Assignment 5, Due at 11:59pm, Tue Oct 14

Objectives

Sample problems and sample solutions

Sample problem 1

A string of characters is a palindrome if it reads the same from left to right as from right to left. For example, the names "anna", "bob",and "otto" are palindromes. A former prime minister of Cambodia was "lon nol", which is a palindrome. Phrases such as "step on no pets" and "rats live on no evil star" are palindromes.

You are to write a function that takes an input string and returns true if the input is a palindrome, and false otherwise. You will write an iterative and a recursive version of the function, whose signatures are as follows. You must use the signature (i.e. prototype) given. No helper function is accepted.

Note that by definition an empty string is a palindrome. So your function must return true if the input string is empty. Also, you can assume that all characters are in lower case. 

bool iterative_palindrome(const string& str) 
{
    // your code goes here
}

For the recursive solution, given an input string str we will call the following function with

recursive_palindrome(str, 0, str.length())

In particular, note that end is one more than the index of the last character. (Recall the size_t issue with iterative binary search 2 in the lecture slides.) 

bool recursive_palindrome(const string& str, size_t start, size_t end) 
{
    // your code goes here
}
Sample solution 1
The iterative solution 
// Would you agree that it's much cleaner than the recursive one?
bool iterative_palindrome(const string& str) 
{
    for (size_t i=0; i<str.length()/2; i++) {
        if (str[i] != str[n-1-i]) return false;
    }
    return true;
}
The recursive solution 
// the initial call is recursive_palindrome(str, 0, str.length()) 
bool recursive_palindrome(const string& str, size_t start, size_t end) 
{
    if (start >= end) return true;
    return (str[start] == str[end-1]) && 
           recursive_palindrome(str, start+1, end-1);
}
Sample problem 2
Given a non-negative integer n, write the iterative and recursive versions of a function that takes a non-negative integer n and returns a string which represents n in binary. For example, You must use the signature (i.e. prototype) given. No helper function is accepted. 
// the iterative solution
string iterative_binrep(size_t n) 
{
    // your code goes here
}

// the recursive solution
string recursive_binrep(size_t n) 
{
    // your code goes here
}
Sample solution 2
// the iterative solution
string iterative_binrep(size_t n) {
    string ret;
    do {
        ret.insert(0, (n%2 == 0? "0" : "1"));
        n = n/2;
    } while (n > 0);
    return ret;
}

// the recursive solution. Would you agree that it's much cleaner?
string recursive_binrep(size_t n) {
    if (n == 0) return "0";
    if (n == 1) return "1";
    return recursive_binrep(n/2) + (n%2 == 0? "0" : "1");
}

What to do? Solve the following problems

Problem 1
Write the iterative and recursive versions of a function that takes in a stack of integers and returns the number of negative integers from the stack. You must use the signature (i.e. prototype) given. No helper function is accepted. 
// the iterative solution
size_t iterative_num_negatives(stack<int> int_stack)
{
    // your code goes here
}

// the recursive solution, the initial call is 
size_t recursive_num_negatives(stack<int> int_stack)
{
    // your code goes here
}
Problem 2
Write the iterative and recursive versions of a function that takes in two vectors a and b, both are vector<int>, and returns whether a is a sub-vector of b a is a sub-vector of b if we can find an exact copy of a in some contiguous block of elements of b. For example, [1 -2 5 3] is a sub-vector of [10 -2 1 -2 5 3 4 6 8], but it is not a sub-vector of [10 -2 1 -2 5 4 3 6 8]. You must use the signature (i.e. prototype) given. No helper function is accepted. 
// the iterative solution
bool iterative_sub_vector(vector<int>& a, vector<int> b)
{
    // your code goes here
}

/** 
 * the recurive solution, you CAN NOT call erase NOR copy many elements of 
 * b into a separate vector. The function prototyp is already a hint
 * the initial call is recursive_sub_vector(a, b, 0)
 */
bool recursive_sub_vector(vector<int>& a, vector<int> b, size_t k)
{
    // your code goes here
}
Problem 3
In this problem, you are free to pick any type of solution (iterative or recursive) you want. You are to write a function called sum_to_target that takes a vector of integers int_vec and a target integer target. The function returns true if there is a subset of integers in int_vec that sums to target, and false otherwise. If target == 0, then the answer is always true, because the empty subset sums to 0. If your solution is recursive, feel free to add extra parameters to your function to accomodate the recursion. (For example, recursive_sub_vector above has an extra parameter.) In that case, please indicate the initial call to get the recursion started.

How to submit

Please type all your functions in properly indented cpp; put them in the same text file, named a5.cpp. Please only include those functions in the submission; You can (and should) compile and test your functions, but when you submit please remove the extra pieces of codes you use to test them. (For example, #include<iostream> and main() should not be included in the submission. We grade the submission by reading only the code you put in the functions' bodies. Then, 
submit_cse250 a5.cpp
Note that the above line only works if you logged in to your CSE account and the file a5.cpp is there. All previous things can be done at home, as long as you remember to upload the final a5.cpp file to your CSE account and run the submit script from there.

Grading