Binary Search function that displays all matching values? - c++

Question

I have an assignment that requires me to create a binary search function that will search an array of structs that contain dates for a specified month and then print all of those entries with matching months.
I am having a very difficult time getting the binary search to work properly when I am searching for multiple values, and can't seem to figure out where I'm going wrong.
Here is my binary search function:
void binsearch(Event* ev_ptr[], int size, int month)
{
int low = 0, high = size - 1, first_index = -1, last_index = -1;
while (low <= high) //loop to find first occurence
{
int mid = (low + high) / 2;
if (ev_ptr[mid]->date.month < month)
{
low = mid + 1;
}
else if (ev_ptr[mid]->date.month > month)
{
first_index = mid;
high = mid - 1;
}
else if (ev_ptr[mid]->date.month == month)
{
low = mid + 1;
}
}
low = 0; high = size - 1; //Reset so we can find the last occurence
while (low <= high) //loop to find last occurence
{
int mid = (low + high) / 2;
if (ev_ptr[mid]->date.month < month)
{
last_index = mid;
low = mid + 1;
}
else if (ev_ptr[mid]->date.month > month)
{
high = mid - 1;
}
else if (ev_ptr[mid]->date.month == month)
{
high = mid + 1;
}
}
for (int i = first_index; i <= last_index; i++)
{
cout << "\nEntry found: "
<< endl << ev_ptr[i]->desc
<< endl << "Date: " << ev_ptr[i]->date.month << '/' << ev_ptr[i]->date.day << '/' << ev_ptr[i]->date.year
<< endl << "Time: " << setw(2) << setfill('0') << ev_ptr[i]->time.hour << ':' << setw(2) << setfill('0') << ev_ptr[i]->time.minute << endl;
}
}
and here is my main function:
const int MAX = 50;
int main()
{
Event* event_pointers[MAX];
int count, userMonth;
char userString[80];
count = readEvents(event_pointers, MAX);
sort_desc(event_pointers, count);
display(event_pointers, count);
cout << "\n\nEnter a search string: ";
cin.getline(userString, 80, '\n');
cin.ignore();
linsearch(event_pointers, count, userString);
sort_date(event_pointers, count);
display(event_pointers, count);
cout << "\n\nEnter a month to list Events for: ";
cin >> userMonth;
cin.ignore();
binsearch(event_pointers, count, userMonth);
for (int j = 0; j < count; j++) //Cleanup loop
delete event_pointers[j];
cout << "\nPress any key to continue...";
(void)_getch();
return 0;
}
I've gotten everything else to work as I need to for this assignment, but it's just this binary search that seems to be causing problems. I have tried using some things I found online in the most recent iteration (What I posted above), but to no avail. Any help would be greatly appreciated!

Answer 1

Don't set theses indices with binsearch. Search for an occurence than loop downwards and upwards until the conditions fails. Something like
else if (ev_ptr[mid]->date.month == month)
{
// mid = some occurence found
// increment and decrement mid until condition fails
}```

Answer 2

To design correct binary search function, don't try to guess the solution, it's hard to get it right. Use the method of loop invariants. The function that finds the first occurrence is called lower_bound in the standard library, so let's use this name here, too:
template<class It, typename T>
It lower_bound(It first, std::size_t size, const T& value);
Let's introduce the last variable: auto last = first + size. We will be looking for a transition point pt, such that in the range [first, pt), all elements have values < value, and in the range [pt, last), all elements have values >= value. Let's introduce two iterators (pointers) left and right with the loop invariants:
in the range [first, left) all elements have values < value,
in the range [right, last) all elements have values >= value.
These ranges represent elements examined so far. Initially, left = first, and right = last, so both ranges are empty. At each iteration one of them will be expanded. Finally, left = right, so the whole range [first, last) has been examined. From the definitions above, it follows that pt = right.
The following algorithm implements this idea:
template<class It, typename T>
It lower_bound(const It first, const std::size_t size, const T& value) {
const auto last = first + size;
auto left = first;
auto right = last;
while (left < right) {
const auto mid = left + (right - left) / 2;
if (*mid < value) // examined [first, left)
left = mid + 1;
else // examined [right, last)
right = mid;
}
return right;
}
Here we can reuse variables first and last to represent left and right. I didn't do it for clarify.
Now let's analyze your implementation. I can infer the following loop invariants:
[first, low) - all elements have values < value,
(high, last) - all elements have values >= value.
These are the same invariants, with right being replaced with high + 1. The while loop itself is correct, but the condition, which can be rewritten as
if (*mid <= value)
low = mid + 1;
else {
first_index = mid;
high = mid - 1;
}
is broken. With this condition, the range [first, low) will contain all elements with values <= value. This corresponds to the upper_bound. The comparison should be <, not <=.
You can analyse the second loop in the same way. In that loop at least one assignment of mid is incorrect.
int mid = (low + high) / 2;
...
high = mid + 1;
...
This is potentially an infinite loop. If high = low + 1, then mid = low, and you set high to mid + 1 = high. You modify neither low, nor high, and the loop becomes infinite.
The first approach, with two half-open ranges is beneficial IMO. It is symmetrical and is easier to reason about. If no value has been found, last = first + size is returned, which is a natural choice to represent the end of the range. You should check for first_index and last_index after the loops. What if they have not been reassigned and still hold -1?

Answer 3

1 Define you struct as this example,
struct element {
YourDate date;
...
operator int() const { return date.month;}
};
2 Sort elements as,
std::sort(elements.begin(), elements.end(), std::less<int>());
3 use
std::equal_range(elements.begin(), elements.end(), your_target_month);
4 print what you get from std::equal_range