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POWhat's the order of the following algorithm?
 

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  1. POWhat's the order of the following algorithm?
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    <p>Below is a simple algorithm that I wrote for recursively visiting all of a cell's neighbors in a grid:</p> <pre><code>#include &lt;stdio.h&gt; #include &lt;string.h&gt; #define N 2 // Tracks number of times a cell has been visited. static int visited[N][N]; // If 1, means a cell has already been visited in the current path // through the grid. static int been[N][N]; void visit(int x, int y, int level) { int i; int j; visited[x][y] += 1; been[x][y] = 1; for (i = -1; i &lt; 2; i++) for (j = -1; j &lt; 2; j++) { // Neighbor has to be in the grid and not already visited // in the current path to be visited. if (x + i &gt; -1 &amp;&amp; x + i &lt; N &amp;&amp; y + j &gt; -1 &amp;&amp; y + j &lt; N) { if (been[x + i][y + j] != 1) { visit(x + i, y + j, level + 1); } } } been[x][y] = 0; } void main(void) { int x; int y; int total; // Initialization. for (x = 0; x &lt; N; x++) for (y = 0; y &lt; N; y++) { visited[x][y] = 0; been[x][y] = 0; } // Algorithm. for (x = 0; x &lt; N; x++) for (y = 0; y &lt; N; y++) { visit(x, y, 0); } // Print results. total = 0; for (x = 0; x &lt; N; x++) for (y = 0; y &lt; N; y++) { printf("x: %d, y: %d, visited: %d\n", x, y, visited[x][y]); total += visited[x][y]; } printf("N: %d, total: %d\n", N, total); } </code></pre> <p>I'm curious as to the order of this algorithm. When I run it with N = 2, the output is:</p> <pre><code>x: 0, y: 0, visited: 16 x: 0, y: 1, visited: 16 x: 1, y: 0, visited: 16 x: 1, y: 1, visited: 16 N: 2, total: 64 </code></pre> <p>When I run it with N = 3, I get:</p> <pre><code>x: 0, y: 0, visited: 1373 x: 0, y: 1, visited: 1037 x: 0, y: 2, visited: 1373 x: 1, y: 0, visited: 1037 x: 1, y: 1, visited: 665 x: 1, y: 2, visited: 1037 x: 2, y: 0, visited: 1373 x: 2, y: 1, visited: 1037 x: 2, y: 2, visited: 1373 N: 3, total: 10305 </code></pre> <p>I was surprised to see the middle of the 3x3 grid visited the least number of times and the corners visited the most. I thought the corners would be visited the least because they have only have 3 neighbors while the middle of the grid has 8.</p> <p>Thoughts?</p>
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