StackOverflow2013

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Id
14466081
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2013-01-22T19:05:21.350
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2017-05-29T18:08:09.783
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2017-05-29T18:08:09.783
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Score
27
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text
Body
I'll first give you the code and then explain it a bit: <pre class="lang-cpp prettyprint-override"><code>// direction vectors const int dx[] = {+1, 0, -1, 0}; const int dy[] = {0, +1, 0, -1}; // matrix dimensions int row_count; int col_count; // the input matrix int m[MAX][MAX]; // the labels, 0 means unlabeled int label[MAX][MAX]; void dfs(int x, int y, int current_label) { if (x < 0 || x == row_count) return; // out of bounds if (y < 0 || y == col_count) return; // out of bounds if (label[x][y] || !m[x][y]) return; // already labeled or not marked with 1 in m // mark the current cell label[x][y] = current_label; // recursively mark the neighbors for (int direction = 0; direction < 4; ++direction) dfs(x + dx[direction], y + dy[direction], current_label); } void find_components() { int component = 0; for (int i = 0; i < row_count; ++i) for (int j = 0; j < col_count; ++j) if (!label[i][j] && m[i][j]) dfs(i, j, ++component); } </code></pre> This is a common way of solving this problem. The direction vectors are just a nice way to find the neighboring cells (in each of the four directions). The dfs function performs a depth-first-search of the grid. That simply means it will visit all the cells reachable from the starting cell. Each cell will be marked with current_label The find_components function goes through all the cells of the grid and starts a component labeling if it finds an unlabeled cell (marked with 1). This can also be done iteratively using a stack. If you replace the stack with a queue, you obtain the bfs or breadth-first-search.
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