DIFFICULTY:

EASY

PREREQUISITES:

Modulus Operator , Linear Search

PROBLEM:

```
We have to find the maximum modulus of a pair of number from an array.
```

Explanation:

```
1) Naive Approach:
We can compute the modulo function for every possible pair of elements in an array of size N with a complexity of O(N^2).
Pseudo Code :
maxmodulo=0;
for i in range 0 to n-1:
for j in range i+1 to n-1:
if max(i,j)%min(i,j)>maxmodulo :
maxmodulo=max(i,j)%min(i,j);
end if
end for
end for
Time Complexity : O(N^2)
But this approach will fail as N <= 10^6 and it will give a TLE (Time Limit Exceed) Error.
2) Optimized Approach :
One can easily compute the result by taking modulo operator over the second largest and the largest element of the array.
Result = Second_Largest_Element % Largest_Element
Time Complexity : O(N);
```

Editorialistâ€™s Solution:

Can be found here.