CareerCup

sum = 0

{
For ( i = 0 ; i < rowsize ;i++ )

{
if ( i == (rowsize -1 - i ))
{
sum = sum + a[i][i]
}
else{
sum = sum + a[i][i] + a[rowsize -1 - i][rowsize -1 - i]
}
}


}

This means u need to exclude the intersecting element of two diagonals

Huh? Are you sure that's all? It's easy (assume 0 indexed):
{{
for(i=0; i<n/2; i++)
sum+= A[i][i] + A[i][n-i] + A[n-i][i] + A[n][n];

return ( sum + A[(n+1)/2][(n+1)/2] );
}}

For meaning of this code, sit down and work it through (it's only 2 lines really)

JavaScript

(function(){

  var a = [
    [3, 5, 9, 2, 6],
    [7, 9, 2, 1, 2],
    [4, 7, 2, 0, 9],
    [6, 8, 3, 5, 6],
    [1, 1, 2, 3, 4]
  ];

  alert(getSum(a));

})();

function getSum(a){

  // the diagonal elements of the array are:
  //
  // [x       x]
  // [  x   x  ]
  // [    +    ]
  // [  x   x  ]
  // [x       x]
  //
  // with the intersecting element marked with +

  // so, you need to add the elements at these locations:
  //
  //  \ diagonal: [0,0] [1,1] [2,2] [3,3] [4,4]
  //  / diagonal: [0,4] [1,3] [2,2] [3,1] [4,0]
  //
  // but only add the [2,2] element once
  //
  // this can be accomplished with a single loop through the array, i.e.
  //
  // [0,0] + [0,4] + [1,1] + [1,3] + [2,2] + [3,3] + [3,1] + [4,4] + [4,0]

  var i, j, n = a.length, sum = 0;

  for(i=0;i<n;i++) {
    j = n - i - 1;
    sum += a[i][i] + ( i == j ? 0 : a[i][j] );
  }

  return sum;

}

Give xplanation

sum = 0;

for (i=1; i<=n ; i++ )
{
if( 2i == n+1)
{
sum = sum + array[i,i]
}
else
{
sum = sum + array[i,i] + array [i,n-i+1]
}
}