Find sum of 2 biggest nonadjacent integers in the array

Question

I found this interview question on some site and thought about it's solution.

The best solution I come to is to iterate over the whole array while saving the 4 biggest numbers and their indices.

After that I will need to find the biggest pair of these numbers ensuring that the selected numbers are not adjacent.

I think this ensures the correct solution to the question but I'm not sure it's the best solution.

My simple code is below.
Can someone give me a better idea to do this?

public int findMaxNonAdjacent(int [] array){
    int big1=0, big2=0,big3=0,big4=0;
    int i1=0,i2=0,i3=0,i4=0;
    for(int i=0;i<array.length;i++)
    {
        if(array[i]>=big1){
            big4=big3;
            big3=big2;
            big2=big1;
            big1=array[i];
            i4=i3;
            i3=i2;
            i2=i1;
            i1=i;
        }else if(array[i]>=big2){
            big4=big3;
            big3=big2;
            big2=array[i];
            i4=i3;
            i3=i2;
            i2=i;
        }else if(array[i]>=big3){
            big4=big3;
            big3=array[i];
            i4=i3;
            i3=i;
        }else if(array[i]>=big3){
            big4=array[i];
            i4=i;
        }
    }
    if(Math.abs(i1-i2)>1)
        return big1+big2;
    else if(Math.abs(i1-i3)>1){
        return big1+big3;
    }else if((big1+big4>=big2+big3) &&(Math.abs(i1-i4)>1)){
        return big1+big4;
    }else if((big1+big4<=big2+big3) &&(Math.abs(i2-i3)>1)){
        return big2+big3;
    } else
        return big3+big4;
}

Answer 1

Using 1-based indexing; Find the index of the biggest element in the array. If it's 1 , then find the biggest in the range [3, n] and return it's sum. If the biggest is at index n , then find the biggest in the range [1, n-2] and return it's sum. Else if the index of the biggest is i , then find the index of the biggest in [1, i-2] and the index of the biggest in [i+2, n] . Let them be l and r respectively. Then the answer will be max(A[i-1] + A[i+1], A[i] + max(A[l], A[r])) .

Answer 2

Why do you want to keep 4 indices in your code? In my opinion, only 3 elements are sufficient according to pigeonhole principle. Another thing is to check if the input array has less than 3 elements because it's an invalid input.