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PORotating a 2-d array by 90 degrees
 

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  1. PORotating a 2-d array by 90 degrees
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    <p>A frequent question that props up during array manipulation exercises is to rotate a two dimensional array by 90 degrees. There are a few SO posts that answer how to do it in a variety of programming languages. My question is to clarify one of the answers that is out there and explore what sort of thought-process is required in order to get to the answer in an organic manner.</p> <p>The solution to this problem that I found goes as follows:</p> <pre><code>public static void rotate(int[][] matrix,int n) { for( layer = 0;layer &lt; n/2;++layer){ int first = layer; int last = n -1 - layer; for(int i = first;i&lt;last;++i){ int offset = i - first; int top = matrix[first][i]; matrix[first][i] = matrix[last-offset][first]; matrix[last-offset][first] = matrix[last][last-offset]; matrix[last][last-offset] = matrix[i][last]; matrix[i][last] = top; } } } </code></pre> <p>I have somewhat of an idea what the code above is trying to do, it is swapping out the extremities/corners by doing a four-way swap and doing the same for the other cells separated by some offset.</p> <p>Stepping through this code I know it works, what I do not get is the mathematical basis for the above given algorithm. What is the rationale behind the 'layer','first','last' and the offset?</p> <p>How did 'last' turn out to be <code>n-1-layer</code>? Why is the offset <code>i-first</code>? What is the offset in the first place?</p> <p>If somebody could explain the genesis of this algorithm and step me through the thought process to come up with the solution, that will be great.</p> <p>Thanks</p>
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    1. COjust run it in a debugger or print the intermediate results ...
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      1. USDr. belisarius
 

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