Question

Write pseudocode to selection sort an array of pairs: (p_0, v_0), . . . , (p_n-1, v_n-1)

Answer 1

Answer:

Let’s start with an array of pairs with elements containing ‘n’ elements be defined as follows:

(p_0,v_0), (p_1,v_1), …, (p_n-1, v_n-1)

Let us sort this array, in ascending order, on the basic of first member of each pair of an array element, i.e., p_i (0<=i<n) be the key according to which this array will be sorted. To break conflict in case when p_i is equal to p_j, then we will compare v_i and v_j to finding the shorter one. If that matches too, then the element which occur first is choosen.

The pseudocode for the selection sort is-

function selectionSort (Argument Array, Argument arrayLength)

            Initialize iterator, for the array, i to zero

            While i is lesser than arrayLength

                        Initialize iterator, for the array, j to i+1

                        Initialize minimum_element_index to i

                        While j is lesser than arrayLength

if Array[j].p is less than Array[minimum_element_index].p

                                                minimum_element_index = j

else if Array[j].p is equal to Array[minimum_element_index]. p

if Array[j].v is less than Array[minimum_element_index].v

                                                            minimum_element_index = j

                                                End if

                                    End else-if

                                    Increment j by 1

                        End While

                        Swap Array[i] with Array[minimum_element_index]

                        Increment i by 1

            End While

            Return the Array

End of function selectionSort

Image of the pseudoCode to emphasize on indentation:

In this code, two arguments are passed are-

1. Array – contains the unsorted array of pair
2. arrayLength – length of the above array

We first initialize the iterator ‘i’ to zero(0). After this, a while loop is ran across the whole array using the iterator ‘i’ i.e. up to ‘arrayLength’.

Within this loop another iterator ‘j’ is initialized to ‘i+1’ and a variable ‘minimum_element_index’ to ‘i’. One more loop is used which is ran across the whole array until ‘j’ is lesser ‘than arrayLength’.

In this loop, we check if the pair (p_j,v_j) is lesser than (p_ minimum_element_index, v_ minimum_element_index) or not. To do this, first we check if p_i is lesser than p_ minimum_element_index or not, if true than ‘j’ is assigned to ‘minimum_element_index‘, else we check if v_j is lesser than v_ minimum_element_index or not, if true than ‘j’ is assigned to ‘minimum_element_index‘. Once the loop condition is evaluated to false (i.e. j < arrayLength), loop is terminated. Finally, ‘j’ is incremented by one(‘1’).

After the inner loop is executed, we swap the pair (p_i,v_i) with (p_ minimum_element_index, v_ minimum_element_index). Finally ‘i’ is incremented by one(‘1’). Once the loop condition is evaluated to false (i.e. i < arrayLength), loop is terminated.

Finally the sorted array ‘Array’ is returned and function ends.

Note: Array[i].p is equivalent to p_i part of pair (p_i, v_i) while Array[i] represents the pair (p_i, v_i).