Example:
Input:
{4, 2, 5, 8, 21, 34, 10}
key = 24
Output:
Pair found (34, 10)
This problem can be solved in 2 ways.
Solution 1: Brute force method.
Explanation:
Step 1: Take 2 loops, outer loop and an inner loop.
Step 2: The element from outer loop will pick every other element in the inner loop and checks if the difference matches or not.
Time complexity will be O( n ^2 ).
Example:
Input {4, 2, 34, 10} key = 24
Pass 1:
4 – 2 or 4 – 2 == 24? No
4 – 34 or 34 – 4 == 24? No
4 – 10 or 10 -4 == 24? No
Pass 2:
2 - 4 or 4 – 2 == 24? No
2 – 34 or 34 – 2 == 24? No
2 – 10 or 10 – 2 == 24? No
Pass 3:
34 – 10 or 10 - 34 == 24 ? Yes. Return the elements.
Solution 1 in c:
#include<stdio.h>
void findElementsWithKeyDifference(int arr[], int length, int key)
{
int outer_loop = 0;
int inner_loop = 0;
int diff = 0;
for(outer_loop = 0; outer_loop < length; outer_loop ++)
{
for(inner_loop = outer_loop+1; inner_loop < length; inner_loop++)
{
if( (arr[inner_loop] - arr[outer_loop] )== key || (arr[outer_loop] - arr[inner_loop]) == key)
{
printf("Elements found %d and %d\n", arr[outer_loop], arr[inner_loop] );
return ;
}
}
}
printf("Elements not found" );
}
int main()
{
int arr [100] = {4, 2, 5, 8, 21, 34, 10};
int key = 24;
int length = 7;
findElementsWithKeyDifference(arr, length, key);
}
Output:
Elements found 34 and 10
Solution 2: Sort the array and then find the elements are present or not.
Step 1: Sort the array in ascending order.
Step 2: Take 2 variables “i” and “j” initialize “ i = 0” and “j = 1”
Step 3:
Inside while loop, Check if a[j] – a[i] == key If true return Else If a[j] – a[i] < key Increment j Else Increment i Loop until “i” and “j” value is less than array length.
Here the time complexity for the second step will be O ( n );
Solution 2 in c:
#include<stdio.h>
void swap (int *num_1, int *num_2)
{
int temp = *num_1;
*num_1 = *num_2;
*num_2 = temp;
}
void bubble_sort (int array[], int length)
{
int outer_loop = 0;
int inner_loop = 0;
for(outer_loop = 0; outer_loop < length - 1; outer_loop ++)
{
for(inner_loop = 0; inner_loop < length - outer_loop - 1 ; inner_loop ++)
{
if(array [inner_loop] > array[inner_loop+1])
{
swap(&array[inner_loop], &array [inner_loop+1]);
}
}
}
}
void findElementsWithKeyDifference(int arr[], int length, int key)
{
int i = 0;
int j = 1;
while(i < length && j < length)
{
if(i != j && arr [j] - arr[i] == key)
{
printf("Elements found %d and %d\n", arr[i], arr[j] );
return ;
}
else if (arr [j] - arr[i] < key)
j++;
else
i++;
}
printf("Elements not found" );
}
int main()
{
int arr [100] = {4, 2, 5, 8, 21, 34, 10};
int key = 24;
int length = 7;
bubble_sort (arr, length);
findElementsWithKeyDifference(arr, length, key);
}
Output:
Elements found 34 and 10
