Efficiently counting rooms from a floorplan

Question

Note this was the wrong version of the code. The updated version is here: Efficiently counting rooms from a floorplan (version 2) My apologies!

Update

Final version 3 with test harness here: Multithreaded testing for counting rooms from a floor plan solution

---

I was inspired by Calculating the number of rooms in a 2D house and decided to see if I could come up with efficient code to solve the same problem.

To recap, the problem (from here) is this:

You are given a map of a building, and your task is to count the number of rooms. The size of the map is \$n \times m\$ squares, and each square is either floor or wall. You can walk left, right, up, and down through the floor squares.

Input

The first input line has two integers \$n\$ and \$m\$: the height and width of the map.

Then there are \$n\$ lines of \$m\$ characters that describe the map. Each character is . (floor) or # (wall).

Output

Print one integer: the number of rooms.

Constraints

\$1\le n,m \le 2500\$

Example

Input:

5 8
########
#..#...#
####.#.#
#..#...#
########

Output:

3

Strategy

It seemed to me to be possible to solve the problem by processing line at a time, so that's what my code does. Specifically, it keeps a tracking std::vector<std::size_t> named tracker that corresponds to the rooms from the previous row and starts with all zeros.

As it reads each line of input, it processes the line character at a time. If it's non-empty (that is, if it's a wall), set the corresponding tracker entry to 0.

Otherwise, if the previous row (that is, the matching value from the tracker vector) was a room, then this is part of the same room.

If the previous character in the same row was a room, this is the same room.

The code also has provisions for recognizing that what it "thought" was two rooms turns out to be one room, and adjusts both the tracker vector and the overall roomcount.

Because I wanted to be able to test it with many different inputs, my version of the code keeps reading and processing each floor plan until it gets to the end of the file.

The code is time efficient because it makes only a single pass through the input, and it's memory efficient because it only allocates a single \$1 \times m\$ vector.

Questions

1. Correctness - The code works correctly on every input I've tried, but if there is any error in either the code or the algorithm, I'd like to know.
2. Efficiency - Could the code be made even more efficient?
3. Reusability - This works for a 2D map, but I'd like to adapt it to 3 or more dimensions. Are there things I could do in this code to make such adaptation simpler?

Any hints on style or any other aspect of the code would be welcome as well.

rooms.cpp

#include <iostream>
#include <vector>
#include <string>
#include <algorithm>

std::size_t rooms(std::istream &in) {
    std::size_t height;
    std::size_t width;
    std::size_t roomcount{0};
    static constexpr char empty{'.'};
    in >> height >> width;
    if (!in)
        return roomcount;
    std::vector<std::size_t> tracker(width, 0);
    for (auto i{height}; i; --i) {
        std::string row;
        in >> row;
        if (row.size() != width) {
            in.setstate(std::ios::failbit);
            return roomcount;
        } 
        for (std::size_t j{0}; j < width; ++j) {
            if (row[j] == empty) {
                // continuation from line above?
                if (tracker[j]) {
                    // also from left?
                    if (j && tracker[j-1] && (tracker[j-1] != tracker[j])) {
                        tracker[j] = tracker[j-1] = std::min(tracker[j], tracker[j-1]);
                        --roomcount;
                    }
                } else {
                    // continuation from left?
                    if (j && tracker[j-1]) {
                        tracker[j] = tracker[j-1];
                    } else {
                        tracker[j] = ++roomcount;
                    }
                }
            } else {
                tracker[j] = 0;
            }
        }
    }
    return roomcount;
}


int main() {
    auto r = rooms(std::cin);
    while (std::cin) {
        std::cout << r << '\n';
        r = rooms(std::cin);
    }
}

test.in

5 8
########
#..#...#
####.#.#
#..#...#
########
9 25
#########################
#.#.#.#.#.#.#.#.#.#.#.#.#
#########################
#.#.#.#.#.#.#.#.#.#.#.#.#
#########################
#.#.#.#.#.#.#.#.#.#.#.#.#
#########################
#.#.#.#.#.#.#.#.#.#.#...#
#########################
3 3
...
...
...
3 3
###
...
###
3 3
###
###
###
7 9
#########
#.#.#.#.#
#.#.#.#.#
#.#...#.#
#.#####.#
#.......#
#########
5 8
########
#..#.#.#
##.#.#.#
#..#...#
########
7 8
########
#..#.#.#
##.#.#.#
#..#...#
########
#..#...#
########
7 9
#########
#.#.#.#.#
#.#.#.#.#
#.#.#.#.#
#.#.#.#.#
#.......#
#########
7 9
#########
#.#.##..#
#.#.##.##
#.#.##..#
#.#...#.#
#...#...#
#########
7 9
#########
#.#.....#
#.#.###.#
#.#...#.#
#.#####.#
#.......#
#########
7 9
#########
#.......#
#.#####.#
#.#.#.#.#
#.#.#.#.#
#.......#
#########

Results

Running the program as rooms <test.in produces this expected result:

3
47
1
1
0
2
2
4
1
1
1
1

Answer 1

The program does not work correctly for all input. As an example, the output is 0 (zero rooms) for the input

5 8
########
######.#
#......#
##.#...#
########