Find a hash function to malfunction insertion sort - algorithm

Question

Below is the original pseudocode for Insertion Sort:
function INSERTIONSORT(A[0..n−1])
for i←1 to n−1 do
j←i−1
while j≥0 and A[j+1]<A[j] do
SWAP(A[j+1],A[j])
j←j−1
A company is using Insertion Sort inside one of their products. You are a cybersecurity expert that was hired by this company to assess any security flaws with their code. After a few tries, you managed to attack their Insertion Sort code and modify it in the following way:
function INSERTIONSORT(A[0..n−1])
for i←1 to n−1 do
j←i−1
while j≥0 and HASH(A,j+1) < HASH(A,j) do
SWAP(A[j+1],A[j])
j←j−1
In other words, instead of indexing the array as A[j] and A[j+1]inside the “while” condition, you now have a hash function that takes the array and a index as the arguments and return an integer. Your job is to implement specific hash functions that will cause the algorithm to malfunction in different ways.
a) Implement a hash function that causes Insertion Sort to keep the original array unchanged. Explain why your solution works.
b) Implement a hash function that causes Insertion Sort to always run in the worst case complexity, even if the resulting array does not end up getting sorted. Explain why your solution works.
c) Implement a hash function that causes Insertion Sort to sort the array in reverse. Explain why your solution works.
I think (a) and (b) is hash(A,j)=j and hash(A,j)=-j, but have no idea if that is correct and have no clue to c.

Answer 1

**Part a) Original array unchanged
#include <stdio.h>
int hash(int arr[], int i) {
return i;
}
void insertionSort(int arr[], int n) {
int i, j, temp;
for (i = 1 ; i <= n - 1; i++)
{
j = i-1;
while ( j >= 0 && hash(arr, j+1) < hash(arr, j))
{
temp = arr[j];
arr[j] = arr[j+1];
arr[j+1] = temp;
j--;
}
}
}
int main()
{
int i;
int arr[] = {5, 6, 7, 3, 2 , 9, 4};
int n = sizeof(arr)/sizeof(arr[0]);
insertionSort(arr, n);
printf("Original array unchanged:\n");
for (i = 0; i <= n - 1; i++)
{
printf("%d\n", arr[i]);
}
return 0;
}
Part b) Worst Case insertion sort
#include <stdio.h>
int hash(int arr[], int i) {
return -i;
}
void insertionSort(int arr[], int n) {
int i, j, temp;
for (i = 1 ; i <= n - 1; i++)
{
j = i-1;
while ( j >= 0 && hash(arr, j+1) < hash(arr, j))
{
temp = arr[j];
arr[j] = arr[j+1];
arr[j+1] = temp;
j--;
}
}
}
int main()
{
int i;
int arr[] = {5, 6, 7, 3, 2 , 9, 4};
int n = sizeof(arr)/sizeof(arr[0]);
insertionSort(arr, n);
printf("In worst case(number of swaps maximum)\n");
for (i = 0; i <= n - 1; i++)
{
printf("%d\n", arr[i]);
}
return 0;
}
Part c) Sorted in reverse order.**
#include <stdio.h>
int hash(int arr[], int i) {
return -arr[i];
}
void insertionSort(int arr[], int n) {
int i, j, temp;
for (i = 1 ; i <= n - 1; i++)
{
j = i-1;
while ( j >= 0 && hash(arr, j+1) < hash(arr, j))
{
temp = arr[j];
arr[j] = arr[j+1];
arr[j+1] = temp;
j--;
}
}
}
int main()
{
int i;
int arr[] = {5, 6, 7, 3, 2 , 9, 4};
int n = sizeof(arr)/sizeof(arr[0]);
insertionSort(arr, n);
printf("Sorted in reverse order:\n");
for (i = 0; i <= n - 1; i++)
{
printf("%d\n", arr[i]);
}
return 0;
}