Find Two largest numbers in a list without using Array

If you exceed your maximum number (max1st), your new maximum number will be set to num. But your second largest number will be the current maximum number. So try this condition:

if (num > max1st) {
    max2nd = max1st;
    max1st = num;
} else if (num > max2nd) {
    max2nd = num;
}