Midterm Practice Question Solutions

1. Suppose lst is a vector<string>. Re-write the following code using a C-style for-loop with an index variable:

   for(string& s : lst) {
       cout << s << "\n";
   }
   

   Sample solution:

   for(int i = 0; i < lst.size(); ++i) {
      cout << lst[i] << "\n";
   }
   

2. Consider the following code fragment:

   void example() {
       vector<float*> nums = {new float(1),
                              new float(2),
                              new float(3)
                             };
   
       // ... code that uses nums ...
   }
   

   Add a fragment of code to example() that ensures there are no memory leaks due to the values nums points to.

   Sample solution:

   for(float* p : nums) {
      delete p;
   }
   

3. Suppose 4 friends are playing 7-card poker. What is the probability that one of them is dealt a hand with all 4 aces?

   While you could solve this problem purely mathematically, don’t do it that way here. Instead, simulate shuffling a deck of cards and dealing 4 7-card hands, and then check each hand to see if one contains all 4 aces.

   Repeat this, say, a million times, and keep a count of how many times someone gets 4 aces. Divide the final count by a million to get an estimate of the probability of getting four aces.

   Sample solution:

   #include "error.h"
   #include <iostream>
   #include <vector>
   #include <algorithm>
   #include <ctime>
   
   using namespace std;
   
   // 0, 1, 2, and 3 are the aces
   bool is_ace(int c) {
       return 0 <= c && c <= 3;
   }
   
   // Returns true just when all the aces appear in cards[begin], ...
   // cards[end-1].
   bool has_four_aces(const vector<int>& cards, int begin, int end) {
       int count = 0;
       for(int i = begin; i < end; ++i) {
           if (is_ace(cards[i])) {
               count++;
           }
       }
       return count == 4;
   }
   
   int main() {
       // initialize random number generator based on time
       srand(time(NULL));
   
       // create the deck of cards, values 0 to 51
       vector<int> cards(52);
       for(int i = 0; i < cards.size(); ++i) {
           cards[i] = i;
       }
   
       const int NUM_TRIES = 10000000;
       int count = 0;
       for(int tries = 1; tries <= NUM_TRIES; ++tries) {
           random_shuffle(cards.begin(), cards.end());
           if (has_four_aces(cards, 0, 7)   || has_four_aces(cards, 7, 14) ||
               has_four_aces(cards, 14, 21) || has_four_aces(cards, 21, 28))
           {
               count++;
           }
           if (tries % 1000000 == 0)
               cout << "tries = " << tries
                    << " of " << NUM_TRIES
                    << "\n";
       }
   
       cout << "Probability: "
            << count << " / " << NUM_TRIES << " = "
            << double(count) / NUM_TRIES
            << "\n";
   }