Enviroment Setting

Say we have a 2D grid with $R$ rows and $C$ columns. Assume $(r,c)$ represents the current cell we are processing. There are many cases where we need to find out all neighbors of this cell and loop them into a subroutine. What will be a quick and precise way to loop through all of them and at the mean time testing if a coordinate is valid?

Neighbor Coordinate Changes

First, we use two array to store the relative change of all neighbors.

int dr[] = {1, 1, 0, -1, -1, -1,  0,  1};
int dc[] = {0, 1, 1,  1,  0, -1, -1, -1};
// (dr[i], dc[i]) pair gives one possible neighbor relative coordinate.
// ordered: S, SE, E, NE, N, NW, W, SW
-1,-1 -1,0 -1,1
0,-1 r,c 0,1
1,-1 1,0 1,1

given this setting, we can easily loop through all possible neighbors. Next we will get to how to quickly check if within bounds.

Validate Coordinate

Assume $(r, c)$ now contains the new coordinate of a possible neighbor, which is calculated base on above relative neighbor position. We can use the following function to quickly test if it is still valid:

bool validate_coordinate(const int R, const int C, const int r, const int c){
  if (r < 0 || r > R || c < 0 || c > C) return false;
  return true;

Application: Flood Fill

This is a very common problem of finding and counting the number of connected parts. The following approach is a depth first one. A bfs one works very similarly. It is also called coloring in CS terminology. It is also known as “flood fill” and usually performed on implicit graphs.

int floodfill(int r, int c, char c1, char c2) { // returns the size of CC
  if (r < 0 || r >= R || c < 0 || c >= C) return 0; // outside grid
  if (grid[r][c] != c1) return 0; // does not have color c1
  int ans = 1; // adds 1 to ans because vertex (r, c) has c1 as its color
  grid[r][c] = c2; // now recolors vertex (r, c) to c2 to avoid cycling!
  for (int d = 0; d < 8; d++)
    ans += floodfill(r + dr[d], c + dc[d], c1, c2);
  return ans; // the code is neat due to dr[] and dc[]


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