Commit 789e7506 authored by Martin Mareš's avatar Martin Mareš
Browse files

Tree successor

parent d5df0222
test: tree_successor_test
CXXFLAGS=-std=c++11 -O2 -Wall -Wextra -g -Wno-sign-compare
tree_successor_test: tree_successor.h tree_successor_test.cpp test_main.cpp
$(CXX) $(CXXFLAGS) $^ -o $@
rm -f tree_successor_test
.PHONY: clean test
#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;
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)
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;
found = true;
if (!found) {
cerr << "Unknown test " << required_test << endl;
return 1;
return 0;
// A node of the tree
class Node {
int key;
Node* left;
Node* right;
Node* parent;
// Constructor
Node(int key, Node* parent=nullptr) {
this->key = key;
this->parent = parent;
this->left = nullptr;
this->right = nullptr;
// Binary tree
class Tree {
// Pointer to root of the tree; nullptr if the tree is empty.
Node* root = nullptr;
// Insert a key into the tree.
// If the key is already present, nothing happens.
void insert(int key) {
if (!root) {
root = new Node(key);
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;
// Return successor of the given node.
// The successor of a node is the node with the next higher key.
// Return nullptr if there is no such node.
// If the argument is nullptr, return the node with the smallest key.
Node* successor(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;
#include <algorithm>
#include <functional>
#include <cstdint>
#include <string>
#include <utility>
#include <vector>
#include "tree_successor.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);
void test(const vector<int>& sequence) {
Tree tree;
for (const auto& element : sequence)
vector<int> sorted_sequence(sequence);
sort(sorted_sequence.begin(), sorted_sequence.end());
Node* node = tree.successor(nullptr);
for (const auto& element : sorted_sequence) {
EXPECT(node, "Expected successor " + to_string(element) + ", got nullptr");
EXPECT(node->key == element,
"Expected successor " + to_string(element) + ", got " + to_string(node->key));
node = tree.successor(node);
EXPECT(!node, "Expected no successor, got " + to_string(node->key));
vector<pair<string, function<void()>>> tests = {
{"right_path", []
{ vector<int> numbers;
for (int i = 0; i < 10000; i++) numbers.push_back((int)(7.13*i));
{"left_path", []
{ vector<int> numbers;
for (int i = 9999; i >= 0; i--) numbers.push_back((int)(7.13*i));
{"random_tree", []
{ vector<int> numbers = {997};
for (int i = 2; i < 199999; i++)
numbers.push_back((numbers.back() * int64_t(997)) % 199999);
#!/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.left = left
self.right = right
self.parent = parent
class Tree:
"""A simple binary search tree"""
def __init__(self, root=None):
self.root = root
def insert(self, key):
"""Insert key into the tree.
If the key is already present, do nothing.
if self.root is None:
self.root = Node(key)
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
if node.right is None:
node.right = Node(key, parent=node)
node = node.right
def successor(self, node=None):
"""Return successor of the given node.
The successor of a node is the node with the next greater key.
Return None if there is no such node.
If the argument is None, return the node with the smallest key.
# TODO: Implement
raise NotImplementedError
#!/usr/bin/env python3
import sys
import tree_successor
def test_sequence(sequence):
tree = tree_successor.Tree()
for i in sequence: tree.insert(i)
node = tree.successor(None)
for element in sorted(sequence):
assert node is not None, "Expected successor {}, got None".format(element)
assert node.key == element, "Expected successor {}, got {}".format(element, node.key)
node = tree.successor(node)
assert node is None, "Expected no successor, got {}".format(node.key)
def gen_increasing_seq():
return [int(7.13*i) for i in range(10000)]
tests = [
("right_path", lambda: test_sequence(gen_increasing_seq())),
("left_path", lambda: test_sequence(list(reversed(gen_increasing_seq())))),
("random_tree", lambda: test_sequence([pow(997, i, 199999) for i in range(1, 199999)])),
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)
raise ValueError("Unknown test {}".format(name))
Given an implementation of a simple binary search tree including parent
pointers, implement a `successor` method. The methods is given a node
and it should return another node of the tree with the next higher key
(i.e., the smallest of keys which are greater than the given one).
- If there is no such node, it should return a null pointer.
- The given node can also be a null pointer, in which case the method should
return the smallest node in the tree.
You can expect that `successor` method is never called on an empty tree.
You should submit the file `tree_successor.*` (but not the
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