test/interviews/think-cell/IntervalMap.cpp

/* Check .vimrc.local defs.
VIM: let g:lcppflags="-std=c++11 -O2 -pthread"
VIM: let g:wcppflags="/O2 /EHsc /DWIN32"
VIM: let g:argv=""
*/
#include <assert.h>
#include <map>
#include <limits>
#include <iostream>
#include <sstream>


// interval_map<K,V> is a data structure that efficiently associates intervals of keys of type K with values of type V. 
// Your task is to implement the assign member function of this data structure, which is outlined below. 

// interval_map<K, V> is implemented on top of std::map. In case you are not entirely sure which functions std::map provides,
// what they do and which guarantees they provide, we have attached an excerpt of the C++1x draft standard at the end of this
// file for your convenience. 

// Each key-value-pair (k,v) in the m_map member means that the value v is associated to the interval from k (including) to
// the next key (excluding) in m_map.
// Example: the std::map (0,'A'), (3,'B'), (5,'A') represents the mapping
// 0 -> 'A'
// 1 -> 'A'
// 2 -> 'A'
// 3 -> 'B'
// 4 -> 'B'
// 5 -> 'A' 
// 6 -> 'A'
// 7 -> 'A'
// ... all the way to numeric_limits<key>::max()

// The representation in m_map must be canonical, that is, consecutive map entries must not have the same value: 
// ..., (0,'A'), (3,'A'), ... is not allowed.
// Initially, the whole range of K is associated with a given initial value, passed to the constructor.
template<class K, class V>
class interval_map {
	friend void IntervalMapTest();
	
private:	
	std::map<K,V> m_map;

public:
	// constructor associates whole range of K with val by inserting (K_min, val) into the map
	interval_map( V const& val) {
		m_map.insert(m_map.begin(),std::make_pair(std::numeric_limits<K>::min(),val));
	};

	// Assign value val to interval [keyBegin, keyEnd). 
	// Overwrite previous values in this interval. Do not change values outside this interval.
	// Conforming to the C++ Standard Library conventions, the interval includes keyBegin, but excludes keyEnd.
	// If !( keyBegin < keyEnd ), this designates an empty interval, and assign must do nothing.
	void assign( K const& keyBegin, K const& keyEnd, const V& val ) {
		//
		// If !( keyBegin < keyEnd ), this designates an empty interval, and
		// assign must do nothing.
		//
		if ( !(keyBegin < keyEnd ) )
			return;
		//
		// - is bounded below, with the lowest value being std::numeric_limits<K>::min();
		//	std::numeric_limits<duble>::min() actually is not the smalles number.
		//
		if (keyBegin < std::numeric_limits<K>::min())
			throw std::runtime_error("K should be bounded below, with the lowest value being std::numeric_limits<K>::min().");
		//
		// Find the interval pointer before which the new interval ends.
		//
		auto ie = m_map.lower_bound(keyEnd);
		//
		// If there is a need to break the last interval with keyEnd do it now.
		// Everything prior 'ie' till 'ib' will be removed later.
		//
		if ( ie == m_map.end() && keyEnd < std::numeric_limits<K>::max()
			|| ie != m_map.end() && keyEnd < ie->first ) {
			if (!( std::prev(ie)->second == val ))
				ie = m_map.insert(ie, std::make_pair(keyEnd,std::prev(ie)->second));
		}
		//
		//	If the interval next to the inserting one should be joined?
		//
		else if (ie != m_map.end() && ie->second == val)
			++ie;
		//
		// Find the interval pointer before which the new interval begins.
		//
		auto ib = m_map.lower_bound( keyBegin );
		//
		//	If the interval before should be joined then ...
		//	Note: there should always be std::numeric_limits<K>::min()
		//
		if (ib != m_map.begin() && std::prev(ib)->second == val)
			--ib;
		//
		//	If keyBegin is less than 'ib' then insert an new interval.
		//
		else if ( ib == m_map.end() || keyBegin < ib->first )
			ib = m_map.insert(ib, std::make_pair(keyBegin, val));
		//
		//	Otherwise just change the value since keyBegin matches with an 
		//	existing interval.
		//
		else
			ib->second = val;
		//
		//	Removed the range between ib and ie.
		//
		m_map.erase( ++ib, ie );
	}

	// look-up of the value associated with key
	V const& operator[]( K const& key ) const {
		return ( --m_map.upper_bound(key) )->second;
	}

private:
	//
	//	Since this is a template class, I assume this method will be
	//	instantiated only in IntervalMapTest. Hence, key and value are pretty
	//	printable.
	//
	std::ostream& print( std::ostream& os ) const {
		for( auto e: m_map ) 
			os << '[' << e.first << ',' << e.second << ']';
		return os;
	}
};

// Key type K
// - besides being copyable and assignable, is less-than comparable via operator< ;
// - is bounded below, with the lowest value being std::numeric_limits<K>::min();
// - does not implement any other operations, in particular no equality comparison or arithmetic operators.
template<typename T>
class test_key {
	T value;
public:
	/*explicit*/ test_key( T v )
		: value(v)
	{}

	bool operator < ( const test_key& op ) const {
		return value < op.value;
	}

	std::ostream& print( std::ostream& os ) const {
		return os << value;
	}
};
namespace std {
	//
	//	I hope this much of implementation of numeric_limits is enough for my
	//	tests.
	//
	template <typename T>
	struct numeric_limits<::test_key<T> > : public numeric_limits<T> {
		typedef ::test_key<T> value_type;
		typedef numeric_limits<T> base_type;
		static value_type min() {
			return value_type( base_type::min() );
		}
		static value_type max() {
			return value_type( base_type::max() );
		}
	};
}
template <typename T>
inline std::ostream& operator << ( std::ostream& os, test_key<T> t ) {
	return t.print(os);
}
template <typename T>
void test_test_key() {

	typedef test_key<T> test_type;
	test_type a(T(3.5));
	test_type b(T(5.5));

	std::cout << "a<b before a=b: " << (a < b) << std::endl;
	a = b;
	std::cout << "a<b after a=b: " << (a < b) << std::endl;
	std::cout << "min: " << std::numeric_limits<test_type>::min() << std::endl;
	std::cout << "max: " << std::numeric_limits<test_type>::max() << std::endl;
}

// Value type V
// - besides being copyable and assignable, is equality-comparable via operator== ;
// - does not implement any other operations.
template<typename T>
class test_value {
	T value;
public:
	/*explicit*/ test_value( T v )
		: value(v)
	{}

	bool operator == ( const test_value& op ) const {
		return value == op.value;
	}
	
	std::ostream& print( std::ostream& os ) const {
		return os << value;
	}
};
template <typename T>
void test_test_value() {
	test_value<T> a(T(3.5));
	test_value<T> b(T(5.5));

	std::cout << "a==b before a=b: " << (a == b) << std::endl;
	a = b;
	std::cout << "a==b after a=b: " << (a == b) << std::endl;
}
template <typename T>
inline std::ostream& operator << ( std::ostream& os, test_value<T> t ) {
	return t.print(os);
}

//
//	Test throws this exception if fails.
//
struct test_failed : public std::logic_error {
	test_failed()
		: logic_error("Test failed.")
	{}
};
//
// The representation in m_map must be canonical, that is, consecutive map entries must not have the same value: 
// ..., (0,'A'), (3,'A'), ... is not allowed.
//
template <class C>
void test_if_canonical(const C& c) {
	for (auto it = std::next(c.begin()); it != c.end(); ++it) {
		if (it->second == std::prev(it)->second)
			throw test_failed();
	}
}
// Provide a function IntervalMapTest() here that tests the functionality of the interval_map,
// for example using a map of unsigned int intervals to char.
// Many solutions we receive are incorrect. Consider using a randomized test to discover 
// the cases that your implementation does not handle correctly.
void IntervalMapTest() {
try {
#if 0
	std::cout << "=============================================" << std::endl;
	std::cout << "Test test_key<int>" << std::endl;
	test_test_key<int>();

	std::cout << "=============================================" << std::endl;
	std::cout << "Test test_key<double>" << std::endl;
	test_test_key<double>();

	std::cout << "=============================================" << std::endl;
	std::cout << "Test test_value<int>" << std::endl;
	test_test_value<int>();

	std::cout << "=============================================" << std::endl;
	std::cout << "Test test_value<double>" << std::endl;
	test_test_value<double>();
#endif

	//	Check that key value is not less the std::numeric_limits<key>::min().
	try {
		interval_map<test_key<double>, test_value<double>> im(0);
		im.assign(0, 500, 3);
		throw test_failed();
	}
	catch (const std::runtime_error&) {
	}

	//
	//	Check map for some interesting values.
	//
	typedef test_key<int> key;
	typedef test_value<int> val;
	interval_map<key, val> im(0);

	std::stringstream log;
	auto TEST = [&log,&im](const std::string& golden ) {
		test_if_canonical(im.m_map);
		std::stringstream ss;
		im.print(ss);
		log << ss.str() << std::endl;
		if (ss.str() != golden)
			throw test_failed();
	};
	// check initial state.
	TEST("[-2147483648,0]");

	im.assign(std::numeric_limits<key>::min(), std::numeric_limits<key>::min(), -1);
	TEST("[-2147483648,0]");

	im.assign(std::numeric_limits<key>::max(), std::numeric_limits<key>::max(), -1);
	TEST("[-2147483648,0]");

	im.assign(0, 0, -1);
	TEST("[-2147483648,0]");

	im.assign(std::numeric_limits<key>::min(), std::numeric_limits<key>::max(), -1);
	TEST("[-2147483648,-1]");

	im.assign(1000, 2000, 1);
	TEST("[-2147483648,-1][1000,1][2000,-1]");

	im.assign(500, 1500, 1);
	TEST("[-2147483648,-1][500,1][2000,-1]");

	im.assign(1000, 1500, 2);
	TEST("[-2147483648,-1][500,1][1000,2][1500,1][2000,-1]");

	im.assign(0, 500, 3);
	TEST("[-2147483648,-1][0,3][500,1][1000,2][1500,1][2000,-1]");

	im.assign(-1000, -500, 3);
	TEST("[-2147483648,-1][-1000,3][-500,-1][0,3][500,1][1000,2][1500,1][2000,-1]");

	im.assign(-500, 0, 3);
	TEST("[-2147483648,-1][-1000,3][500,1][1000,2][1500,1][2000,-1]");

	im.assign(-500, 0, 4);
	TEST("[-2147483648,-1][-1000,3][-500,4][0,3][500,1][1000,2][1500,1][2000,-1]");

	im.assign(2000, std::numeric_limits<key>::max(), 4);
	TEST("[-2147483648,-1][-1000,3][-500,4][0,3][500,1][1000,2][1500,1][2000,4]");

	im.assign(3000, std::numeric_limits<key>::max(), 5);
	TEST("[-2147483648,-1][-1000,3][-500,4][0,3][500,1][1000,2][1500,1][2000,4][3000,5]");

	im.assign(2000, 3000, 5);
	TEST("[-2147483648,-1][-1000,3][-500,4][0,3][500,1][1000,2][1500,1][2000,5]");

	im.assign(std::numeric_limits<key>::min(), -1000, 4);
	TEST("[-2147483648,4][-1000,3][-500,4][0,3][500,1][1000,2][1500,1][2000,5]");

	im.assign(std::numeric_limits<key>::min(), -2000, 5);
	TEST("[-2147483648,5][-2000,4][-1000,3][-500,4][0,3][500,1][1000,2][1500,1][2000,5]");

	im.assign(-2000, -1000, 5);
	TEST("[-2147483648,5][-1000,3][-500,4][0,3][500,1][1000,2][1500,1][2000,5]");

	im.assign(-750, 1750, 4);
	TEST("[-2147483648,5][-1000,3][-750,4][1750,1][2000,5]");

	im.assign(-1000, 2000, 5);
	TEST("[-2147483648,5]");

	std::cout << log.str() << std::endl;
	std::cout << "PASS" << std::endl;
}
catch (const test_failed&) {
	std::cerr << "FAIL: test_failed" << std::endl;
}
catch (const std::exception& e)
{
	std::cerr << std::endl
		<< "FAIL: std::exception(\"" << e.what() << "\")" << std::endl;
}
catch (...)
{
	std::cerr << std::endl
		<< "FAIL: unknown exception." << std::endl;
}}

int main(int argc, char* argv[]) {
	IntervalMapTest();
	return 0;
}

/*
The following paragraphs from the final draft of the C++1x ISO standard describe the available 
operations on a std::map container, their effects and their complexity.

23.2.1 General container requirements 

<EFBFBD>1	Containers are objects that store other objects. They control allocation and deallocation of 
these objects through constructors, destructors, insert and erase operations.

<EFBFBD>6	begin() returns an iterator referring to the first element in the container. end() returns 
an iterator which is the past-the-end value for the container. If the container is empty, 
then begin() == end();

24.2.1 General Iterator Requirements

<EFBFBD>1	Iterators are a generalization of pointers that allow a C++ program to work with different 
data structures.

<EFBFBD>2	Since iterators are an abstraction of pointers, their semantics is a generalization of most 
of the semantics of pointers in C++. This ensures that every function template that takes 
iterators works as well with regular pointers.

<EFBFBD>5	Just as a regular pointer to an array guarantees that there is a pointer value pointing past 
the last element of the array, so for any iterator type there is an iterator value that points 
past the last element of a corresponding sequence. These values are called past-the-end values. 
Values of an iterator i for which the expression *i is defined are called dereferenceable. 
The library never assumes that past-the-end values are dereferenceable. Iterators can also have 
singular values that are not associated with any sequence. [ Example: After the declaration of 
an uninitialized pointer x (as with int* x;), x  must always be assumed to have a singular 
value of a pointer. <20>end example ] Results of most expressions are undefined for singular 
values; the only exceptions are destroying an iterator that holds a singular value, the 
assignment of a non-singular value to an iterator that holds a singular value, and, for 
iterators that satisfy the DefaultConstructible requirements, using a value-initialized 
iterator as the source of a copy or move operation.

<EFBFBD>10 An invalid iterator is an iterator that may be singular. (This definition applies to pointers, 
since pointers are iterators. The effect of dereferencing an iterator that has been invalidated 
is undefined.)

23.2.4 Associative containers

<EFBFBD>1	Associative containers provide fast retrieval of data based on keys. The library provides four 
basic kinds of associative containers: set, multiset, map and multimap.

<EFBFBD>4	An associative container supports unique keys if it may contain at most one element for each key. 
Otherwise, it supports equivalent keys. The set and map classes support unique keys; the multiset 
and multimap classes support equivalent keys.

<EFBFBD>5	For map and multimap the value type is equal to std::pair<const Key, T>. Keys in an associative 
container are immutable.

<EFBFBD>6	iterator of an associative container is of the bidirectional iterator category.
(i.e., an iterator i can be incremented and decremented: ++i; --i;)

<EFBFBD>9	The insert member functions (see below) shall not affect the validity of iterators and references 
to the container, and the erase members shall invalidate only iterators and references to the erased 
elements.

<EFBFBD>10	The fundamental property of iterators of associative containers is that they iterate through the 
containers in the non-descending order of keys where non-descending is defined by the comparison 
that was used to construct them.

Associative container requirements (in addition to general container requirements):

std::pair<iterator, bool> insert(std::pair<const key_type, T> const& t)
Effects: Inserts t if and only if there is no element in the container with key equivalent to the key of t. 
The bool component of the returned pair is true if and only if the insertion takes place, and the iterator 
component of the pair points to the element with key equivalent to the key of t.
Complexity: logarithmic

iterator insert(const_iterator p, std::pair<const key_type, T> const& t)
Effects: Inserts t if and only if there is no element with key equivalent to the key of t in containers with
unique keys. Always returns the iterator pointing to the element with key equivalent to the key of t.
Complexity: logarithmic in general, but amortized constant if t is inserted right before p.

size_type erase(key_type const& k)  
Effects: Erases all elements in the container with key equivalent to k. Returns the number of erased elements.
Complexity: log(size of container) + number of elements with key k

iterator erase(const_iterator q) 
Effects: Erases the element pointed to by q. Returns an iterator pointing to the element immediately following 
q prior to the element being erased. If no such element exists, returns end().
Complexity: Amortized constant

iterator erase(const_iterator q1, const_iterator q2)
Effects: Erases all the elements in the left-inclusive and right-exclusive range [q1,q2). Returns q2.
Complexity: Amortized O(N) where N has the value distance(q1, q2).

void clear() 
Effects: erase(begin(), end())
Post-Condition: empty() returns true
Complexity: linear in size().

iterator find(key_type const& k);
Effects: Returns an iterator pointing to an element with the key equivalent to k, or end() if such an element is not found
Complexity: logarithmic

size_type count(key_type const& k) 
Effects: Returns the number of elements with key equivalent to k
Complexity: log(size of map) + number of elements with key equivalent to k

iterator lower_bound(key_type const& k)
Effects: Returns an iterator pointing to the first element with key not less than k, or end() if such an element is not found.
Complexity: logarithmic

iterator upper_bound(key_type const& k)
Effects: Returns an iterator pointing to the first element with key greater than k, or end() if such an element is not found.
Complexity: logarithmic

23.4.1 Class template map

<EFBFBD>1 	A map is an associative container that supports unique keys (contains at most one of each key value) and provides 
for fast retrieval of values of another type T based on the keys. The map class supports bidirectional iterators.

23.4.1.2 map element access

T& operator[](const key_type& x);
Effects: If there is no key equivalent to x in the map, inserts value_type(x, T()) into the map. 
Returns: A reference to the mapped_type corresponding to x in *this.
Complexity: logarithmic.

T& at(const key_type& x);
const T& at(const key_type& x) const;
Returns: A reference to the element whose key is equivalent to x.
Throws: An exception object of type out_of_range if no such element is present.
Complexity: logarithmic.
*/