1A)
apvector<int> CalculateModes(const apvector<int> &tally) {
       apvector<int> result;
       int a=0;
       int max = FindMax(tally);
       // find out how many modes we have
       for (int c = 0; c < tally.length(); c++)
          if (tally[c] == max) a++;
       result.resize(a); // now make enough room for it
       // now set the results
       a = 0;
       for (int c = 0; c < tally.length(); c++) {
          if (tally[c] == max) result[a++] = c;
       return result;
       }

1B)
int KthDataValue(const apvector<int> &tally, int k) {
    int index = 0;
    while (k>0) {
       k = k - tally[index];
       index++;
       }
    index--;
    return index;
}

2A)
void ChangePrices(GroceryStore &store, istream &input) {
    apstring groceryname;
    double newprice;
    while (input >> groceryname >> newprice) {
       store.SetPrice(groceryname, newprice);
       }
    }

2B)
apstring BargainItem(const GroceryStore &store, char category) {
    apvector<apstring> items= store.GetItems(category);
    if (category == "P" || category == "M" || category == "D") {
    double bestbargain = store.GetPrice(items[0]) / store.GetSize(items[0])
    apstring bestname = items[0];
    for (int a = 0; a < items.length(); a++)
       if (bestbargain > (store.GetPrice(items[a]) / store.GetSize(items[a]))) {
          bestbargain = store.GetPrice(items[a])/ store.GetSize(items[a]);
          bestname = items[a]; 
       }
    return bestname;
}
else return "none";
}

3A)

Position Position::Northeast () const {
    return North().East();
}

3B)

Neighborhood Fish::ForwardNbrs(const Environment &env) {
    Neighborhood result;
    if (myDir == "N") {
       if (env.isempty(myPos.North()) result.Add(myPos.North());
       if (env.isempty(myPos.Northeast()) result.Add(myPos.Northeast();
       if (env.isempty(myPos.Northwest()) result.Add(myPos.Northwest();
       }
    else if (myDir == "NE") {
       if (env.isempty(myPos.North()) result.Add(myPos.North());
       if (env.isempty(myPos.Northeast()) result.Add(myPos.Northeast());
       if (env.isempty(myPos.East()) result.Add(myPos.East());
    }
    ... // the other cases, which the prompt says we can use ... to indicate
    return result;
    }

3C)
 
apstring Position::DirectionTo(const Position & other) const {
    apstring result;  
    if (other.equals(myPos.North()) result = "N";
    if (other.equals(myPos.Northeast()) result = "NE";
    ... // the other cases
    return result;
    }

4A)
int Flight::EmptySeatCount(const apstring & seatType) const {
    int countseats = 0;
    for (int a = 0; a < mySeats.numrows(); a++)
       for (int b = 0; b < mySeats.numcols(); b++)  {
          if (seatType == "any" && mySeats[a][b].GetPassenger().GetName()== "") countseats++;
          else if (mySeats[a][b].GetType() == seatType && mySeats[a][b].GetPassenger().GetName() == "") countseats++;
       }
    return countseats;
}

4B)

int Flight::FindBlock(int row, int seatsNeeded) const {
    bool found = false;
    int seatsfound=0;
    int indexfound = 0;
    for (int a = 0; a < mySeats.numcols(); a++) {
       if (mySeats[row][a].GetPassenger().GetName() == "") {
          seatsfound = 1;
          indexfound = a;
          for (;(a < mySeats.numcols() && seatsfound < seatsNeeded) && (mySeats[row][a].GetPassenger().GetName() == ""); a++) {
              seatsfound++;
            }         
          if (seatsfound == seatsNeeded) {
            found = true;
            break;
          }
         }
        }
     if (found==true) return indexfound;
      return -1;
}

4C)

bool Flight::AssignGroup(const apvector<Passenger> &group) {    
    bool result = false;
    int startindex;
      for (int row = 0; row < mySeats.numrows(); row++) {
       startindex = FindBlock(row, group.length());
       if (startindex != -1) {
          result = true;
          for (int col = 0; col < group.length(); col++)
             mySeats[row][col+startindex] = group[col];
            }
       if (result == true) break; // don't do this more than once
       }
    return result;
}