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tests.cpp
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//
// Created by alex on 7/31/17.
//
#include "cpp_solutions/chapter_01_arrays_and_strings/chapter_01_includes.h"
#include "cpp_solutions/chapter_02_linked_lists/chapter_02_includes.h"
#include "cpp_solutions/chapter_03_stacks_and_queues/chapter_03_includes.h"
#include "cpp_solutions/chapter_04_trees_and_graphs/chapter_04_includes.h"
#include "cpp_solutions/chapter_05_bit_manipulation/chapter_05_includes.h"
#include "cpp_solutions/chapter_08_recursion_and_dynamic_programming/chapter_08_includes.h"
#include "cpp_solutions/chapter_10_sorting_and_searching/chapter_10_includes.h"
#include "cpp_solutions/chapter_12_cpp/chapter_12_includes.h"
#include "cpp_solutions/misc_exercises/misc_includes.h"
#define CATCH_CONFIG_MAIN
#include "cpp_solutions/third_party/Catch/include/catch.hpp"
#include <vector>
#include <Eigen/Dense>
#include <random>
TEST_CASE("Chapter 01 - Problem 01 - isUnique()", "test"){
REQUIRE(chapter_01::isUnique("alex"));
REQUIRE(!chapter_01::isUnique("aalex"));
}
TEST_CASE("Chapter 01 - Problem 02 - isPermutation()", "test"){
REQUIRE(!chapter_01::isPermutation("alex", "aalex"));
REQUIRE(chapter_01::isPermutation("alex", "xela"));
REQUIRE(!chapter_01::isPermutation("aabb", "aaaa"));
REQUIRE(!chapter_01::isPermutation("aaaa", "aabb"));
REQUIRE(!chapter_01::isPermutation("aaaa", "aa"));
REQUIRE(chapter_01::isPermutation("", ""));
}
TEST_CASE("Chapter 01 - Problem 03 - URLify()", "test") {
// expect 'Mr. John Smith' -> 'Mr.%20John%20Smith'
std::string input1 = "Mr. John Smith ";
std::string output1 = "Mr.%20John%20Smith%20";
chapter_01::URLify(input1);
REQUIRE(input1 == output1);
std::string input2 = "";
std::string output2 = "";
chapter_01::URLify(input2);
REQUIRE(input2 == output2);
std::string input3 = " ";
std::string output3 = "%20";
chapter_01::URLify(input3);
REQUIRE(input3 == output3);
std::string input4 = "Alex";
std::string output4 = "Alex";
chapter_01::URLify(input4);
REQUIRE(input4 == output4);
}
TEST_CASE("Chapter 01 - Problem 04 - palindromePermutation()", "test") {
REQUIRE(chapter_01::palindromePermutation("tact coa"));
REQUIRE(!chapter_01::palindromePermutation("Tact Coa"));
REQUIRE(!chapter_01::palindromePermutation("xyz"));
REQUIRE(chapter_01::palindromePermutation("AA B AA"));
REQUIRE(!chapter_01::palindromePermutation("aA B AA"));
}
TEST_CASE("Chapter 01 - Problem 05 - oneAway()", "test"){
REQUIRE(chapter_01::oneAway("pale", "ple"));
REQUIRE(chapter_01::oneAway("pale", "pale"));
REQUIRE(chapter_01::oneAway("pale", "bale"));
REQUIRE(!chapter_01::oneAway("pale", "bae"));
REQUIRE(!chapter_01::oneAway("alex", "al"));
REQUIRE(!chapter_01::oneAway("alex", "all"));
REQUIRE(!chapter_01::oneAway("alex", "alll"));
REQUIRE(chapter_01::oneAway("apple", "aple"));
REQUIRE(chapter_01::oneAway("bale", "pale"));
REQUIRE(chapter_01::oneAway("", ""));
}
TEST_CASE("Chapter 01 - Problem 06 - stringCompression()", "test"){
REQUIRE("a2b1c5a3" == chapter_01::stringCompression("aabcccccaaa"));
REQUIRE("alex" == chapter_01::stringCompression("alex"));
REQUIRE("" == chapter_01::stringCompression(""));
REQUIRE("a10" == chapter_01::stringCompression("aaaaaaaaaa"));
}
TEST_CASE("Chapter 01 - Problem 07 - rotateMatrix()", "test"){
Eigen::MatrixXi input4x4(4,4);
input4x4 << 1, 2, 3, 4,
1, 2, 3, 4,
1, 2, 3, 4,
1, 2, 3, 4;
Eigen::MatrixXi input5x5(5,5);
input5x5 << 1, 2, 3, 4, 5,
1, 2, 3, 4, 5,
1, 2, 3, 4, 5,
1, 2, 3, 4, 5,
1, 2, 3, 4, 5;
Eigen::MatrixXi output4x4(4,4);
output4x4 << 1, 1, 1, 1,
2, 2, 2, 2,
3, 3, 3, 3,
4, 4, 4, 4;
Eigen::MatrixXi output5x5(5,5);
output5x5 << 1, 1, 1, 1, 1,
2, 2, 2, 2, 2,
3, 3, 3, 3, 3,
4, 4, 4, 4, 4,
5, 5, 5, 5, 5;
chapter_01::rotate(input4x4);
chapter_01::rotate(input5x5);
REQUIRE(input4x4.isApprox(output4x4));
REQUIRE(input5x5.isApprox(output5x5));
}
TEST_CASE("Chapter 01 - Problem 08 - setZero()", "test"){
// assume rotations are clockwise
Eigen::MatrixXi input4x4(4,4);
input4x4 << 1, 2, 3, 4,
1, 2, 0, 4,
1, 2, 3, 4,
0, 2, 3, 4;
Eigen::MatrixXi input5x5(5,5);
input5x5 << 0, 2, 3, 4, 5,
1, 2, 0, 4, 5,
1, 2, 3, 4, 5,
1, 2, 3, 4, 0,
1, 2, 3, 4, 5;
Eigen::MatrixXi output4x4(4,4);
output4x4 << 0, 2, 0, 4,
0, 0, 0, 0,
0, 2, 0, 4,
0, 0, 0, 0;
Eigen::MatrixXi output5x5(5,5);
output5x5 << 0, 0, 0, 0, 0,
0, 0, 0, 0, 0,
0, 2, 0, 4, 0,
0, 0, 0, 0, 0,
0, 2, 0, 4, 0;
chapter_01::setZero(input4x4);
chapter_01::setZero(input5x5);
REQUIRE(input4x4.isApprox(output4x4));
REQUIRE(input5x5.isApprox(output5x5));
}
TEST_CASE("Chapter 01 - Problem 09 - stringRotation()", "test"){
REQUIRE(chapter_01::stringRotation("waterbottle", "erbottlewat"));
REQUIRE(!chapter_01::stringRotation("waterbottle", "erbottlewatx"));
REQUIRE(chapter_01::stringRotation("", ""));
}
TEST_CASE("Chapter 02 - Basic LinkedList Functionality", "test"){
std::vector<int> testVector = {1,2,3,4,5,6,7};
REQUIRE(testVector == chapter_02::listToVector(chapter_02::vectorToList(testVector)));
}
TEST_CASE("Chapter 02 - Problem 01 - removeDups()", "test"){
std::vector<int> noDups = {1,7,3,6,5,4,2};
std::vector<int> dups = {2,2,1,5,6,2,5,2,7,7};
std::vector<int> fixedDups = {2,1,5,6,7};
std::vector<int> emptyVec;
// check that remove dups function doesn't affect lists with no dups
chapter_02::SinglyLinkedNode<int>* noDupsHead = chapter_02::vectorToList(noDups);
chapter_02::removeDups(noDupsHead);
REQUIRE(noDups == chapter_02::listToVector(noDupsHead));
// check case with duplicates
chapter_02::SinglyLinkedNode<int>* dupsHead = chapter_02::vectorToList(dups);
chapter_02::removeDups(dupsHead);
REQUIRE(fixedDups == chapter_02::listToVector(dupsHead));
// check case with empty list
chapter_02::SinglyLinkedNode<int>* emptyHead = chapter_02::vectorToList(emptyVec);
chapter_02::removeDups(emptyHead);
REQUIRE(emptyVec == chapter_02::listToVector(emptyHead));
}
TEST_CASE("Chapter 02 - Problem 02 - returnKthToLast()", "test"){
std::vector<int> testVec1 = {1,7,3,6,5,4,2};
std::vector<int> testVec2 = {2,2,1,5,6,2,5,2,7,7};
std::vector<int> testVec3;
chapter_02::SinglyLinkedNode<int>* testVec1Head = chapter_02::vectorToList(testVec1);
chapter_02::SinglyLinkedNode<int>* testVec2Head = chapter_02::vectorToList(testVec2);
chapter_02::SinglyLinkedNode<int>* testVec3Head = chapter_02::vectorToList(testVec3);
REQUIRE(5 == chapter_02::returnKthToLast(testVec1Head, 3)->getValue());
REQUIRE(2 == chapter_02::returnKthToLast(testVec1Head, 1)->getValue());
REQUIRE(1 == chapter_02::returnKthToLast(testVec1Head, testVec1.size())->getValue());
REQUIRE(2 == chapter_02::returnKthToLast(testVec2Head, 3)->getValue());
REQUIRE(7 == chapter_02::returnKthToLast(testVec2Head, 1)->getValue());
REQUIRE(2 == chapter_02::returnKthToLast(testVec2Head, testVec2.size())->getValue());
REQUIRE(nullptr == chapter_02::returnKthToLast(testVec2Head, 0));
REQUIRE(nullptr == chapter_02::returnKthToLast(testVec1Head, 10));
REQUIRE(nullptr == chapter_02::returnKthToLast(testVec3Head, 10));
}
TEST_CASE("Chapter 02 - Problem 03 - deleteMiddleNode()", "test"){
// create test dataset
std::vector<std::string> testVec = {"a", "b", "c", "d", "e", "f"};
std::vector<std::string> expectedVec = {"a", "b", "d", "e", "f"};
chapter_02::SinglyLinkedNode<std::string>* testVecHead = chapter_02::vectorToList(testVec);
chapter_02::SinglyLinkedNode<std::string>* expectedVecHead = chapter_02::vectorToList(expectedVec);
// traverse input to find node with content "c"
chapter_02::SinglyLinkedNode<std::string>* head = testVecHead;
while (head != nullptr && head->getValue() != "c"){
head = head->getNext();
}
// head is not at location "c". call delete function
chapter_02::deleteMiddleNode(head);
// check that vec 1 and vec 2 are the same
while (testVecHead != nullptr && expectedVecHead != nullptr){
REQUIRE(testVecHead->getValue() == expectedVecHead->getValue());
testVecHead = testVecHead->getNext();
expectedVecHead = expectedVecHead->getNext();
}
}
TEST_CASE("Chapter 02 - Problem 04 - partition()", "test"){
// create test dataset
std::vector<int> inputVec = {3, 5, 8, 5, 10, 2, 1};
std::vector<int> expectedVec = {1, 2, 3, 5, 8, 5, 10};
chapter_02::SinglyLinkedNode<int>* inputVecHead = chapter_02::vectorToList(inputVec);
chapter_02::SinglyLinkedNode<int>* expectedVecHead = chapter_02::vectorToList(expectedVec);
// perform partition
inputVecHead = chapter_02::partition(inputVecHead, 5);
// check that vec 1 and vec 2 are the same
while (inputVecHead != nullptr && expectedVecHead != nullptr){
REQUIRE(inputVecHead->getValue() == expectedVecHead->getValue());
inputVecHead = inputVecHead->getNext();
expectedVecHead = expectedVecHead->getNext();
}
}
TEST_CASE("Chapter 02 - Problem 05 - sumLists()", "test"){
// create test dataset
// 9423 + 951 = 10374
std::vector<uint8_t> n1Vec = {3, 2, 4, 9};
std::vector<uint8_t> n2Vec = {1, 5, 9};
std::vector<uint8_t> sumVecExpected = {4, 7, 3, 0, 1};
chapter_02::SinglyLinkedNode<uint8_t>* n1Head = chapter_02::vectorToList(n1Vec);
chapter_02::SinglyLinkedNode<uint8_t>* n2Head = chapter_02::vectorToList(n2Vec);
std::vector<uint8_t> sumVecActual = chapter_02::listToVector(chapter_02::sumLists(n1Head, n2Head));
REQUIRE(sumVecExpected == sumVecActual);
};
TEST_CASE("Chapter 02 - Problem 06 - palindrome()", "test"){
// create test dataset
std::vector<int> list1 = {0, 4, 7, 0, 0, 7, 4, 0};
std::vector<int> list2 = {3, 5, 2, 5, 3};
std::vector<int> list3 = {0, 1, 0, 1, 0, 1};
std::vector<std::string> list4 = {"a", "l", "e", "x"};
std::vector<std::string> list5 = {"A", "B", "B", "A"};
chapter_02::SinglyLinkedNode<int>* head1 = chapter_02::vectorToList(list1);
chapter_02::SinglyLinkedNode<int>* head2 = chapter_02::vectorToList(list2);
chapter_02::SinglyLinkedNode<int>* head3 = chapter_02::vectorToList(list3);
chapter_02::SinglyLinkedNode<std::string>* head4 = chapter_02::vectorToList(list4);
chapter_02::SinglyLinkedNode<std::string>* head5 = chapter_02::vectorToList(list5);
REQUIRE(chapter_02::palindrome(head1));
REQUIRE(chapter_02::palindrome(head2));
REQUIRE(!chapter_02::palindrome(head3));
REQUIRE(!chapter_02::palindrome(head4));
REQUIRE(chapter_02::palindrome(head5));
};
TEST_CASE("Chapter 02 - Problem 07 - intersection()", "test") {
// list 1
chapter_02::SinglyLinkedNode<int>* node1_6 = new chapter_02::SinglyLinkedNode<int>(1, nullptr);
chapter_02::SinglyLinkedNode<int>* node1_5 = new chapter_02::SinglyLinkedNode<int>(2, node1_6);
chapter_02::SinglyLinkedNode<int>* node1_4 = new chapter_02::SinglyLinkedNode<int>(7, node1_5);
chapter_02::SinglyLinkedNode<int>* node1_3 = new chapter_02::SinglyLinkedNode<int>(9, node1_4);
chapter_02::SinglyLinkedNode<int>* node1_2 = new chapter_02::SinglyLinkedNode<int>(5, node1_3);
chapter_02::SinglyLinkedNode<int>* node1_1 = new chapter_02::SinglyLinkedNode<int>(1, node1_2);
chapter_02::SinglyLinkedNode<int>* node1_0 = new chapter_02::SinglyLinkedNode<int>(3, node1_1);
// list 2
chapter_02::SinglyLinkedNode<int>* node2_1 = new chapter_02::SinglyLinkedNode<int>(6, node1_4); // intersection point
chapter_02::SinglyLinkedNode<int>* node2_0 = new chapter_02::SinglyLinkedNode<int>(4, node2_1);
// list 3
chapter_02::SinglyLinkedNode<int>* node3_1 = new chapter_02::SinglyLinkedNode<int>(6, nullptr);
chapter_02::SinglyLinkedNode<int>* node3_0 = new chapter_02::SinglyLinkedNode<int>(4, node3_1);
REQUIRE(node1_4 == chapter_02::intersection(node1_0, node2_0));
REQUIRE(nullptr == chapter_02::intersection(node1_0, node3_0));
REQUIRE(nullptr == chapter_02::intersection(static_cast<chapter_02::SinglyLinkedNode<int>*>(nullptr), static_cast<chapter_02::SinglyLinkedNode<int>*>(nullptr)));
}
TEST_CASE("Chapter 02 - Problem 08 - findLoop()", "test") {
// see problem_2_8_explanation.pdf
// example 1
chapter_02::SinglyLinkedNode<int>* node1_7 = new chapter_02::SinglyLinkedNode<int>(7, nullptr);
chapter_02::SinglyLinkedNode<int>* node1_6 = new chapter_02::SinglyLinkedNode<int>(6, node1_7);
chapter_02::SinglyLinkedNode<int>* node1_5 = new chapter_02::SinglyLinkedNode<int>(5, node1_6);
chapter_02::SinglyLinkedNode<int>* node1_4 = new chapter_02::SinglyLinkedNode<int>(4, node1_5);
chapter_02::SinglyLinkedNode<int>* node1_3 = new chapter_02::SinglyLinkedNode<int>(3, node1_4);
chapter_02::SinglyLinkedNode<int>* node1_2 = new chapter_02::SinglyLinkedNode<int>(2, node1_3);
chapter_02::SinglyLinkedNode<int>* node1_1 = new chapter_02::SinglyLinkedNode<int>(1, node1_2);
chapter_02::SinglyLinkedNode<int>* node1_0 = new chapter_02::SinglyLinkedNode<int>(0, node1_1);
node1_7->setNext(node1_5);
REQUIRE(node1_5 == chapter_02::findLoop(node1_0));
// example 2
chapter_02::SinglyLinkedNode<int>* node2_10 = new chapter_02::SinglyLinkedNode<int>(10, nullptr);
chapter_02::SinglyLinkedNode<int>* node2_9 = new chapter_02::SinglyLinkedNode<int>(9, node2_10);
chapter_02::SinglyLinkedNode<int>* node2_8 = new chapter_02::SinglyLinkedNode<int>(8, node2_9);
chapter_02::SinglyLinkedNode<int>* node2_7 = new chapter_02::SinglyLinkedNode<int>(7, node2_8);
chapter_02::SinglyLinkedNode<int>* node2_6 = new chapter_02::SinglyLinkedNode<int>(6, node2_7);
chapter_02::SinglyLinkedNode<int>* node2_5 = new chapter_02::SinglyLinkedNode<int>(5, node2_6);
chapter_02::SinglyLinkedNode<int>* node2_4 = new chapter_02::SinglyLinkedNode<int>(4, node2_5);
chapter_02::SinglyLinkedNode<int>* node2_3 = new chapter_02::SinglyLinkedNode<int>(3, node2_4);
chapter_02::SinglyLinkedNode<int>* node2_2 = new chapter_02::SinglyLinkedNode<int>(2, node2_3);
chapter_02::SinglyLinkedNode<int>* node2_1 = new chapter_02::SinglyLinkedNode<int>(1, node2_2);
chapter_02::SinglyLinkedNode<int>* node2_0 = new chapter_02::SinglyLinkedNode<int>(0, node2_1);
node2_10->setNext(node2_3);
REQUIRE(node2_3 == chapter_02::findLoop(node2_0));
// example 3
REQUIRE(static_cast<chapter_02::SinglyLinkedNode<int>*>(nullptr) == chapter_02::findLoop(static_cast<chapter_02::SinglyLinkedNode<int>*>(nullptr)));
}
TEST_CASE("Chapter 03 - Stack", "test"){
chapter_03::Stack<int> myStack;
for (int i = 1; i <= 4; i++){
myStack.push(i);
}
std::vector<int> tooShort = {3,2,1};
std::vector<int> incorrect = {5,3,2,1};
std::vector<int> justRight = {4,3,2,1};
std::vector<int> tooLong = {4,3,2,1,1};
std::vector<int> empty = {};
REQUIRE(myStack!=tooShort);
REQUIRE(myStack!=tooLong);
REQUIRE(myStack!=incorrect);
REQUIRE(myStack==justRight);
REQUIRE(myStack.peek()==4);
REQUIRE(!myStack.isEmpty());
while (!myStack.isEmpty()){
empty.push_back(myStack.pop());
}
REQUIRE(empty==justRight);
REQUIRE(myStack.isEmpty());
REQUIRE(myStack.pop()==0);
REQUIRE(myStack.peek()==0);
}
TEST_CASE("Chapter 03 - Problem 02 - StackMin()", "test"){
chapter_03::StackMin<int> myStack;
myStack.push(-8);
myStack.push(-5);
myStack.push(1);
myStack.push(-6);
REQUIRE(myStack.seeMin() == -8);
myStack.push(-9);
REQUIRE(myStack.seeMin() == -9);
myStack.push(-15);
myStack.push(-30);
myStack.pop();
myStack.pop();
REQUIRE(myStack.seeMin() == -9);
}
TEST_CASE("Chapter 03 - Problem 04 - QueueViaStacks()", "test"){
chapter_03::QueueViaStacks<int> myQueue;
for (int i = 0; i < 10; i++) myQueue.enqueue(i);
for (int i = 0; i < 5; i++) REQUIRE(myQueue.dequeue() == i);
for (int i = 0; i < 5; i++) myQueue.enqueue(i);
for (int i = 5; i < 10; i++) REQUIRE(myQueue.dequeue() == i);
for (int i = 0; i < 5; i++) REQUIRE(myQueue.dequeue() == i);
}
TEST_CASE("Chapter 03 - Problem 05 - sortStack()", "test") {
chapter_03::Stack<int> stack;
std::vector<int> vector = {7, 6, 3, 5, 1, 2, 4};
for (int x : vector) {
stack.push(x);
}
chapter_03::sortStack(stack);
for (int x = 1; x <= 7; x++) {
REQUIRE(stack.pop() == x);
}
}
TEST_CASE("Chapter 03 - Problem 06 - AnimalShelter", "test") {
chapter_03::AnimalShelter shelter;
auto catA = chapter_03::Cat("a");
auto dogB = chapter_03::Dog("b");
auto dogC = chapter_03::Dog("c");
auto catD = chapter_03::Cat("d");
auto dogE = chapter_03::Dog("e");
auto catF = chapter_03::Cat("f");
shelter.enqueue(&catA);
shelter.enqueue(&dogB);
shelter.enqueue(&dogC);
shelter.enqueue(&catD);
shelter.enqueue(&dogE);
shelter.enqueue(&catF);
REQUIRE("a" == shelter.dequeueAny()->getName());
REQUIRE("b" == shelter.dequeueAny()->getName());
REQUIRE("c" == shelter.dequeueDog()->getName());
REQUIRE("d" == shelter.dequeueCat()->getName());
REQUIRE("e" == shelter.dequeueAny()->getName());
REQUIRE("f" == shelter.dequeueAny()->getName());
REQUIRE(nullptr == shelter.dequeueAny());
}
TEST_CASE("Chapter 04 - Basic Graph Functionality", "test"){
chapter_02::TetraGraphNode<int> node(1);
chapter_02::TetraGraphNode<int>* child0 = new chapter_02::TetraGraphNode<int>(0);
chapter_02::TetraGraphNode<int>* child1 = new chapter_02::TetraGraphNode<int>(1);
chapter_02::TetraGraphNode<int>* child2 = new chapter_02::TetraGraphNode<int>(2);
chapter_02::TetraGraphNode<int>* child3 = new chapter_02::TetraGraphNode<int>(3);
node.addChild(child0, 0);
node.addChild(child1, 1);
node.addChild(child2, 2);
node.addChild(child3, 3);
std::vector<chapter_02::TetraGraphNode<int>*> children;
node.getChildren(children);
REQUIRE(children[0] == child0);
REQUIRE(children[1] == child1);
REQUIRE(children[2] == child2);
REQUIRE(children[3] == child3);
node.removeChild(0);
node.removeChild(1);
node.removeChild(2);
node.removeChild(3);
std::vector<chapter_02::TetraGraphNode<int>*> deletedChildren;
node.getChildren(deletedChildren);
REQUIRE(deletedChildren.size() == 0);
// no need to delete children, because removeChildren does that for us.
}
TEST_CASE("Chapter 04 - Problem 01 - Route Between Nodes", "test"){
/*
Implements this directed graph:
1 -> 2 -> 3
|
v
4 -> 5 -> 6
| ^
v |
7 -> 8
*/
chapter_02::TetraGraphNode<int>* node1 = new chapter_02::TetraGraphNode<int>(1);
chapter_02::TetraGraphNode<int>* node2 = new chapter_02::TetraGraphNode<int>(2);
chapter_02::TetraGraphNode<int>* node3 = new chapter_02::TetraGraphNode<int>(3);
chapter_02::TetraGraphNode<int>* node4 = new chapter_02::TetraGraphNode<int>(4);
chapter_02::TetraGraphNode<int>* node5 = new chapter_02::TetraGraphNode<int>(5);
chapter_02::TetraGraphNode<int>* node6 = new chapter_02::TetraGraphNode<int>(6);
chapter_02::TetraGraphNode<int>* node7 = new chapter_02::TetraGraphNode<int>(7);
chapter_02::TetraGraphNode<int>* node8 = new chapter_02::TetraGraphNode<int>(8);
node1->addChild(node2, 0);
node2->addChild(node3, 0);
node2->addChild(node4, 1);
node4->addChild(node5, 0);
node4->addChild(node7, 1);
node5->addChild(node6, 0);
node7->addChild(node8, 0);
node8->addChild(node5, 0);
REQUIRE(chapter_04::pathExistsDFS(node1, node6));
REQUIRE(chapter_04::pathExistsDFS(node7, node5));
REQUIRE(!chapter_04::pathExistsDFS(node3, node8));
REQUIRE(chapter_04::pathExistsDFS(node1, node8));
REQUIRE(!chapter_04::pathExistsDFS(static_cast<chapter_02::TetraGraphNode<int>*>(nullptr), static_cast<chapter_02::TetraGraphNode<int>*>(nullptr)));
REQUIRE(!chapter_04::pathExistsDFS(node1, static_cast<chapter_02::TetraGraphNode<int>*>(nullptr)));
delete node1;
delete node2;
delete node3;
delete node4;
delete node5;
delete node6;
delete node7;
delete node8;
}
TEST_CASE("Chapter 04 - Problem 02 - minimalTree()", "test"){
// test 1
std::vector<int> sortedArray1 = {8, 9, 10, 11, 12, 13, 14};
chapter_02::BinaryNode<int>* head1 = chapter_04::minimalTree(sortedArray1);
std::vector<int> expectedPostOrderTraversal1 = {8, 10, 9, 12, 14, 13, 11};
std::vector<int> actualPostOrderTraversal1;
chapter_02::bstToVector(actualPostOrderTraversal1, head1);
REQUIRE(expectedPostOrderTraversal1.size() == actualPostOrderTraversal1.size());
for (int i = 0; i < actualPostOrderTraversal1.size(); i++) {
REQUIRE(actualPostOrderTraversal1[i] == expectedPostOrderTraversal1[i]);
}
// test 2
std::vector<int> sortedArray2 = {9, 10, 11, 12, 13, 14};
chapter_02::BinaryNode<int>* head2 = chapter_04::minimalTree(sortedArray2);
std::vector<int> expectedPostOrderTraversal2 = {10, 9, 12, 14, 13, 11};
std::vector<int> actualPostOrderTraversal2;
chapter_02::bstToVector(actualPostOrderTraversal2, head2);
REQUIRE(expectedPostOrderTraversal2.size() == actualPostOrderTraversal2.size());
for (int i = 0; i < actualPostOrderTraversal2.size(); i++) {
REQUIRE(actualPostOrderTraversal2[i] == expectedPostOrderTraversal2[i]);
}
}
TEST_CASE("Chapter 04 - Problem 03 - makeLL()", "test"){
/*
* Construct a binary tree of the form
* 0
* 12
* 3456
*/
chapter_02::BinaryNode<int>* head = new chapter_02::BinaryNode<int>(0);
chapter_02::BinaryNode<int>* child1 = new chapter_02::BinaryNode<int>(1);
chapter_02::BinaryNode<int>* child2 = new chapter_02::BinaryNode<int>(2);
chapter_02::BinaryNode<int>* child3 = new chapter_02::BinaryNode<int>(3);
chapter_02::BinaryNode<int>* child4 = new chapter_02::BinaryNode<int>(4);
chapter_02::BinaryNode<int>* child5 = new chapter_02::BinaryNode<int>(5);
chapter_02::BinaryNode<int>* child6 = new chapter_02::BinaryNode<int>(6);
head->setLeft(child1);
head->setRight(child2);
child1->setLeft(child3);
child1->setRight(child4);
child2->setLeft(child5);
child2->setRight(child6);
// execute conversion to linked list
std::vector<chapter_02::SinglyLinkedNode<int>*> vectorOfHeads;
std::vector<chapter_02::SinglyLinkedNode<int>*> vectorOfTails;
std::vector<int> expected = {0, 1, 2, 3, 4, 5, 6};
chapter_04::makeLL(vectorOfHeads, vectorOfTails, head);
std::vector<int> actual = chapter_04::vectorFromVectorOfLLs(vectorOfHeads);
// test
for (int i = 0; i < expected.size(); i++) {
REQUIRE(expected[i] == actual[i]);
}
}
TEST_CASE("Chapter 04 - Problem 04 - checkBalanced()", "test") {
/*
balanced tree:
node111,
node121,node122,
node131,node132,nullptr,nullptr,
nullptr,nullptr,nullptr,nullptr,
*/
chapter_02::BinaryNode<int> node132(132, nullptr, nullptr);
chapter_02::BinaryNode<int> node131(131, nullptr, nullptr);
chapter_02::BinaryNode<int> node122(122, nullptr, nullptr);
chapter_02::BinaryNode<int> node121(121, &node131, &node132);
chapter_02::BinaryNode<int> node111(111, &node121, &node122);
chapter_04::NodeStatus status1 = chapter_04::checkBalanced(&node111);
REQUIRE(status1.balanced);
REQUIRE(status1.subtreeSize == 3);
/*
unbalanced tree:
node211,
node221,node222,
node231,node232,nullptr,nullptr,
node241,nullptr,nullptr,nullptr,
nullptr,nullptr,
*/
chapter_02::BinaryNode<int> node241(241, nullptr, nullptr);
chapter_02::BinaryNode<int> node232(232, nullptr, nullptr);
chapter_02::BinaryNode<int> node231(231, &node241, nullptr);
chapter_02::BinaryNode<int> node222(222, nullptr, nullptr);
chapter_02::BinaryNode<int> node221(221, &node231, &node232);
chapter_02::BinaryNode<int> node211(211, &node221, &node222);
chapter_04::NodeStatus status2 = chapter_04::checkBalanced(&node211);
REQUIRE(!status2.balanced);
REQUIRE(status2.subtreeSize == 4);
}
TEST_CASE("Chpater 04 - Problem 05 - validateBST()", "test") {
// construct a binary tree
chapter_02::BinaryNode<int> node1(1);
chapter_02::BinaryNode<int> node2(2);
chapter_02::BinaryNode<int> node3(3);
chapter_02::BinaryNode<int> node4(4);
chapter_02::BinaryNode<int> node5(5);
chapter_02::BinaryNode<int> node6(6);
chapter_02::BinaryNode<int> node8(8);
chapter_02::BinaryNode<int> node10(10);
/*
8
4, 10
2, 6,
1, 3, 5,
*/
node8.setLeft(&node4);
node8.setRight(&node10);
node4.setLeft(&node2);
node4.setRight(&node6);
node2.setLeft(&node1);
node2.setRight(&node3);
node6.setLeft(&node5);
REQUIRE(chapter_04::validateBST(&node8));
// add node that breaks BST rule
chapter_02::BinaryNode<int> node9(9);
node6.setRight(&node9);
REQUIRE(!chapter_04::validateBST(&node8));
}
TEST_CASE("Chapter 04 - Problem 06 - successor()", "test"){
// construct a binary tree
chapter_02::BinaryNode<int>* node0 = new chapter_02::BinaryNode<int>(0);
chapter_02::BinaryNode<int>* node1 = new chapter_02::BinaryNode<int>(1);
chapter_02::BinaryNode<int>* node2 = new chapter_02::BinaryNode<int>(2);
chapter_02::BinaryNode<int>* node3 = new chapter_02::BinaryNode<int>(3);
chapter_02::BinaryNode<int>* node4 = new chapter_02::BinaryNode<int>(4);
chapter_02::BinaryNode<int>* node5 = new chapter_02::BinaryNode<int>(5);
chapter_02::BinaryNode<int>* node6 = new chapter_02::BinaryNode<int>(6);
chapter_02::BinaryNode<int>* node7 = new chapter_02::BinaryNode<int>(7);
chapter_02::BinaryNode<int>* node8 = new chapter_02::BinaryNode<int>(8);
chapter_02::BinaryNode<int>* node9 = new chapter_02::BinaryNode<int>(9);
chapter_02::BinaryNode<int>* node10 = new chapter_02::BinaryNode<int>(10);
/*
8
4 10
2 6
1 3 5
0 9
In-order traversal:
1, 2, 0, 3, 9, 4, 5, 6, 8, 10
*/
node0->setParent(node3);
node1->setParent(node2);
node3->setParent(node2);
node2->setParent(node4);
node5->setParent(node6);
node6->setParent(node4);
node4->setParent(node8);
node9->setParent(node3);
node10->setParent(node8);
node8->setLeft(node4);
node8->setRight(node10);
node4->setLeft(node2);
node4->setRight(node6);
node2->setLeft(node1);
node2->setRight(node3);
node6->setLeft(node5);
node3->setLeft(node0);
node3->setRight(node9);
REQUIRE(node8 == chapter_04::successor(node6));
REQUIRE(node5 == chapter_04::successor(node4));
REQUIRE(node0 == chapter_04::successor(node2));
REQUIRE(node3 == chapter_04::successor(node0));
REQUIRE(node4 == chapter_04::successor(node9));
REQUIRE(nullptr == chapter_04::successor(node10));
}
TEST_CASE("Chapter 04 - Problem 07 - buildOrder()", "test") {
// no circular dependencies
std::vector<char> projects1 = {'a', 'b', 'c', 'd', 'e', 'f'};
std::vector<std::pair<char, char>> dependencies1 = {
std::pair<char, char>('a', 'd'),
std::pair<char, char>('f', 'b'),
std::pair<char, char>('b', 'd'),
std::pair<char, char>('f', 'a'),
std::pair<char, char>('d', 'c')};
std::vector<char> projects2 = {'a', 'b', 'c', 'd', 'e', 'f', 'g'};
std::vector<std::pair<char, char>> dependencies2 = {
std::pair<char, char>('f', 'c'),
std::pair<char, char>('f', 'b'),
std::pair<char, char>('f', 'a'),
std::pair<char, char>('c', 'a'),
std::pair<char, char>('b', 'a'),
std::pair<char, char>('a', 'e'),
std::pair<char, char>('b', 'e'),
std::pair<char, char>('d', 'g')};
// add circular dependency
std::vector<std::pair<char, char>> dependencies3 = {
std::pair<char, char>('a', 'd'),
std::pair<char, char>('f', 'b'),
std::pair<char, char>('b', 'd'),
std::pair<char, char>('f', 'a'),
std::pair<char, char>('d', 'c'),
std::pair<char, char>('c', 'a')};
// verify output
std::vector<char> actualBuildOrder1 = {};
std::vector<char> actualBuildOrder2 = {};
std::vector<char> actualBuildOrder3 = {};
std::vector<char> expectedBuildOrder1 = {'e', 'f', 'b', 'a', 'd', 'c'};
std::vector<char> expectedBuildOrder2 = {'d', 'f', 'g', 'c', 'b', 'a', 'e'};
chapter_04::buildOrder(projects1, dependencies1, actualBuildOrder1);
chapter_04::buildOrder(projects2, dependencies2, actualBuildOrder2);
chapter_04::buildOrder(projects1, dependencies3, actualBuildOrder3);
for (int i = 0; i < actualBuildOrder1.size(); i++) {
REQUIRE(actualBuildOrder1[i] == expectedBuildOrder1[i]);
}
for (int i = 0; i < actualBuildOrder2.size(); i++) {
REQUIRE(actualBuildOrder2[i] == expectedBuildOrder2[i]);
}
REQUIRE(actualBuildOrder3.empty());
}
TEST_CASE("Chapter 04 - Problem 08 - firstCommonAncestor()", "test") {
/*
construct binary tree
7
4 3
10 5 6 15
21 17
25
*/
chapter_02::BinaryNode<int> n21(21);
chapter_02::BinaryNode<int> n17(17);
chapter_02::BinaryNode<int> n15(15, &n21, &n17);
chapter_02::BinaryNode<int> n6(6);
chapter_02::BinaryNode<int> n3(3, &n6, &n15);
chapter_02::BinaryNode<int> n10(10);
chapter_02::BinaryNode<int> n5(5);
chapter_02::BinaryNode<int> n4(4, &n10, &n5);
chapter_02::BinaryNode<int> n7(7, &n4, &n3);
chapter_02::BinaryNode<int> n25(25);
REQUIRE(&n3 == chapter_04::firstCommonAncestor(&n7, &n6, &n21));
REQUIRE(&n7 == chapter_04::firstCommonAncestor(&n7, &n10, &n21));
REQUIRE(nullptr == chapter_04::firstCommonAncestor(&n7, &n15, &n25));
REQUIRE(nullptr == chapter_04::firstCommonAncestor(&n7, &n7, &n7)); // a node is not its own ancestor
REQUIRE(&n7 == chapter_04::firstCommonAncestor(&n7, &n3, &n4));
}
TEST_CASE("Chapter 04 - Problem 10 - checkSubtree()", "test") {
/*
construct binary tree
7
4 3
10 5 6 15
21 17
25
*/
chapter_02::BinaryNode<int> n21(21);
chapter_02::BinaryNode<int> n17(17);
chapter_02::BinaryNode<int> n15(15, &n21, &n17);
chapter_02::BinaryNode<int> n6(6);
chapter_02::BinaryNode<int> n3(3, &n6, &n15);
chapter_02::BinaryNode<int> n10(10);
chapter_02::BinaryNode<int> n5(5);
chapter_02::BinaryNode<int> n4(4, &n10, &n5);
chapter_02::BinaryNode<int> n7(7, &n4, &n3);
chapter_02::BinaryNode<int> n25(25);
/*
construct disconnected binary tree
30
31 32
*/
chapter_02::BinaryNode<int> n31(31);
chapter_02::BinaryNode<int> n32(32);
chapter_02::BinaryNode<int> n30(30, &n31, &n32);
REQUIRE(chapter_04::checkSubtree(&n7, &n15));
REQUIRE(chapter_04::checkSubtree(&n7, &n7));
REQUIRE(chapter_04::checkSubtree(&n7, &n21));
REQUIRE(chapter_04::checkSubtree(&n7, &n4));
REQUIRE(!chapter_04::checkSubtree<int>(&n7, nullptr));
REQUIRE(!chapter_04::checkSubtree(&n7, &n30));
REQUIRE(!chapter_04::checkSubtree(&n7, &n31));
REQUIRE(!chapter_04::checkSubtree(&n25, &n31));
REQUIRE(chapter_04::checkSubtree(&n30, &n31));
REQUIRE(!chapter_04::checkSubtree<int>(nullptr, nullptr));
}
TEST_CASE("Chapter 04 - Problem 11 - randomBST()", "test"){
std::vector<int> valuesList = {10, 13, 14, 11, 7, 7, 8, 7, 4, 10};
chapter_04::RandBinaryNode<int> head(valuesList[0]);
for (int i = 1; i < valuesList.size(); i++) {
head.insert(valuesList[i]);
}
int occurrenceSum4 = 0;
int occurrenceSum7 = 0;
int occurrenceSum10 = 0;
int occurrenceSum13 = 0;
// using 10,000 random samples, assert that occurence of values in random samples approximately
// the same as the occurence of the values in the tree
std::mt19937 gen(0); // standard mersenne_twister_engine seeded with zero
for (int i = 0; i < 10000; i++) {
int randValue = head.getRandomNode(-1, &gen)->getValue();
switch (randValue){
case 4 : occurrenceSum4 ++; break;
case 7 : occurrenceSum7 ++; break;
case 10 : occurrenceSum10 ++; break;
case 13 : occurrenceSum13 ++; break;
}
}
REQUIRE(((950 <= occurrenceSum4) && (occurrenceSum4 <= 1050)));
REQUIRE(((2950 <= occurrenceSum7) && (occurrenceSum7 <= 3050)));
REQUIRE(((1950 <= occurrenceSum10) && (occurrenceSum10 <= 2050)));
REQUIRE(((950 <= occurrenceSum13) && (occurrenceSum13 <= 1050)));
}
TEST_CASE("Chapter 04 - Problem 12 - pathsWithSum()", "test"){
/*
construct binary tree like in textbook example
10
5 -3
3 1 __ 11
3 -2 __ 2
*/
// leaf nodes at depth = 3
chapter_02::BinaryNode<int> n3_leaf(3);
chapter_02::BinaryNode<int> n_minus2(-2);
chapter_02::BinaryNode<int> n2(2);
// nodes at depth = 2
chapter_02::BinaryNode<int> n3(3, &n3_leaf, &n_minus2);
chapter_02::BinaryNode<int> n1(1, nullptr, &n2);
chapter_02::BinaryNode<int> n11(11);
// nodes at depth = 1
chapter_02::BinaryNode<int> n5(5, &n3, &n1);
chapter_02::BinaryNode<int> n_minus3(-3, nullptr, &n11);
// root node at depth = 0
chapter_02::BinaryNode<int> n10(10, &n5, &n_minus3);
// count paths that sum to 8
REQUIRE(3 == chapter_04::pathsWithSum(8, &n10));
}
TEST_CASE("Chapter 05 - Problem 01 - insertion()", "test"){
REQUIRE(chapter_05::insertion(0b10000000000, 0b10011, 2, 6) == 0b10001001100);
}
TEST_CASE("Chapter 05 - Problem 02 - binaryToString()", "test") {
std::string binary_string_1 = "";
std::string binary_string_2 = "";
std::string binary_string_3 = "";
std::string binary_string_4 = "";
REQUIRE(chapter_05::binaryToString(0.5, binary_string_1) == 0);
REQUIRE(chapter_05::binaryToString(0.25, binary_string_2) == 0);
REQUIRE(chapter_05::binaryToString(1.5, binary_string_3) == -1);
REQUIRE(chapter_05::binaryToString(0.722, binary_string_4) == 0);
REQUIRE(binary_string_1 == "0.1");
REQUIRE(binary_string_2 == "0.01");
REQUIRE(binary_string_3 == "");
REQUIRE(binary_string_4 == "0.10111000110101001111110111110011"); // needs double precision to work
}
TEST_CASE("Chapter 05 - Problem 06 - conversion()", "test"){
REQUIRE(chapter_05::conversion(0b11001100, 0b11110000) == 4);
REQUIRE(chapter_05::conversion(29, 15) == 2);
}
TEST_CASE("Chapter 05 - Problem 07 - pairwiseSwap()", "test"){
REQUIRE(chapter_05::pairwiseSwap(0b10101010) == 0b01010101);
REQUIRE(chapter_05::pairwiseSwap(0b11110000) == 0b11110000);
REQUIRE(chapter_05::pairwiseSwap(0b110) == 0b1001);
}
TEST_CASE("Chapter 08 - Problem 01 - tripleStep()", "test"){
REQUIRE(chapter_08::tripleStep(3) == 4);
REQUIRE(chapter_08::tripleStep(4) == 7);
REQUIRE(chapter_08::tripleStep(5) == 13);
}
TEST_CASE("Chapter 08 - Problem 02 - robotGrid()", "test"){
Eigen::MatrixXd maze(5, 5);
maze << 1, 1, 1, 0, 1,
0, 0, 1, 1, 1,
0, 1, 1, 0, 0,
0, 1, 1, 0, 1,
1, 1, 1, 1, 1;
std::vector<Eigen::Vector2d> expectedPath = {Eigen::Vector2d(0,0),
Eigen::Vector2d(0,1),
Eigen::Vector2d(0,2),
Eigen::Vector2d(1,2),
Eigen::Vector2d(2,2),
Eigen::Vector2d(3,2),
Eigen::Vector2d(4,2),
Eigen::Vector2d(4,3),
Eigen::Vector2d(4,4)};
std::vector<Eigen::Vector2d> path;
REQUIRE(chapter_08::robotGrid(maze, path));
REQUIRE(path == expectedPath);
}
TEST_CASE("Chapter 08 - Problem 03 - magicIndex()", "test"){
std::vector<int> noMagicIndex = {-1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
std::vector<int> magicIndex5 = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
std::vector<int> magicIndex7 = {-40, -20, -1, 1, 2, 3, 5, 7, 9, 12, 13};
REQUIRE(chapter_08::magicIndex(noMagicIndex) == -1);
REQUIRE(chapter_08::magicIndex(magicIndex5) == 5);
REQUIRE(chapter_08::magicIndex(magicIndex7) == 7);
}
TEST_CASE("Chapter 08 - Problem 04 - powerSet()", "test"){
std::vector<int> set123 = {1, 2, 3};
std::vector<int> set12 = {1, 2};
std::vector<int> set13 = {1, 3};
std::vector<int> set23 = {2, 3};
std::vector<int> set1 = {1};
std::vector<int> set2 = {2};
std::vector<int> set3 = {3};
std::vector<int> emptySet = {};
std::vector<std::vector<int>> powerSet123 = {emptySet, set1, set2, set12, set3, set13, set23, set123};
std::vector<std::vector<int>> powerSet12 = {emptySet, set1, set2, set12};
std::vector<std::vector<int>> powerSet1 = {emptySet, set1};
std::vector<std::vector<int>> testPowerSet = {};
chapter_08::createPowerSet(set123, testPowerSet);
REQUIRE(testPowerSet == powerSet123);
testPowerSet = {};
chapter_08::createPowerSet(set12, testPowerSet);
REQUIRE(testPowerSet == powerSet12);
testPowerSet = {};
chapter_08::createPowerSet(set1, testPowerSet);
REQUIRE(testPowerSet == powerSet1);
};
TEST_CASE("Chapter 08 - Problem 05 - recursiveMultiply()", "test"){
REQUIRE(chapter_08::recursiveMultiply(1, 1) == 1);
REQUIRE(chapter_08::recursiveMultiply(1, 2) == 2);
REQUIRE(chapter_08::recursiveMultiply(0, 1) == 0);
REQUIRE(chapter_08::recursiveMultiply(9, 10) == 90);
REQUIRE(chapter_08::recursiveMultiply(9, 11) == 99);
REQUIRE(chapter_08::recursiveMultiply(12, 12) == 144);
}
TEST_CASE("Chapter 08 - Problem 07 - permutationsNoDups()", "test") {
std::unordered_set<std::string> actual1 = {};
std::unordered_set<std::string> actual2 = {};
std::unordered_set<std::string> actual3 = {};
std::unordered_set<std::string> actual4 = {};
std::unordered_set<std::string> expected1 = {"a"};
std::unordered_set<std::string> expected2 = {"al", "la"};
std::unordered_set<std::string> expected3 = {"ela", "lea", "lae", "eal", "ael", "ale"};
std::unordered_set<std::string> expected4 = {"xela", "exla", "elxa", "elax",
"xlea", "lxea", "lexa", "leax",
"xlae", "lxae", "laxe", "laex",
"xeal", "exal", "eaxl", "ealx",
"xael", "axel", "aexl", "aelx",
"xale", "axle", "alxe", "alex"};
chapter_08::permutationsNoDups("a", actual1);
chapter_08::permutationsNoDups("al", actual2);
chapter_08::permutationsNoDups("ale", actual3);
chapter_08::permutationsNoDups("alex", actual4);
REQUIRE(actual1 == expected1);
REQUIRE(actual2 == expected2);
REQUIRE(actual3 == expected3);
REQUIRE(actual4 == expected4);
}
TEST_CASE("Chapter 08 - Problem 08 - permutationsWithDups()", "test") {
std::unordered_set<std::string> actual1 = {};
std::unordered_set<std::string> actual2 = {};
std::unordered_set<std::string> actual3 = {};
std::unordered_set<std::string> expected1 = {"ala", "laa", "aal"};
std::unordered_set<std::string> expected2 = {"aala", "alaa", "alaa", "laaa", "aala", "aaal"};
std::unordered_set<std::string> expected3 = {"xela", "exla", "elxa", "elax",
"xlea", "lxea", "lexa", "leax",
"xlae", "lxae", "laxe", "laex",
"xeal", "exal", "eaxl", "ealx",
"xael", "axel", "aexl", "aelx",
"xale", "axle", "alxe", "alex"};
chapter_08::permutationsWithDups("ala", actual1);
//chapter_08::permutationsWithDups("alaa", actual2);
//chapter_08::permutationsWithDups("alex", actual3);
REQUIRE(actual1 == expected1);
//REQUIRE(actual2 == expected2);
//REQUIRE(actual3 == expected3);
}
TEST_CASE("Chapter 08 - Problem 10 - paintFill()", "test"){
Eigen::MatrixXi image(6, 6);
image << 0, 1, 1, 0, 0, 3,
1, 1, 1, 1, 0, 0,
0, 1, 1, 0, 0, 2,
0, 0, 0, 0, 2, 2,
0, 2, 2, 2, 2, 2,
0, 0, 0, 2, 2, 2;
Eigen::MatrixXi zerosFilled(6, 6);
zerosFilled << 0, 1, 1, 5, 5, 3,
1, 1, 1, 1, 5, 5,
5, 1, 1, 5, 5, 2,
5, 5, 5, 5, 2, 2,
5, 2, 2, 2, 2, 2,
5, 5, 5, 2, 2, 2;
Eigen::MatrixXi onesFilled(6, 6);
onesFilled << 0, 5, 5, 0, 0, 3,
5, 5, 5, 5, 0, 0,
0, 5, 5, 0, 0, 2,
0, 0, 0, 0, 2, 2,
0, 2, 2, 2, 2, 2,
0, 0, 0, 2, 2, 2;
Eigen::MatrixXi twosFilled(6, 6);
twosFilled << 0, 1, 1, 0, 0, 3,
1, 1, 1, 1, 0, 0,
0, 1, 1, 0, 0, 5,
0, 0, 0, 0, 5, 5,
0, 5, 5, 5, 5, 5,
0, 0, 0, 5, 5, 5;
Eigen::MatrixXi threeFilled(6, 6);
threeFilled << 0, 1, 1, 0, 0, 5,
1, 1, 1, 1, 0, 0,
0, 1, 1, 0, 0, 2,
0, 0, 0, 0, 2, 2,
0, 2, 2, 2, 2, 2,
0, 0, 0, 2, 2, 2;
Eigen::MatrixXi expectedZerosFilled = image;
Eigen::MatrixXi expectedOnesFilled = image;
Eigen::MatrixXi expectedTwosFilled = image;