{"id":3514,"date":"2017-12-31T23:34:45","date_gmt":"2017-12-31T18:04:45","guid":{"rendered":"http:\/\/theoryofprogramming.azurewebsites.net\/?p=3514"},"modified":"2023-12-09T13:00:04","modified_gmt":"2023-12-09T13:00:04","slug":"rotate-matrix-clockwise","status":"publish","type":"post","link":"https:\/\/theoryofcoding.com\/index.php\/2017\/12\/31\/rotate-matrix-clockwise\/","title":{"rendered":"Rotate matrix clockwise"},"content":{"rendered":"\n

Problem statement<\/strong> – Given an array of N rows and N columns (square matrix), rotate the matrix by 90\u00b0 in clockwise direction.<\/p>\n\n\n\n

\"Rotate<\/a><\/figure>\n\n\n\n

Solution – This is an implementation based problem, which means that when asked in an interview, the interviewer is mainly testing your skill to write a program which follows some set of rules. There are no tricky cases here but you might struggle in the interview if you don’t have the right approach.<\/p>\n\n\n\n

For this problem, let us define a cycle like this –<\/p>\n\n\n\n

\"Rotate<\/a><\/figure>\n\n\n\n

So the cycle is a ring of elements which consists of mirroring row and column. We will solve this problem cycle-by-cycle, which means, we will rotate the 0th<\/sup> cycle, then the 1st<\/sup> cycle and so on.<\/p>\n\n\n\n

Now our rotation will start from the upper left corner element. This element’s vertices (i, j) can be easily evaluated from the cycle number it is in.<\/p>\n\n\n\n

\"Rotate<\/a><\/figure>\n\n\n\n

So, if the upper left corner element of a cycle is in the cycle number c<\/em>, then its position in the matrix will be (c, c)<\/em>. Now that we have defined one corner of our cycle, let us find the others. If n<\/em> is the size of the matrix, can you find the indexes of other corners?<\/p>\n\n\n\n

\"Rotate<\/a><\/figure>\n\n\n\n

Okay so n – 1 – c<\/em> seems to be an important term, let us call it l<\/em> (like last index).<\/p>\n\n\n\n

\"Rotate<\/a><\/figure>\n\n\n\n

Now to rotate these values, we need to do –<\/p>\n\n\n\n