Reverse Integer leetcode: Why does overflow occur only if 7 or greater is added to INT_MAX?

Question

I have the solution provided by Leetcode and the part that confuses me is the fact that adding 7 (or a lower value) to Integer.MAX_VALUE or adding -8 (or a lower value) to Integer.MIN_VALUE does not result in overflow or underflow respectively.

My logic is that if you have Integer.MAX_VALUE, adding 1 will cause overflow. And if you have Integer.MIN_VALUE, subtracting 1 will cause underflow. Where is my understanding of overflow and underflow wrong?

class Solution {
    public int reverse(int x) {
        int rev = 0;
        while (x != 0) {
            int pop = x % 10;
            x /= 10;
            if (rev > Integer.MAX_VALUE/10 || (rev ==     Integer.MAX_VALUE / 10 && pop > 7)) return 0;
            if (rev < Integer.MIN_VALUE/10 || (rev == Integer.MIN_VALUE / 10 && pop < -8)) return 0;
            rev = rev * 10 + pop;
        }
        return rev;
    }
}

Answer 1

Yes, normally adding 1 to Integer.MAX_VALUE will result in overflow, as will subtracting 1 from Integer.MIN_VALUE . But that is not what is happening here.

This code is performing integer division by 10 , which truncates any decimal portion. When dividing Integer.MAX_VALUE ( 2147483647 ) by 10, the code anticipates multiplying by 10 and adding the next digit. That quotient is 214748364 , and multiplying by 10 is 2147483640 , with the possibility of adding another 7 without overflowing. Similarly on the negative side, dividing Integer.MAX_VALUE ( -2147483648 ) by 10 yields -214748364 , multiplying by 10 yields -2147483640 , with the possibility of adding another -8 without overflowing.

This code takes into account the last digit of the extremes of the range of Integer values and carefully avoids overflow.

Answer 2

Integer.MAX_VALUE is 2147483647

That means: Integer.MAX_VALUE/10 is 214748364

And you're about to do: rev = rev * 10 + pop

So if rev > 214748364 , then rev * 10 will cause overflow.

Or if rev == 214748364 , then rev * 10 is 2147483640 , and rev * 10 + pop will cause overflow if pop > 7 .