title: Matrix, algorithm interview question
body: <p>This was one of my interview questions. </p>
  
  <p>We have a matrix containing integers (no range provided). The matrix is randomly populated with integers. We need to devise an algorithm which finds those rows which match exactly with a column(s). We need to return the row number and the column number for the match. The order of of the matching elements is the same. For example, If, i'th row matches with j'th column, and i'th row contains the elements - [1,4,5,6,3]. Then jth column would also contain the elements - [1,4,5,6,3]. Size is n x n.
  My solution:</p>
  
  <pre><code>RCEQUAL(A,i1..12,j1..j2)// A is n*n matrix
  if(i2-i1==2 &amp;&amp; j2-j1==2 &amp;&amp; b[n*i1+1..n*i2] has [j1..j2])
     use brute force to check if the rows and columns are same.
  if (any rows and columns are same)
     store the row and column numbers in b[1..n^2].//b[1],b[n+2],b[2n+3].. store row no,
                                                   // b[2..n+1] stores columns that 
                                                   //match with row 1, b[n+3..2n+2] 
                                                   //those that match with row 2,etc..
  
  else
     RCEQUAL(A,1..n/2,1..n/2);
     RCEQUAL(A,n/2..n,1..n/2);
     RCEQUAL(A,1..n/2,n/2..n);
     RCEQUAL(A,n/2..n,n/2..n);
  </code></pre>
  
  <p>Takes O(n^2). Is this correct? If correct, is there a faster algorithm?</p>