1. Lecture 5: Floodfill

2. Floodfill Overview First assume that there are no walls Give each cell a distance from the goal. The goal has distance 0. Repeat until we reach the goal: Go to the neighboring cell with the smallest distance to the goal Run the update distances algorithm (see later slide)

3. Example

4. Maze Representation Each cell has a distance (0-252 for a 16 x 16 maze) and Each cell can be represented by 4 walls or 2 walls If you have 4 walls for each cell, then you need to update 2 places on discovering a new wall. If you have 2 walls for each cell, then you need an extra “dummy” row and column. You may also want to have a “visited” bit for speed runs. If you use the “visited” bit, then you don’t need to run the Update Distances algorithm on cells that you have already visited, meaning you can go faster on them.

5. Two Options For Maze Representation +-----+-----+-----+ | N | N | N | |W E|W E|W E| | S | S | S | +-----+-----+-----+ | N | N | N | |W E|W E|W E| | S | S | S | +-----+-----+-----+ | N | N | N | |W E|W E|W E| | S | S | S | +-----+-----+-----+ 3x3 Maze with duplicate walls +-----+-----+-----+-----+ | | | | | |W X |W X |W X |W X | | S | S | S | S | +-----+-----+-----+-----+ | | | | | |W |W |W |W X | | S | S | S | S | +-----+-----+-----+-----+ | | | | | |W |W |W |W X | | S | S | S | S | +-----+-----+-----+-----+ | | | | | |W |W |W |W X | | S | S | S | S | +-----+-----+-----+-----+ 3x3 Maze with Dummy row/column X = dummy cell

6. Print maze function It is essential for debugging to be able to print out your maze Should look something like this: +---+---+---+ |*5 *4 V3 | +---+---+ + | 0 1 2 | +---+---+---+ Use ‘+’ for posts. Use “---” for north/south walls. Use ‘|’ (pipe) for east/west walls. Use ‘*’ for visited. Use, ^, V for the direction of the mouse. If you display distances in base 10, then you will need to do something else when you have 3 digit distances.

7. The System Stack Space is allocated for each function call de-allocated for function return Where local variables are stored Only 1 kB max by default in our project files 1 MB by default on Windows 8 MB by default on Linux Recursion and large local arrays are bad on embedded systems due to the limited memory

8. Dynamic Memory Allocation Allocate memory at runtime on System Heap malloc and free (c standard library) new and delete (c++) Bad on embedded systems Takes an unpredictable amount of time Fragmentation may require moving arrays of data System Heap is small, similar to System Stack Makes your code more complicated and buggy Memory leaks are more difficult to detect No OS to kill your process, tell you what happened

9. Update Distances Algorithm Use a stack method instead of recursion Have stack S as a global variable (should be statically sized, not dynamic) This algorithm runs every time a new cell is visited by the mouse: If there are any new walls discovered: Make sure S is empty Push current cell and cells adjacent to new walls onto S While S is not empty: currCell = pop(S) correctDist = min(all open neighbor distances) + 1 if currCell.dist != correctDist and currCell.dist != 0: currCell.dist = correctDist push all open neighbors to S

10. Tips Run your Update Distances algorithm as soon as your mouse enters the cell, not when it reaches the center of the cell. You can use Green’s maze generation excel sheet to create test mazes to run your algorithm. For example “bool readLeftWall(), bool readRightWall(), bool readFrontWall()” will read from Green’s array instead of the mouse’s IR sensors. The stack size for the update distances algorithm should be around 512. It is possible to add a cell more than once, therefore 255 may not be enough.