Insertion Sort

// Assumes DataType has been defined

void insertionSort(DataType theArray[], int n)

// ---------------------------------------------------
// Sorts the items in an array into ascending order.
// Precondition: theArray is an array of n items.
// Postcondition: theArray is sorted into ascending
// order; n is unchanged.
// ---------------------------------------------------

{
   // unsorted = first index of the unsorted region,
   // loc = index of insertion in the sorted region,
   // nextItem = next item in the unsorted region
   // initially, sorted region is theArray[0],
   // unsorted region is theArray[1..n-1];
   // in general, sorted region is
   // theArray[0..unsorted-1],
   // unsorted region is theArray[unsorted..n-1]

/*

The for-loop below iterates n-1 times.  

*/

   for (int unsorted = 1; unsorted < n; ++unsorted)

   {  // Invariant: theArray[0..unsorted-1] is sorted
      // find the right position (loc) in
      // theArray[0..unsorted] for theArray[unsorted],
      // which is the first item in the unsorted
      // region; shift, if necessary, to make room

      DataType nextItem = theArray[unsorted];
      int loc = unsorted;

/*

The for-loop below performs as many as 'unsorted' moves and comparisons.  The
variable 'unsorted' ranges from 1 to (n-1).  Therefore the algorithm performs
as many as 1+2+3+...+(n-2)+(n-1) = n(n-1)/2 moves and comparisons.

*/

      for (;(loc > 0) && (theArray[loc-1 ]> nextItem);
           --loc)

         // shift theArray[loc-1] to the right

         theArray[loc] = theArray[loc-1];

      // Assertion: theArray[loc] is where nextItem
      // belongs

      // insert nextItem into Sorted region

      theArray[loc] = nextItem;

   } // end for

} // end insertionSort