Question

I have a piece of code which will find out the repeating elements in an array of size n where the elements satisfy 1 <= arr[i] <= n, the code is given below:

#include<stdio.h>
#include<stdlib.h>

void printTwoElements(int arr[], int size)
{
    int i;
    printf("\n The repeating element is");

    for(i = 0; i < size; i++)
    {
        if(arr[abs(arr[i])-1] > 0)
        {
            arr[abs(arr[i])-1] = -arr[abs(arr[i])-1];
        }
        else
        {
            printf(" %d ", abs(arr[i]));
        }
    }
}

/* Driver program to test above function */
int main()
{
    int arr[] = {7, 3, 4, 5, 5, 6, 2};
    int  n = sizeof(arr)/sizeof(arr[0]);
    printTwoElements(arr, n);
    return 0;
}

I would like to know the use of abs() in this given code?

Answer 1

In the course of the algorithm, some array entries are set to negative values as a marker. Therefore the entries’ absolute value has to be taken when they are used as indices into the array.

In the hope of not spoiling anything:

The algorithm requires that the array entries of an n-element array all are between 1 and n inclusive.
If any entry is larger than n or smaller than -n or 0, it will access invalid addresses, and if any element is negative, the marking logic will fail.

The logic of the algorithm is:

for each array element e:
    if the value at (e-1) is positive, e has not yet been seen,
                   negate the value at (e-1) to mark e as seen
    otherwise, e has already been seen, so print it

So since array entries become negative in the course of running the algorithm, the absolute value has to be taken to obtain valid indices.

Let us follow the algorithm for a modified example to see how it works:

before: arr = { 7, 3, 4, 5, 5, 3, 2}
i == 0: arr[0] = 7
        arr[7-1] is 2 > 0 ~> negate
        arr = { 7, 3, 4, 5, 5, 3, -2}
i == 1: arr[1] = 3
        arr[3-1] is 4 > 0 ~> negate
        arr = { 7, 3, -4, 5, 5, 3, -2}
i == 2: arr[2] is -4 ~> abs for indexing
        arr[4-1] is 5 > 0 ~> negate
        arr = { 7, 3, -4,-5, 5, 3, -2}
i == 3: arr[3] is -5 ~> abs for indexing
        arr[5-1] is 5 > 0 ~> negate
        arr = { 7, 3, -4, -5, -5, 3, -2}
i == 4: arr[4] is -5 ~> abs for indexing
        arr[5-1] is -5 < 0 ~> print abs(-5) as duplicate
i == 5: arr[5] is 3
        arr[3-1] is -4 < 0 ~> print abs(3) as duplicate
i == 6: arr[6] is -2 ~> abs for indexing
        arr[2-1] is 3 > 0 ~> negate
        arr = { 7, -3, -4, -5, -5, 3, -2}

        indices of positive entries: 0, 5 ~> 1 and 6 not in original array
        indices of negative entries: 1, 2, 3, 4, 6 ~> 2, 3, 4, 5, 7 in original array