ cerr << "Last argument must be either 'std' or 'naive'" << endl;
+ return 1;
+ }
+
+ for (const auto& test : tests) {
+ if (test.first == which_test)
+ {
+ cout.precision(12);
+ test.second();
+ return 0;
+ }
+ }
+ cerr << "Unknown test " << which_test << endl;
+ return 1;
+}
diff --git a/03-splay_experiment/python/Makefile b/03-splay_experiment/python/Makefile
new file mode 100644
index 0000000000000000000000000000000000000000..ac6c02d43598e1fd3745820a9a7b3995e8377774
--- /dev/null
+++ b/03-splay_experiment/python/Makefile
@@ -0,0 +1,15 @@
+STUDENT_ID ?= PLEASE_SET_STUDENT_ID
+
+.PHONY: test
+test: splay_experiment.py
+ @rm -rf out && mkdir out
+ @for test in sequential random subset ; do \
+ for mode in std naive ; do \
+ echo t-$$test-$$mode ; \
+ ./splay_experiment.py $$test $(STUDENT_ID) $$mode >out/t-$$test-$$mode ; \
+ done ; \
+ done
+
+.PHONY: clean
+clean:
+ rm -rf out
diff --git a/03-splay_experiment/python/splay_experiment.py b/03-splay_experiment/python/splay_experiment.py
new file mode 100755
index 0000000000000000000000000000000000000000..8cf3d6d6af1564973bd17a43f2fa731cce083da7
--- /dev/null
+++ b/03-splay_experiment/python/splay_experiment.py
@@ -0,0 +1,127 @@
+#!/usr/bin/env python3
+
+import sys
+import random
+
+from splay_operation import Tree
+
+class BenchmarkingTree(Tree):
+ """ A modified Splay tree for benchmarking.
+
+ We inherit the implementation of operations from the Tree class
+ and extend it by keeping statistics on the number of splay operations
+ and the total number of rotations. Also, if naive is turned on,
+ splay uses only single rotations.
+ """
+
+ def __init__(self, naive=False):
+ Tree.__init__(self)
+ self.do_naive = naive
+ self.reset()
+
+ def reset(self):
+ """Reset statistics."""
+ self.num_rotations = 0;
+ self.num_operations = 0;
+
+ def rotate(self, node):
+ self.num_rotations += 1
+ Tree.rotate(self, node)
+
+ def splay(self, node):
+ self.num_operations += 1
+ if self.do_naive:
+ while node.parent is not None:
+ self.rotate(node)
+ else:
+ Tree.splay(self, node)
+
+ def rot_per_op(self):
+ """Return the average number of rotations per operation."""
+ if self.num_operations > 0:
+ return self.num_rotations / self.num_operations
+ else:
+ return 0
+
+def test_sequential():
+ for n in range(100, 3001, 100):
+ tree = BenchmarkingTree(naive)
+ for elem in range(n):
+ tree.insert(elem)
+
+ for _ in range(5):
+ for elem in range(n):
+ tree.lookup(elem)
+
+ print(n, tree.rot_per_op())
+
+def test_random():
+ for exp in range(32, 64):
+ n = int(2**(exp/4))
+ tree = BenchmarkingTree(naive)
+
+ for elem in random.sample(range(n), n):
+ tree.insert(elem)
+
+ for _ in range(5*n):
+ tree.lookup(random.randrange(n))
+
+ print(n, tree.rot_per_op())
+
+def make_progression(seq, A, B, s, inc):
+ """An auxiliary function for constructing arithmetic progressions.
+
+ The array seq will be modified to contain an arithmetic progression
+ of elements in interval [A,B] starting from position s with step inc.
+ """
+ for i in range(len(seq)):
+ while seq[i] >= A and seq[i] <= B and s + inc*(seq[i]-A) != i:
+ pos = s + inc*(seq[i]-A)
+ seq[i], seq[pos] = seq[pos], seq[i]
+
+def test_subset():
+ for sub in [10, 100, 1000]:
+ for exp in range(32,64):
+ n = int(2**(exp/4))
+ if n < sub:
+ continue
+
+ # We will insert elements in order, which contain several
+ # arithmetic progressions interspersed with random elements.
+ seq = random.sample(range(n), n)
+ make_progression(seq, n//4, n//4 + n//20, n//10, 1)
+ make_progression(seq, n//2, n//2 + n//20, n//10, -1)
+ make_progression(seq, 3*n//4, 3*n//4 + n//20, n//2, -4)
+ make_progression(seq, 17*n//20, 17*n//20 + n//20, 2*n//5, 5)
+
+ tree = BenchmarkingTree(naive)
+ for elem in seq:
+ tree.insert(elem)
+ tree.reset()
+
+ for _ in range(10000):
+ tree.lookup(seq[random.randrange(sub)])
+
+ print(sub, n, tree.rot_per_op())
+
+tests = {
+ "sequential": test_sequential,
+ "random": test_random,
+ "subset": test_subset,
+}
+
+if len(sys.argv) == 4:
+ test, student_id = sys.argv[1], sys.argv[2]
+ if sys.argv[3] == "std":
+ naive = False
+ elif sys.argv[3] == "naive":
+ naive = True
+ else:
+ raise ValueError("Last argument must be either 'std' or 'naive'")
+ random.seed(student_id)
+ if test in tests:
+ tests[test]()
+ else:
+ raise ValueError("Unknown test {}".format(test))
+else:
+ raise ValueError("Usage: {} <test> <student-id> (std|naive)".format(sys.argv[0]))
diff --git a/03-splay_experiment/task.md b/03-splay_experiment/task.md
new file mode 100644
index 0000000000000000000000000000000000000000..8120d9a05a42ccdcb2ddee6ab285255a1c8d890e
--- /dev/null
+++ b/03-splay_experiment/task.md
@@ -0,0 +1,85 @@
+## Goal
+
+The goal of this assignment is to evaluate your implementation of Splay trees
+experimentally and to compare it with a "naive" implementation which splays
+using single rotations only.
+
+You are given a test program (`splay_experiment`) which calls your
+implementation from the previous assignment to perform the following
+experiments:
+
+- _Sequential test:_ Insert _n_ elements sequentially and then repeatedly
+ find them all in sequential order.
+- _Random test:_ Insert _n_ elements in random order and then find _5n_
+ random elements.
+- _Subset test:_ Insert a sequence of _n_ elements, which contains arithmetic
+ progressions interspersed with random elements. Then repeatedly access
+ a small subset of these elements in random order. Try this with subsets of
+ different cardinalities.
+
+The program tries each experiment with different values of _n_. In each try,
+it prints the average number of rotations per splay operation.
+
+You should perform these experiments and write a report, which contains the following
+plots of the measured data. Each plot should show the dependence of the average
+number of rotations on the set size _n_.
+
+- The sequential test: one curve for the standard implementation, one for the naive one.
+- The random test: one curve for the standard implementation, one for the naive one.
+- The subset test: three curves for the standard implementation with different sizes
+ of the subset, three for the naive implementation with the same sizes.
+
+The report should discuss the experimental results and try to explain the observed
+behavior using theory from the lectures. (If you want, you can carry out further
+experiments to gain better understanding of the data structure and include these
+in the report. This is strictly optional.)
+
+You should submit a PDF file with the report (and no source code).
+You will get 1 temporary point upon submission if the file is syntantically correct;
+proper points will be assigned later.
+
+## Test program
+
+The test program is given three arguments:
+- The name of the test (`sequential`, `random`, `subset`).
+- The random seed: you should use the last 2 digits of your student ID (you can find
+ it in the Study Information System – just click on the Personal data icon). Please
+ include the random seed in your report.
+- The implementation to test (`std` or `naive`).
+
+The output of the program contains one line per experiment, which consists of:
+- For the sequential and random test: the set size and the average number of rotations.
+- For the subset test: the subset size, the set size, and the average number of rotations
+ per find. The initial insertions of the full set are not counted.
+
+## Your implementation
+
+Please use your implementation from the previous exercise. Methods `splay()`
+and `rotate()` will be augmented by the test program. If you are performing
+a double rotation directly instead of composing it from single rotations, you
+need to adjust the `BenchmarkingTree` class accordingly.
+
+## Hints
+
+The following tools can be useful for producing nice plots:
+- [pandas](https://pandas.pydata.org/)
+- [matplotlib](https://matplotlib.org/)
+- [gnuplot](http://www.gnuplot.info/)
+
+A quick checklist for plots:
+- Is there a caption explaining what is plotted?
+- Are the axes clearly labelled? Do they have value ranges and units?
+- Have you mentioned that this axis has logarithmic scale? (Logarithmic graphs
+ are more fitting in some cases, but you should tell.)
+- Is it clear which curve means what?
+- Is it clear what are the measured points and what is an interpolated
+ curve between them?
+- Are there any overlaps? (E.g., the most interesting part of the curve
+ hidden underneath a label?)
+
+In your discussion, please distinguish the following kinds of claims.
+It should be always clear which is which:
+- Experimental results (i.e., the raw data you obtained from the experiments)
+- Theoretical facts (i.e., claims we have proved mathematically)
+- Your hypotheses (e.g., when you claim that the graph looks like something is true,
+ but you are not able to prove rigorously that it always holds)