Question

Is it possible to find the second maximum number from an array of integers by traversing the array only once?

As an example, I have a array of five integers from which I want to find second maximum number. Here is an attempt I gave in the interview:

#define MIN -1
int main()
{
    int max=MIN,second_max=MIN;
    int arr[6]={0,1,2,3,4,5};
    for(int i=0;i<5;i++){
        cout<<"::"<<arr[i];
    }
    for(int i=0;i<5;i++){
        if(arr[i]>max){
            second_max=max;
            max=arr[i];          
        }
    }
    cout<<endl<<"Second Max:"<<second_max;
    int i;
    cin>>i;
    return 0;
}

The interviewer, however, came up with the test case int arr[6]={5,4,3,2,1,0};, which prevents it from going to the if condition the second time.
I said to the interviewer that the only way would be to parse the array two times (two for loops). Does anybody have a better solution?

Answer 1

Your initialization of max and second_max to -1 is flawed. What if the array has values like {-2,-3,-4}?

What you can do instead is to take the first 2 elements of the array (assuming the array has at least 2 elements), compare them, assign the smaller one to second_max and the larger one to max:

if(arr[0] > arr[1]) {
 second_max = arr[1];
 max = arr[0];
} else {
 second_max = arr[0];
 max = arr[1];
}

Then start comparing from the 3rd element and update max and/or second_max as needed:

for(int i = 2; i < arr_len; i++){
    // use >= n not just > as max and second_max can hav same value. Ex:{1,2,3,3}   
    if(arr[i] >= max){  
        second_max=max;
        max=arr[i];          
    }
    else if(arr[i] > second_max){
        second_max=arr[i];
    }
}