Maximum product of 3 integers in an int array

I want to find the maximum product that can be obtained from any 3 integers in an integer array. The optimal solution has time complexity of \$O(n)\$ and space complexity of \$O(1)\$. I managed to write up as solution in Java that only traverses the array twice (so my time complexity is \$O(n)\$) and my space complexity is \$O(1)\$. I do not believe the solution can be any cleaner than this but would still like to see what other people think.

The \$O(n)\$ solution is obtained by keeping track of the max three integers and the min two integers. The max product will either be (min_one min_two max_one) or (max_one max_two max_three).

// Assume input array is of at least length 3.

public int max_prod_three(int[] A){

    int len = A.length;

    // Base case
    if (len == 3) return A[0]*A[1]*A[2];

    int max = A[0], min = A[0], max_index = 0, min_index = 0;

    for (int i = 0; i  max) {

            max = A[i];
            max_index = i;
        }
        else if (A[i]  max_sec) {

            max_third = max_sec;
            max_sec = A[i];
        }
        else if (A[i] > max_third) {
            max_third = A[i];
        }

        if (A[i]  prod_two) return prod_one ;
    return prod_two;
}

You can iterate through the array only once and get the max product but I found that the solution gets a bit too messy (with a lot more if else statements). But if anyone can do it cleanly, I would like to know.

Minor edge case

It's possible that the product of three integers will overflow. For example, three positive integers may produce a negative product and cause your function to return the other product instead. Since your function returns an int, it's not clear what you are supposed to do if that happens. Perhaps you are guaranteed that the values are small enough not to overflow?

Otherwise the function looks correct and easy to understand.

StackExchange Code Review Q#109214, answer score: 6