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CS2134 HOMEWORK 5 Solved
Programming Part:
1. Modify programming problem 1 in assignment 4B1 to not store the duplicates, i.e. 101, 101N, 101S are all the same stop.
2. Create a menu for the user to access the data created in programming problem 1 In the interactive phase,the program will repeatedly prompt the user to take any one of the following actions:
(a) Print out the information about all the train stops on a specific route; if no route is found, you shouldprint out a message informing the user.
(b) Print out the information about a specific train stop; if no train stop is found, you should print outa message informing the user.
(c) Print out all the train stops within a certain distance, where the user enters the geographical coordinates. If no stop is found within the distance, print out a message informing the user. (d) quit
To perform these operations you will define one generic function template2 and four functors.
Write a generic function template called perform if that takes four parameters: two iterators, itrStart, itrEnd, and two functors, pred and op. The two iterators should have have the capability of forward iterators. Both functors will have the overloaded operator() that takes one argument. The functor pred’s overloaded operator() returns a boolean value; the functor op’s overloaded operator() does not return any value. The function will apply pred’s overloaded operator() to each item in the range [itrStart, itrEnd). If pred’s overloaded operator() returns true, the other functor op’s overloaded operator() is then applied to the item, e.g.
if ( pred( *itr ) )
{ op(*itr); how_many++;
}
∗
5% extra credit will be given if you turn this assignment in on Fri Oct 21, 2016 by 5:00 p.m.
1You may use the published solution as long as you cite that you are using it.
2This generic function template should be written in the STL generic template function style and should not written to be used only with the train stop data.
The return value of the generic function template perform if is an int which returns the number of items for which the functor pred returned true.
The four functors you will write are:
(a) Write a functor called isStopOnRoute that has a private member variable called route of type char. The constructor takes a single parameter of type char which it uses to initialize the variable route. It also contains an overloaded operator() that takes a single parameter of type trainStopData; the operator returns true if the train stop is on the route.[1]
(b) Write a functor called isSubwayStop that has a private member variable called stopId of type string. The constructor takes a single parameter of type string which it uses to initialize the variable stopId. It also contains an overloaded operator() that takes a single parameter of type trainStopData; the operator returns true if the train stop has an id which is the same as stopid.
(c) Write a functor called isSubwayStopNearX that has three private member variables called longitude, latitude, and d of type double. The constructor takes three parameters of type double which it uses to initialize the private member variables. It also contains an overloaded operator() that takes a single parameter of type trainStopData; the operator returns true if the distance between the train station location and the value of the functors private member variables, longitude and latitude, is at most d. The distance between two points on a sphere is computed using the haversine formula. The code to compute this formula is on NYU Classes in a file called haversine.txt.[2]
(d) Write a functor called printTrainStopInfo. This class contains a single method, an overloaded operator(), that takes a single parameter of type trainStopData that prints out the train stop information.
3. Rewrite the recursive part of the merge sort algorithm presented in class to work with any container which has random access iterators, and has an overloaded operator< for comparison of items in the container. You will not write your own merge method. Instead you will use the STL merge algorithm. Here is the driver for the mergesort algorithm you will write.
template <class RandItr void mergeSort( RandItr start, RandItr end )
{
int sz = end - start; // or use auto sz = end-start;
typedef typename iterator_traits< RandItr ::value_type Object; //Xcode
// typedef iterator_traits< RandItr ::value_type Object; //Other compilers
// Don’t worry about this line of code vector<Object tmp( sz ); mergeSort( tmp.begin(), start, end );
}
The STL algorithm[3] merge takes five arguments, first1, last1, first2, last2, result. The merge algorithm combines “the elements in the sorted ranges [first1,last1) and [first2,last2), into a new range beginning at result with all its elements sorted.”[4]
4. Create a functor called meFirst which has a private member variable, me, of type string. Its constructor will take one argument of type string that it uses to initialize its private member variable, me. The functor’s overloaded operator( ) takes two arguments of type student and returns a boolean value. It returns true if the first students’ name is less than the second students’ name unless either of the students’ name equals the variable me then that name is always less than the other name. Test your functor using the STL 3 parameter algorithm sort, the student class we discussed in class and some data you create yourself.[5]
The class student is from the lecture notes on C++
class student
{ private:
string name; double gpa;
public:
student ( const string & name, double gpa ): name( name ), gpa( gpa ) { } string get_name() const { return name; } double get_gpa() const { return gpa; } };
5. Write an algorithm to do the following: given a vector of boolean values (true/false), order the container such that the false values come before the true values. Your algorithm must run in O(n) and use O(1) space. You algorithm may not simply count the number of true or false values and then assign the correct number of false and true values in the vector. You should think of your algorithm as the first step in creating an algorithm that sorts based on true/false values, where the items are not simply true/false values, but large objects that evaluate to true/false by using a functor. Hint: Be inspired by one of the sorting algorithms we discussed in class.
6. (Extra Credit) Rather than sorting the numbers in either ascending or descending order, suppose we wanted to sort the an array in a new way. The criteria for this sort is given as: if the index of the i’th element is odd, then that element should be less than it’s neighboring elements. If the index of the i’th element is even, it should be greater than it’s neighboring elements. Your algorithm must run in O(nlogn) time and can use at most O(n) extra space Ex: Consider the array [5, 9, 8, 2, 3, 4]. After the sort the array should have: [5, 2, 4, 3, 9, 8]
Explanation: 5 is at index 0, so it must be greater than it’s neighbors (2)
2 is at index 1, so it must be less than it’s neighbors (5 & 4)
4 is at index 2, so it must be greater than it’s neighbors (2 & 3).... and so on Note: The solution may not be unique.
This function should not have any loops.
Written Part:
1. In programming part 2 of this assignment, you are asked to write a generic function template calledperform_if.
• Write the pseudo code for the three to six main steps need to implement perform_if.
• Write the preconditions and postconditions of the function.
• Using Big-Oh notation, what is the running time of this generic function template?
2. (a) Draw the recursion tree for myRecFunc(4).
(b) What is printed by the following function call: myRecFunc(4).
(c) Look at your recursion tree [6]. What is the running time of myRecFunc(n).
void myRecFunc(int n)
{
cout << n << ": "; if (n < 1) return;
myRecFunc(n/2); myRecFunc(n/2);
for (int i = 1; i < n; ++i) cout << "*";
cout << endl;
}
3. (a) Draw the recursion tree for myRecFunc(4).
(b) What is printed by the following function call: myRecFunc(4).
(c) Look at your recursion tree[7]. Determine what is the big-oh running time for myRecFunc(n).
void myRecFunc(int n)
{
cout << n << ": "; if (n < 1) return;
myRecFunc(n/2);
}
4. For this recursive Fibonacci function, fib, how many function calls are made if n=3; how about if n=4? Using the the number of function calls fib made when when n=3 and when n= 4, compute how many function calls are made when n=5. Show your work.
int fib( int n )
{
if( n <= 1 )
return 1;
else
return fib( n - 1 ) + fib( n - 2 );
}
5. What would be printed out by the following code, if the vector a contained {9,8,−11,2,0,3}, and the function printVec printed out contents of a? (Don’t worry about the exact format of the output, the point is to show how the contents of the vector is or is not changing)
// Simple insertion sort. template<class Comparable
void insertionSort( vector<Comparable & a )
{ int j; for( int p = 1; p < a.size( ); p++ )
{
Comparable tmp = a[ p ]; for( j = p; j 0 && tmp < a[ j - 1 ]; j-- ) a[ j ] = a[ j - 1 ];
a[ j ] = tmp; printVec(a); // prints the contents of the vector in order
}
}
6. What would be printed out by the following code, if the vector a contained {9,8,−11,2,0,3}, and the function printVec printed out contents of a? (Don’t worry about the exact format of the output, the point is to show how the contents of the vector is or is not changing)
template <class Comparable void mergeSort( vector<Comparable & a, vector<Comparable & tmpArray, int left, int right )
{
if( left < right )
{
int center = ( left + right ) / 2; mergeSort( a, tmpArray, left, center ); mergeSort( a, tmpArray, center + 1, right ); mymerge( a, tmpArray, left, center + 1, right ); printVec(a); // prints the contents of the vector in order
}
}
7. What would be printed out by the following code, if the vector a contained {9,8,−11,2,0,3}, and the function printVec printed out contents of a? (Don’t worry about the exact format of the output, the point is to show how the contents of the vector is or is not changing)
void quickSort( vector<int & a, int low, int high )
{ if (low < high)
{
int mid = ( low + high )/2; // select pivot to be element in middle position int pivot = a[ mid ]; swap( a[high], a[mid] ); // put pivot in a[high]
// Begin partitioning int i, j; for( i = low, j = high - 1; ; )
{
while ( a[i ] < pivot ) ++i; while( j i && pivot < a[j ] ) --j; if( i < j ) swap( a[ i++ ], a[ j-- ] );
else break;
}
swap( a[ i ], a[ high ] ); // Restore pivot printVec(a); // prints the contents of the vector in order quickSort( a, low, i - 1 ); // Sort small elements quickSort( a, i + 1, high ); // Sort large elements
}
}
8. Show all the function calls organized as a recursion tree where you include the contents of the containera for:
(a) mergeSort on input a = {28, 10, 2, 27, 5, 1}
(b) quickSort on input a = {28, 10, 2, 27, 5, 1}
9. When all the items in the vector are in ”almost” sorted order (e.g. a contains {2,1,4,3,6,5,...,n/2,n/2− 1,...,n,n − 1}, what is the average running time in Big-Oh notation for:
(a) insertionSort
(b) mergeSort(c) quickSort
10. What is the average running time of the quickSelect algorithm we discussed in class?
11. For the quickSelect algorithm we discussed in class, if after the partition it turns out that i + 1 = k why does the function not recursively call itself?
[1] The train stop route is the first letter of the train stop id. For example, train stop id 202 is on route 2, and train stop id B20 is on route B.
[2] You might need to add #define USE MATH DEFINES.
[3] You might need to add #include<algorithm
[4] The quote is from http://www.cplusplus.com/reference/algorithm/merge/. Don’t forget to copy the elements back into the original container after calling the merge function. The STL merge function does NOT have the same signature as the merge function we discussed in class.
[5] This is a biased sort. One item is always first regardless of the other items.
[6] Hint: draw the recursion tree for myRecFunc(5), myRecFunc(6), etc. You should be able to notice a pattern
[7] Hint: draw the recursion tree for myRecFunc(5), myRecFunc(6), etc. You should be able to notice a pattern
1. Modify programming problem 1 in assignment 4B1 to not store the duplicates, i.e. 101, 101N, 101S are all the same stop.
2. Create a menu for the user to access the data created in programming problem 1 In the interactive phase,the program will repeatedly prompt the user to take any one of the following actions:
(a) Print out the information about all the train stops on a specific route; if no route is found, you shouldprint out a message informing the user.
(b) Print out the information about a specific train stop; if no train stop is found, you should print outa message informing the user.
(c) Print out all the train stops within a certain distance, where the user enters the geographical coordinates. If no stop is found within the distance, print out a message informing the user. (d) quit
To perform these operations you will define one generic function template2 and four functors.
Write a generic function template called perform if that takes four parameters: two iterators, itrStart, itrEnd, and two functors, pred and op. The two iterators should have have the capability of forward iterators. Both functors will have the overloaded operator() that takes one argument. The functor pred’s overloaded operator() returns a boolean value; the functor op’s overloaded operator() does not return any value. The function will apply pred’s overloaded operator() to each item in the range [itrStart, itrEnd). If pred’s overloaded operator() returns true, the other functor op’s overloaded operator() is then applied to the item, e.g.
if ( pred( *itr ) )
{ op(*itr); how_many++;
}
∗
5% extra credit will be given if you turn this assignment in on Fri Oct 21, 2016 by 5:00 p.m.
1You may use the published solution as long as you cite that you are using it.
2This generic function template should be written in the STL generic template function style and should not written to be used only with the train stop data.
The return value of the generic function template perform if is an int which returns the number of items for which the functor pred returned true.
The four functors you will write are:
(a) Write a functor called isStopOnRoute that has a private member variable called route of type char. The constructor takes a single parameter of type char which it uses to initialize the variable route. It also contains an overloaded operator() that takes a single parameter of type trainStopData; the operator returns true if the train stop is on the route.[1]
(b) Write a functor called isSubwayStop that has a private member variable called stopId of type string. The constructor takes a single parameter of type string which it uses to initialize the variable stopId. It also contains an overloaded operator() that takes a single parameter of type trainStopData; the operator returns true if the train stop has an id which is the same as stopid.
(c) Write a functor called isSubwayStopNearX that has three private member variables called longitude, latitude, and d of type double. The constructor takes three parameters of type double which it uses to initialize the private member variables. It also contains an overloaded operator() that takes a single parameter of type trainStopData; the operator returns true if the distance between the train station location and the value of the functors private member variables, longitude and latitude, is at most d. The distance between two points on a sphere is computed using the haversine formula. The code to compute this formula is on NYU Classes in a file called haversine.txt.[2]
(d) Write a functor called printTrainStopInfo. This class contains a single method, an overloaded operator(), that takes a single parameter of type trainStopData that prints out the train stop information.
3. Rewrite the recursive part of the merge sort algorithm presented in class to work with any container which has random access iterators, and has an overloaded operator< for comparison of items in the container. You will not write your own merge method. Instead you will use the STL merge algorithm. Here is the driver for the mergesort algorithm you will write.
template <class RandItr void mergeSort( RandItr start, RandItr end )
{
int sz = end - start; // or use auto sz = end-start;
typedef typename iterator_traits< RandItr ::value_type Object; //Xcode
// typedef iterator_traits< RandItr ::value_type Object; //Other compilers
// Don’t worry about this line of code vector<Object tmp( sz ); mergeSort( tmp.begin(), start, end );
}
The STL algorithm[3] merge takes five arguments, first1, last1, first2, last2, result. The merge algorithm combines “the elements in the sorted ranges [first1,last1) and [first2,last2), into a new range beginning at result with all its elements sorted.”[4]
4. Create a functor called meFirst which has a private member variable, me, of type string. Its constructor will take one argument of type string that it uses to initialize its private member variable, me. The functor’s overloaded operator( ) takes two arguments of type student and returns a boolean value. It returns true if the first students’ name is less than the second students’ name unless either of the students’ name equals the variable me then that name is always less than the other name. Test your functor using the STL 3 parameter algorithm sort, the student class we discussed in class and some data you create yourself.[5]
The class student is from the lecture notes on C++
class student
{ private:
string name; double gpa;
public:
student ( const string & name, double gpa ): name( name ), gpa( gpa ) { } string get_name() const { return name; } double get_gpa() const { return gpa; } };
5. Write an algorithm to do the following: given a vector of boolean values (true/false), order the container such that the false values come before the true values. Your algorithm must run in O(n) and use O(1) space. You algorithm may not simply count the number of true or false values and then assign the correct number of false and true values in the vector. You should think of your algorithm as the first step in creating an algorithm that sorts based on true/false values, where the items are not simply true/false values, but large objects that evaluate to true/false by using a functor. Hint: Be inspired by one of the sorting algorithms we discussed in class.
6. (Extra Credit) Rather than sorting the numbers in either ascending or descending order, suppose we wanted to sort the an array in a new way. The criteria for this sort is given as: if the index of the i’th element is odd, then that element should be less than it’s neighboring elements. If the index of the i’th element is even, it should be greater than it’s neighboring elements. Your algorithm must run in O(nlogn) time and can use at most O(n) extra space Ex: Consider the array [5, 9, 8, 2, 3, 4]. After the sort the array should have: [5, 2, 4, 3, 9, 8]
Explanation: 5 is at index 0, so it must be greater than it’s neighbors (2)
2 is at index 1, so it must be less than it’s neighbors (5 & 4)
4 is at index 2, so it must be greater than it’s neighbors (2 & 3).... and so on Note: The solution may not be unique.
This function should not have any loops.
Written Part:
1. In programming part 2 of this assignment, you are asked to write a generic function template calledperform_if.
• Write the pseudo code for the three to six main steps need to implement perform_if.
• Write the preconditions and postconditions of the function.
• Using Big-Oh notation, what is the running time of this generic function template?
2. (a) Draw the recursion tree for myRecFunc(4).
(b) What is printed by the following function call: myRecFunc(4).
(c) Look at your recursion tree [6]. What is the running time of myRecFunc(n).
void myRecFunc(int n)
{
cout << n << ": "; if (n < 1) return;
myRecFunc(n/2); myRecFunc(n/2);
for (int i = 1; i < n; ++i) cout << "*";
cout << endl;
}
3. (a) Draw the recursion tree for myRecFunc(4).
(b) What is printed by the following function call: myRecFunc(4).
(c) Look at your recursion tree[7]. Determine what is the big-oh running time for myRecFunc(n).
void myRecFunc(int n)
{
cout << n << ": "; if (n < 1) return;
myRecFunc(n/2);
}
4. For this recursive Fibonacci function, fib, how many function calls are made if n=3; how about if n=4? Using the the number of function calls fib made when when n=3 and when n= 4, compute how many function calls are made when n=5. Show your work.
int fib( int n )
{
if( n <= 1 )
return 1;
else
return fib( n - 1 ) + fib( n - 2 );
}
5. What would be printed out by the following code, if the vector a contained {9,8,−11,2,0,3}, and the function printVec printed out contents of a? (Don’t worry about the exact format of the output, the point is to show how the contents of the vector is or is not changing)
// Simple insertion sort. template<class Comparable
void insertionSort( vector<Comparable & a )
{ int j; for( int p = 1; p < a.size( ); p++ )
{
Comparable tmp = a[ p ]; for( j = p; j 0 && tmp < a[ j - 1 ]; j-- ) a[ j ] = a[ j - 1 ];
a[ j ] = tmp; printVec(a); // prints the contents of the vector in order
}
}
6. What would be printed out by the following code, if the vector a contained {9,8,−11,2,0,3}, and the function printVec printed out contents of a? (Don’t worry about the exact format of the output, the point is to show how the contents of the vector is or is not changing)
template <class Comparable void mergeSort( vector<Comparable & a, vector<Comparable & tmpArray, int left, int right )
{
if( left < right )
{
int center = ( left + right ) / 2; mergeSort( a, tmpArray, left, center ); mergeSort( a, tmpArray, center + 1, right ); mymerge( a, tmpArray, left, center + 1, right ); printVec(a); // prints the contents of the vector in order
}
}
7. What would be printed out by the following code, if the vector a contained {9,8,−11,2,0,3}, and the function printVec printed out contents of a? (Don’t worry about the exact format of the output, the point is to show how the contents of the vector is or is not changing)
void quickSort( vector<int & a, int low, int high )
{ if (low < high)
{
int mid = ( low + high )/2; // select pivot to be element in middle position int pivot = a[ mid ]; swap( a[high], a[mid] ); // put pivot in a[high]
// Begin partitioning int i, j; for( i = low, j = high - 1; ; )
{
while ( a[i ] < pivot ) ++i; while( j i && pivot < a[j ] ) --j; if( i < j ) swap( a[ i++ ], a[ j-- ] );
else break;
}
swap( a[ i ], a[ high ] ); // Restore pivot printVec(a); // prints the contents of the vector in order quickSort( a, low, i - 1 ); // Sort small elements quickSort( a, i + 1, high ); // Sort large elements
}
}
8. Show all the function calls organized as a recursion tree where you include the contents of the containera for:
(a) mergeSort on input a = {28, 10, 2, 27, 5, 1}
(b) quickSort on input a = {28, 10, 2, 27, 5, 1}
9. When all the items in the vector are in ”almost” sorted order (e.g. a contains {2,1,4,3,6,5,...,n/2,n/2− 1,...,n,n − 1}, what is the average running time in Big-Oh notation for:
(a) insertionSort
(b) mergeSort(c) quickSort
10. What is the average running time of the quickSelect algorithm we discussed in class?
11. For the quickSelect algorithm we discussed in class, if after the partition it turns out that i + 1 = k why does the function not recursively call itself?
[1] The train stop route is the first letter of the train stop id. For example, train stop id 202 is on route 2, and train stop id B20 is on route B.
[2] You might need to add #define USE MATH DEFINES.
[3] You might need to add #include<algorithm
[4] The quote is from http://www.cplusplus.com/reference/algorithm/merge/. Don’t forget to copy the elements back into the original container after calling the merge function. The STL merge function does NOT have the same signature as the merge function we discussed in class.
[5] This is a biased sort. One item is always first regardless of the other items.
[6] Hint: draw the recursion tree for myRecFunc(5), myRecFunc(6), etc. You should be able to notice a pattern
[7] Hint: draw the recursion tree for myRecFunc(5), myRecFunc(6), etc. You should be able to notice a pattern
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