Jeremy Jeremy - 1 month ago 20
Java Question

How to count comparisons and swaps in insertion sort? (JAVA)

public class Sorting
{
public static int numOfComps = 0,
numOfSwaps = 0;

public static void insertionSort(int[] array)
{
int unsortedValue; // The first unsorted value
int scan; // Used to scan the array

// The outer loop steps the index variable through
// each subscript in the array, starting at 1. The portion of
// the array containing element 0 by itself is already sorted.
for (int index = 1; index < array.length; index++)
{
// The first element outside the sorted portion is
// array[index]. Store the value of this element
// in unsortedValue.
unsortedValue = array[index];

// Start scan at the subscript of the first element
// outside the sorted part.
scan = index;

// Move the first element in the still unsorted part
// into its proper position within the sorted part.
while (scan > 0 && array[scan-1] > unsortedValue)
{
array[scan] = array[scan - 1];
scan--;

// Counts the number of values swaps
numOfSwaps ++;
}

// Insert the unsorted value in its proper position
// within the sorted subset.
array[scan] = unsortedValue;

// Counts the number of values comparisons
numOfComps ++;
}
System.out.println("\n\nNumber of comps = " + numOfComps);
System.out.println("Number of swaps = " + numOfSwaps);
}
}


Newbie here again. How do I code this insertion sort program in Java to count the number of comparisons and the number of swaps? I have inserted comparison and swap codes into the program but not sure they're in the correct place. I have posted the program. Thanks for any help.

Answer

The number of comparisons is the number of times array[scan-1] > unsortedValue is executed. That's not what you are counting.

Tips:

  • while (EXPRESSION) { STATEMENTS } can be rewritten as while (true) { if (!(EXPRESSION)) { break; } STATEMENTS }

  • !(EXPRESSION1 && EXPRESSION2) can be rewritten as !(EXPRESSION1) || !(EXPRESSION2).

  • if (EXPRESSION1 || EXPRESSION2) { break; } can be rewritten as if (EXPRESSION1) { break; } if (EXPRESSION2) { break; }.


The algorithm doesn't swap the value of pairs of variables. However, there is a form of multi-variable swap that occurs (A⇒B, B⇒C, C⇒D, D⇒A). The number of times this occurs is the number of times array[scan] = unsortedValue is executed when scan is different than index. That's not what you are counting.


Notes:

  • Your code is buggy. scan can be -1 when you reach array[scan] = unsortedValue;. This will happen when sorting 2, 1.

  • Note that this is a poor implementation of insertion sort. A binary search should be used instead of a linear search. This will reduce the maximum number of comparisons from N * N to N * log N.