CS302 Midterm, Spring, 2017

James S. Plank

Answers and Grading

Question 1: 21 points

With the exception of part J, the majority answer from the class was right in every circumstance. I have the percentage of correct answers with each part.

Grading: 1.4 points per part. I gave some partial credit, but not a large amount.

Question 2: 15 points

Again, crowdsourcing got the correct answer in each part. Grading: 2.5 points per part.

Question 3: 25 points

Question 4: 15 points

Part A: Each string A corresponds to a substring of S -- you simply need to sort the substring. Another way of looking at it is to consider S to be a set of letters, and each string S corresponds to a subset of S, printed in sorted order. Therefore, this is a power set enumeration. The answer is 2n.

To code this up, first sort s, and then do a power set enumeration to enumerate subsets. For each element in a subset, append it to a string, and after each subset, print the string and clear it. The answer is in q4.cpp, which has a main() that calls OSA with the command line argument:

#include <string>
#include <vector>
#include <algorithm>
#include <iostream>
#include <cstdio>
#include <cstdlib>
using namespace std;

void OSA(string s)
  string a;
  int i, j;

  sort(s.begin(), s.end());

  for (i = 0; i < (1 << s.size()); i++) { 
    for (j = 0; j < s.size(); j++) {
      if (i & (1 << j)) a.push_back(s[j]);
    cout << a << endl;

int main(int argc, char **argv)
  if (argc != 2) { fprintf(stderr, "usage: q2 string\n"); exit(1); }
  return 0;

Grading: 15 points.

Question 5: 14 points

Both of these are straight from the lecture notes. The easiest non-recursive way is to push the elements on the path to the set id onto a vector, and then you run through the vector and set the links fields:

int Disjoint::Find(int element)
  vector <int> q;
  int i;

  while (links[element] != -1) {
    element = links[element];
  for (i = 0; i < q.size(); i++) links[q[i]] = element;
  return element;

Recursion is even easier -- if you're the set id, you're done. Otherwise, call Find() recursively on your link field, and set your link field to the result:

int Disjoint::Find(int element)
  if (links[element] == -1) return element;
  links[element] = Find(links[element]);
  return links[element];

Grading: 7 points per implementation.

Question 6: 10 points

Part A: The variable sp points to the underlying string that is part of s, right after s is set to "0123456789." In the first two calls, the underlying string does not change its location, which means that sp is still pointing it it. However, in the third call, the string library changes where the underlying string is, because the original string is not big enough to accommodate the 13 push_back() calls. That means that sp is no longer pointing to the underlying string -- we don't know what it's pointing to. What we know is that when we print it out, we get nothing.